At 5:37 you said only Zero and One equal Zero and One, however (arguably but accepted by most experts) any number other than Zero, (or infinity, if that is a number) can have its last digit subtracted by one and have repeating nines added to the end of it and it still equals the same number. (Examples: 1=0.999..., 4.3=4.2999...) This can be proven easily: 1/9=.111... and 9*1/9=9*0.111... this shows that 1=0.999.... Therefore, three is the cardinality of all things equal to zero and one.
proof by contradiction that your theorie is wrong. assume: 2^inf > inf [8:38] in your terms: lim 2^x, x->inf = 2^inf and: lim x!, x->inf = 1*2*3...*inf = inf (legit becaus of [7:50]) taylorseries of e^k: e^x = sum( x^k/k! ), k = 0 ... inf let x=2. the sum converges then to e^2 (finite number), therefor the last addend 2^inf/inf must be also finite (its actually zero), which is only possible if inf > 2^inf. contrary to assumption. QED
Infinity doesn't have a point on the complex plane. How is it a number?
Also, n*infinity does not equal infinity if n is negative. Everyone forgets that. Plus, you can state that 0*infinity = any number, since you said that n/infinity = 0 and that means infinity*0 = n.
@TpendragonT ? By DEFINITION if a/b = c, then b*c = a. Try it on some numbers.
Then if you say n/infinity = 0, then 0*infinity = n.
0*infinity = 0, n/infinity = 0. You can't say both of these are true.
And if 0*infinity = 0, then a finite line has an infinite amount of points, and points are length zero, so that means 0*infinite = finite. As long as you're talking an uncountable infinity, 0*infinity is more then zero.
@anticorncob6 If you take a number like 87 and divine it by infinity, you will receive .00000... as your answer. That is equal to 0. Now if somehow you could get to the end of this infinitely repeating decimal, and found a number like 2 (which you never would) then of course .000000...2 * infinity = 87. Since .0000... would be equal to 0 (as we all know this is common maths) The two equations before are true.
@anticorncob6 I agree on infinity NOT being a number, but when you say 0/infinity you are speaking of a vertical asyntote in a x-y cartesian plane, what 0*infinity = n means is that 0*infinity IS 0, IS n and IS infinity. It is the moment of any curve whose tangent line's slope is infinite, and therefore is an indefinite form for any equation because it makes a number equal all numbers. if a number * something = not a number (all numbers), then that something ISN'T a number.
@TpendragonT You take the axiom that defines a Field, then a Vector Space like IR "For all a, b in F, both a + b and a * b are in F". Then if a is any element of IR and b is infinity, when you say n/infinity = 0, then infinity * 0 = n, means any number, or all numbers at the same time. 0*infinity is not one number, it's all of them, so it is not in IR, it's IR itself. IR is not a number then it is not in IR but it's a vector subspace of IR. 0*number = 0 , 0*infinity = ALL NUMBERS, not 0.
infinity is a number coz i can use it in a math question hmm invinity plus invinity 2 infinity.... infinity is a amount not the limit to numbers duh and im 8 ( question how many zeros in infinity 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 zillion billion in 1 infinity just guessing
@thefallingangel2011 If you think there are any "zeros" in infinity, or even that you can find any digit of it at all, you clearly don't understand it. It is precisely this property (it being completely incalculable in any way) that makes it not a number.
A number is often defined as a "quantity" or an "amount". Since the value of infiity is not definite (as you said yourself), then infinity is not ONE value, and is thus not a number.
Zero is a number, because it represents a set with no elements in it. As well, @CombatRocks, your argument implies negatives are not numbers as well.
So you think infinity would be prime? Why?
(and btw there is proof that there is no biggest prime number - take whatever value (let's say n) and do n! + 1
If infinity is a number, can you obtain infinity without using another infinity? What equation would yield infinity without using infinity? Infinity gives definition to itself, meaning it, by itself, does not exist as a number.
@scoreunder You can't use Tan to prove infinity, Tan uses Sin and Cos, which are equations that don't really have an end. That would be like saying 1+2+3+4+5+...=inf. Also, notice how none of these gave JUST infinity(you get infinity and an arbitrary argument)? They didn't just equal infinity, it had to have a second part to it, because infinity on it's own does not exist as a number, It's a concept. Unless you can find x amount solid numbers that equal exactly infinity...
Sin and cos aren't "equations that don't really have an end", they're functions defined by naturally observed phenomena. Solutions of an equation that involve sines and cosines are generally considered to be closed form. You might be referring to the mclauren series for these functions. Note that also I gained positive infinity in the expression that used limits.
@ImmortalAcorn Also I do not think that infinity is a number. Just because it can be gained from operations on numbers does not mean it is a number, in the same way that performing operations on reals does not always mean that the result is real (classic example is (-1)^(1/2) ).
@scoreunder (-1)^(1/2)=i. i is an existent number, it may not be a real number, but it can be reached through logical mathematical means. i does not need another i to make sense. i=(-1)^(1/2), infinity on the other hand = no possible defined equation. i can be achieved by using other real numbers, infinity can only be gotten out of using another infinity. As I said, if you can get infinity using a defined equation(no a/0) without using inf twice(no inf=inf), then inf is a number.
@ImmortalAcorn Anyway, if you take into account the fact that limits can be taken from any direction to achieve infinity of any argument, please tell me how 1/x at x=0 is undefined.
@scoreunder Limits, can be taken from any direction to achieve infinity. Limit were created for infinity because infinity did not fit into math. Like I said before, all your basically saying is inf=inf. Your adding a limit to give the concept of infinity meaning. Infinity on it's own does not exist as a number. a/0 is an undefined number. Write 1/0=? as 0*?=1, what is ? equal to other than itself? So, what can be done? Easy, we introduce a new concept to make sense of this, limits.
Yes, I said it's not a number - but that doesn't mean it can't be found using numbers!
"Easy, we introduce a new concept to make sense of this, limits."
I take it you have never used limits. The limit of (x^2-1)/(x-1) as x approaches 1 is 2. How do we calculate this without limits? We simplify. Limits are merely a calculation aid.
"Limit were created for infinity because infinity did not fit into math."
@ImmortalAcorn Also you have still not explained why you think "1/0" is undefined. Among the reals it is clear that it has exactly 2 possible results, negative and positive infinity.
1/(0.00001) = 100000 and 1/(0.0000001) = 10000000. Once the denominator reaches zero, the result is infinitely large (and if you use negatives, an infinitely large negative). What is so hard to understand about this?
@scoreunder No, Here's the thing... 1/(0.00001) = 100000 is true, 1/(0.0000001) = 10000000 is as well. But, we're not using a .00001, or a .0000001, or even an infinitely small number. We are using 0. We are using a 0.000... The 1 at the end will never be reached, which is why .000... is EXACTLY 0. You used a limit saying that as denominator APPROACHED 0, when we are using 0 exactly(meaning there is no 1 at the end). You used a limit, which again is defining inf using another concept.
@scoreunder Okay then, here's the deal. You keep adding 0s to that 1/0.000xxxx... You inform me when you reach a 1 to make your equation larger than 0.
And if you disagree with this, then please tell me: what number is infinitely small (literally endlessly small, be-all-end-all nothing-can-be-smaller-than-this type of small) but not zero? (There is no such number)
This is almost as bad as debating those that say 0.999 recurring is not exactly equal to 1. They are wrong and do not understand math.
@scoreunder No, 1/inf does not equal 0. You are using a limit now. 1/0.000000... will never ever EVER reach a 1 to make the equation true. You are applying a limit and saying instead of using 0, we're using an infinitely small number. 1/0 does not equal inf, 1/"an infinitely small number"="an infinitely large number." Stop using a limit where your constants should go, Your trying to prove infinity exists WITHOUT using a limit or another infinity.
@ImmortalAcorn So far you've rejected limits because they don't support your mathematical worldview and you have accused me of applying limits where I have not. You still have not answered the question in my previous comment.
Here's a way of thinking about it:
I have a number, "infinitely small". It is not equal to zero.
Thus, there is a number between this number and zero as they are not equal.
There is not, otherwise it contradicts the "infinitely small" property - thus they are equal.
@scoreunder "There is not, otherwise it contradicts the "infinitely small" property - thus they are equal." rephrase -> "This contradicts the statement that the number was "infinitely small" - thus they are equal."
@scoreunder Rejected limits? Not even, I have simply asked you to prove infinity as a NUMBER(math) but you've only proven it as a concept(not math). What sense does it make to say 1/"a number that grows without bounds, eternally"=0. Infinity is not a number, it's a concept. You cannot have 1/concept=0, you can however have a "1/x equals 0, as x approaches a number with no bounds(infinity)". Your using a concept as a number, can you divide 1 by a concept?
@ImmortalAcorn Numbers are all concepts. You can multiply matrices by each other, and they are not numbers - now, please answer this (and stop avoiding!):
Premise 1: I have an infinitely small number that is not equal to zero.
Premise 2: All numbers that are not equal have an infinite amount of numbers between them.
Conclusion 1: From P1. and P2., the infinitely small number is not the closest possible number to zero - thus it is EITHER not infinitely small OR it is equal to zero.
@scoreunder 1/0, log(0) and so on yield an undefined result. Therefor, they more or less equal nothing. If you were to create a concept to give meaning to these nothing numbers at the end of the equation, then obviously, you would get this concept because that's why it was made. log(log(log(0)))=nothing=inf. In order to prove infinity, you need an equation that will give infinity without also giving an undefined number. I can get any other number with a defined equation, so why not infinity?
@ImmortalAcorn "1/0, log(0) and so on yield an undefined result." No - 1/0 is infinity of arbitrary/unknown argument, (thus |1/0| is infinity) and log(0) is infinity plus an imaginary component. No result is undefined -- 0/0 is undefined UNLESS it is part of a continuous function where limits can be taken to find the value.
I received in my email (not in the comments box though, hmm..) a comment from you stating that 1/0 does not exist... by whose standards?
@ImmortalAcorn I can prove that 1/0 exists: 1/2 is the proportion of something you can share equally between 2 people. 1/1 is the proportion of something you can share with only yourself. And of course, if you're sharing with nobody, you can "give" nobody whatever you're sharing an infinite amount of times and you will still have it.
I don't think most mathematicians care whether infinity is a number or not. You can define terms to mean whatever you like of course, and it's not clear what advantage there is in deciding either way.
Actually most mathematicians don't talk about "numbers" because that's too vague a term. They'll say suppose z is a complex number, or a real number, or an integer, or a rational number, or a natural number. But the term "number is not usually defined or used in isolation, as it's vague.
Your basic premise is wrong - neither zero nor infinity are 'numbers'. They are concepts - they have no numeric value. Numbers have measurable values - otherwise they are not numbers!
Mathematicians are not wrong. Mathematicians are the ultimate arbitrers, this isn't a question of semantics. If you say that infinity is a number, it is notsimply your opinion, you are just wrong. The same way if you say that 1=2, it is not a matter of opinion, you are just wrong.
into Wolfram Alpha (a free online algebraic calculator that can work with infinity, complex numbers etc) it says False. I am kind of confused, it says 2^infinity = infinity
@docopoper Infinity is the concept of endlessness.
By asking if "2^infinity = infinity", you're asking the question: If I endlessly increase the power by which I raise two, does the value also endlessly increase?
In the same way, 2^-infinity = 0 -- if you endlessly increase the negative power by which you raise two, the value will constantly get closer and closer to 0.
The main thing that confused me was the contradiction between this video and Wolfram Alpha.
I understand that 2^(-infinity) = 0 ; That is intuitive - I actually would have thought that 2^infinity = infinity ; And that is why I was confused by the inconsistencies between this video and W|A.
If you read the "Uploaders' Comments" then you will notice that he reinforced this by stating:
2^infinity > infinity ;"since you cannot demonstrate a one-one correspondence between these sets."
@docopoper I don't think anyone will follow on with the argument because I don't really think anyone else believes there's no 'real' way to get infinity from an expression without using infinity in the first place. ;)
@scoreunder I believe what the other dude was saying is that when you say 1/0 = infinite you're wrong because 1/0 isn't defined. Lim x->0 1/x = infinite and that is true. There is a difference of saying a limit than just the ecuation. When you use limits ( lim x-> c f(x) = L ), you don't care about what f(c) is, although most of the time f(c) = L, if f is not defined at c L still exists. When you take lim x->0 1/x = infinite and say 1/0 = infinite, you're just misusing the concept of limits.
in my opinion you choose previously the definition of number in the way "infinite" would fit in it. we can give a lot of definitions, some that include infinite, some that don't.if we choose to say, in addition to your definition "you can obtain any real number A by adding 1 to another real number B", this is necessary, even if not enough, to define "number". but wich number B+1 is equal to infinity, if for hypotesis you can't use infinite as B?(that would be circular!). sorry for bad english :)
Excuse me, but you should have taken some Allegra (120mg) prior to making this video to have avoided having to inject so many sniffles throughout your project. Oh, the math, yeah, infinity is a very large number. Or, it is something ABOUT numbers. Sniffle, sniffle...
"Infinity is the cardinality of the set of natural numbers" <- This is where you go wrong, logically, from what I can see. The natural numbers aren't a set. Or, if you argue that they are a set, you've pushed the original problem of including infinity in the definition of "number" over onto including it in the definition of a "set", which is a term that even more heavily suggests finity.
why human beings are so shameless to lie? "Why Infinity is a number ". Definition of number is something that can be measure, it is defined and finite, therefore infinite, and zero are no included in the concept. Dont be fooled because they are into the number line, they are numbers. Zero is the point of reference, to measure something, and infinite is a simbol that stand for a number which cannot be reach but exist. Good understanding needs few words.
At least up to 5:44, your argument is based on the cardinality of a set. Seeing your definition of cardinality at 1:08, take note of the portion "is the number of". By your comparison at 5:44, you are assuming infinity to be a number by saying it is the cardinality of the set of integers.
This is not any different than if someone wants to prove trigonometry with calculus.
Therefore, although your argument is interesting, it is not convincing enough to me to be compared to finite numbers.
The definition of a number is an label describing "finite." Does in-finite describe finite? Math has setup rules that allow infinity to work as a number...what rules do numbers have? Count to infinity for me real fast...infinity can be counted. Infinity works as a number as long as I follow your rules? But using your rules, I should prove you wrong? These rules need to be changed. If X is a number between 1.0 and .999...and 1.0-X=.999...you say1.0-X=0 i say x was zero! and ask what was x4u?
Almost everything in mathematics is based on definitions because it is an invented construct, used as a language to make it easier for us to work on real world problems. Some things are left undefined because not every one can agree on one. The thing is, you will believe what you want. There are areas with different sets of definitions and rules. Your desire to count Inf as a number is allowable within your definition, but one agrees to THEIRs when working with them so one can communicate.
It's undefined because the operation is liable to more than one interpretation, and without knowing more about its use (knowing the equation as opposed to a single operation of div0,) you can't determine what the result should be.
e.g.: 4 states: 0 div 0 = 0 (typical) or 1, N div 0 = 0 or inf (typical)
Each true but if you can't map the function, then you can't determine which is correct.
If so that would mean inf/ inf = inf as well? Well, the answer you could provide is, 0/0 is not zero...but it could be zero!! based on ur premises n/inf = 0 therefore 0/0 = (n/inf)/(n/inf) = inf/inf...treating inf as a number is not my problem, Euler used to do that, but its ur definition of inf as a number...inf has ranks just like u said 2^inf is something bigger thn inf, but like wise 2*inf/inf =2 if both inf's are of the same rank. I ran out of characters...
So, while we can play as inf as a number, and practically, Euler did and people normally do, we cant define it as a num, including ur reasoning of the cardinality of a set containing infinite elements (which is self reference), because either a. Inf is not in Natural numbers, so then there exists a set containing both Inf and N, which is not equal to the set N, but N is a subset of this set, therefore its cardinality must be greater. if inf is of N why not R? what set does it belong to?
I think infinity is an idea rathter than a physical being. What is inf-inf or inf/inf ?
x -> inf, when x -> inf and 1/x -> 0, when x -> inf but when you multiply them with eachother it's x times 1/x (which is x/x) = 1 so if x=inf and 1/inf = 0 then Inf times 0 = 1.
So I say that infinity is NOT a number, it's a concept or an idea that we mark with the "fallen eight"
Interesting argument, but ultimately arbitrary and unimportant to most mathematicians who know the concepts of all numbers and are rightfully unconcerned with verbal definitions. Leave the words to the writers and sophists, it is the knowledge of the concepts of zero and infinity and aleph null, 1, 2 that are important.
If you define infinity as a number, then you can not do math with it. Mathematics is based on the principle of equality (inequality is an attempt to discribe qualities of two no equal functions). If you introduce the number infinity, equality breaks down. 2+infinitiy is greater than infinity but it is also equal to infinity which gives contradiction. To solve this problem you would need to define an infinite number of infinites, and then define an infinite number of those. It is a number.
I don't think it is an number, because of its property is too different from the other numbers, I mean for example take limits, with infinity you are able to sum a geometric series to an EXACT sum whereas you can never do that if you treat it as a number, now since you say infity is a number, it must be the biggest number, but as it is constant the geometric must sum to something but not exact.
I dont see the point. I thought you wanted to show that infinity is an element of N but all you did is define the word "number" in a way that infinity obviously fits it. Thats like saying infinity is a pink elephant by defining pink elephant as the cardinality of N. (So infinity also isnt prime (nor is it not prime) because prime numbers are defined on N (or Z).)
@TechnoMulen Since the chances of a number being prime reach closer and closer to zero among ever larger integers, infinity would be composite; Divisible by every prime number an infinite amount of times.
how can it b a number? any number u can think of or arrive at - add 1 to it. then add 1 again. then keep doing that - for infinity. it never ends, so u can never count up to it, or down to it for that matter cause u get negative scales of counts too.
unless ur changing what number means, to mean something else instead. but then u lose the concept of infinity being endless, which is its point.
I agree with you here. Even though it is not based on solid proof rather than a lot of evidence (in my opinion). If you divide by 0 the result is of an infinite magnitude.
The most basic way of dividing is to see, how many times you need to add up the divider to reach the dividend. The dividend is 6 and the divider is 2. 2 + 2 + 2 = 6 or rather 2 * 3 = 6. You add 2 to itself 3 times to get 6. Let's say now the dividend is 1 and the divider is 0. 0 + 0 + 0 + 0 + 0 + ... is what?
@MajorNr01 Basically you would sit there adding 0 to itself for an infinite amount of time, you add it up infinite times which is the result of the calculation. This is very close to a philosophical question i guess but for me it works pretty well.
Also some thoughts i had about the power of a number, concerning the sign. If you invert one number's power's sign you basically turn the number around the point. What i mean is that you have an infinite amount of numbers on each side of the point.
@MajorNr01 All numbers between 1 and 0 (i dont say between 0 and 1 because i want to point out the direction) and between 1 and infinity. Now if you have a very high number its closer to infinity, the greater it is. In the same way if you divide 1 by that number (number^(-1)), the greater it is, the closer the result is to 0. So i think you can say that also 0 is an infinity. An infinity on the other side of the point in a number.
@MajorNr01 Or rather the infinity for numbers with a negative power. And if you say 0 is a number then i guess you have to call infinity a number, at least if you are agreeing with my comparison of 0 and infinity.
@MajorNr01 Btw i made a little mistake because im german: I said power instead of exponent one or two times because i suck at distinguishing between those two terms.
@MajorNr01 So now we can divide by 0 which gets us infinity as the result, the same way you get 0 when dividing by infinity. So if you divide a number that is not equal to 0 and not equal to infinity then you get the oposite "infinity" (dividing by 0 you get infinity and dividing by infinity you get 0).
The last problem is when multiplying the two numbers. 0 * infinity = ?.
You can basically say e.g.: 1 / 0 = infinity , 1 / infinity = 0. But also: 2 / 0 = infinity , 2 / infinity = 0
@MajorNr01 and 3 / 0 = infinity , 3 / infinity = 0 and so on. So i guess the term 0 * infinity is equal to any finite number. So the solution set of x = 0 * infinity contains an infinite amount of numbers.
@MajorNr01 One last comment: If you divide by 0 (i.e. add 0 to itself until you reach e.g. 1) the only problem that gets in the way is time. You need an infinite amount of time to execute that action. Now remember that in mathematics time does NOT exist. So such an action is executable in mathematics.
@MajorNr01 And finally: I think i could have messed up some mathematical terms because i can speak english pretty well but mathematical terms are something different :D
@MajorNr01 we still havent been able to generalized or axiomized let alone particularized and exceptionalized the theory of infinities.. qualitatively speaking.. it is plausible but quantitatively undecidable. This video is somewhat updated although it lacks the mathematical rigour what most amatuer and professional mathematicians alike use to obtain or describe mathematical systems for both pure and applied.
@PatrickLars - what r u looking 4? things like infinty squared can't actually exist, that'd only be useful to describe something like 2 infinite universes somehow combining with one another, to denote the amount of infinite universes that combined. but infinity is already endless, it can't get more endless.
@randomlaughingman no my friend, that is not how we interpret mathematics, you see some mathematicians are not satisfied with that kind of answer, my position here is neutral, but.. beware of those mathematicians who are obsessed with infinities.. those guys are nuts.. based from my experience.
i got an answer elsewhere yesterday about a different way of seeing infinity, so fair enough - that's them calling something else infinity, or distinguishing it from the usual meaning (that it doesn't end, and that's it) by prefixes in description.
but i'm not sure what bit of my comment ur saying isn't how maths is interpreted.
@randomlaughingman to be honest, its not my specialization.. im more interested in combinatorics, theory of sets and the theory of categories.. so I cant fill you with all the details, search those "nuts" and ask them, but we all have agreed on one thing.. there are lots of mathematical problems that are still undecidable.
@PatrickLars - u should like Donald E. Knuths kinda recent tome on combinatronics then, if u haven't picked it up already. art of computer programming volume 0, i think it's called. there's 4 of them.
i find it difficult to get into, as i didn't even do higher maths...but it's a damn good read once it clicks, i haven't had the chance to read the whole thing. but yeah i'm into sets etc too, database and search & patterning reasons. just an interest.
@PatrickLars - yeah, i like his books also cause he really pushes how important ASM is, and that the higher lev languages are too ephemeral (to focus on entirely). i'm totally like that, i can't stand people doing things wrong, how they eradicate proper computing knowledge from the courses etc. so important they learn about the actual ways to talk directly to the hardware.
i mean, i ihad to find out myself exactly how maths and programming are linked. there's no teachers anymore.
what i'm more meaning is - either nobody teaches anything properly - i asked so many times at school for them to explain what maths is actually for etc. never got any replies, never any sense out of anyone - or - cause education is now so messed up even more, the good teachers there are, they get forced to do shit that has fuck all to do with their subject, or teaching. it's all gone down the same tubes as false industry has, braindead for the most part.
@MajorNr01 - well u could take an infinite (ie - endless) amount of divisions decimally for example, between 0 and 1, so that ur infinitely approaching zero but never actually hitting 0, because it'll always be almost zero like 0.000000000000000003 etc to potentially an infinite amount of decimal places. so yeah that can work too, as infinity is a concept of endlessness.
People who are a mathematician would never call infinity a number... (face palm). Go learn some maths please! From a theoretical computer scientist/mathematician who works in foundation systems around infinity...
I know it's popular on the internet to say you can't divide by zero, but one of the first thing you're taught in Calc 1 is that n/0 = ∞ or -∞, depending on the sign of n, assuming n is not 0.
I realize this is a semantic debate, so I applaud you for saying that straight away, and I suppose by the definition given, infinity is indeed a number, but it seems like a very trivial point.
well, if infinity is a number then it should have to end and begin with 9, unless you want to use 0 as a higher number than 9. this 0 would have to have a preceding number attached to give it value because you can not get to infinity but if infinity did exist you could use 0 to get nearer to it but not as a value. eg. 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 and so on, forever. if that might make sense. also i think if you can keep dividing1-0
@mikeet00n well, who said we needed to us 0 or 1-9 numbers? we desperatly need a subatomic rule for numbers, or basically anything other then physical number set
@EIN771 Well, of course you would have to use different kinds of matrices or sets, and yes I think that when we start to divide 1 by half = 0.5 and half it again, and again, and so on, where does it stop because sooner or later you will reach 0
Remember- infinity is a number which you always have to add to and therefore, it can never be reached. So this complication has to be looked at by trying to divide down fractions. Well thats my theory anyway.
@mikeet00n yes I agree with you there. I think its a similiar to the romans. They didnt have anything to represent "0" and we have no rules to represent maths that dont apply to what we can see and use - if that makes sense
"Infinity is not a number, it is a set of numbers."
No, it is the cardinality of a set of "items". Specifically, it is the cardinality of the set of infinite items.
All numbers are cardinalities of a set of items. The number six, for example, is the cardinality of the set of six items. The number infinite, is the cardinality of the set of infinite items.
My definition of number is a tool used to express the total quantity and such of something in writing or speaking. It can also be used, like you said, to express similar quanitites, but can also be used to find quantities using other quantities (zero is a quantity, infinity is a quantity, they just can't be percieved by the human mind or senses).
you cannot count to infiniti therefore it should not be a number. also how can 2 to the infinite power be smaller than 2^2^infiniti if infiniti is infinite and therefore continues forever? they should be equal because they are both infinite.
@Wigger94 you can't count to pi in the sense like one, two, three, four but pi is still consider a number. also you can't count to the square root of negative one.
I'm not sure if someone already pointed this out, but when you say that infty*n=infty, you should also say that n is positive. Negative values for n ought to give negative infinity.
However, what you can do is measure how fast something approaches infinity.
y=2t appraoches infinty faster then y=t (t = time, the output [y] equalling the quantity) because at 10 seconds (t=10) we get 20 for y=2t and 10 for y=t. the bigger t is, the bigger the gap between y1 and y2 are. Therefore, we can conclude y=2t approaches infinity faster then y=t.
Finally, i can give you every number >3. If i get rid of every number greater then 3, i am left with 3 numbers (1,2,3). this can be represented by infinty-infinty=3
So, we have three different scenarios infinity-infinty=0, infinity, or 3. which is it? trick question, because infinity isn't a number, and the question is a fallacy because you can't subtract infinity from something, or add to it.
infinty isn't a number, its a direction that a limit can approach.
If we decided to treat infinity as a number, imagine this scenario:
I have a set of all natural numbers > 0. if i were to give you all of the numbers, i would have none left, this can be represented by infinity-infinity=0
I have the same set, but this time i only give you every odd number (infinant amount). This leaves me with all the even numbers (infinite amount). This can be represented by infinity-infinity=infinty
Hi, for some reasone i failed to post my coment on youtube.. But i have several things i would like to discuss with you, coz it seems like you are interested in same things as me :) plz answer, hope we can get contact^^
and i just want to say: n/inf=0 is absolutelly wrong.... if we take a random number like 5 instead of n, then: 5/inf=0, then 5=0 x inf, and since n x 0 = 0... you are saying that 5=0 what is wrong :) plz answer^^
I am not here to disprove your theory. I think it was well thought out, and well presented.
What I am here to say, is that we delve into another idea.
We are always taught that the numbers are infinite, and never ending.
So one may be willing to argue the ability to prove infinity as a number which may be what people were expecting. But what they need to prove to you as well, is also in words just as you have proved to the community.
Bullshit, 2^infinity is not greater than infinity. ALTHOUGH, taking the lim of n->infinity, then 2^n > n^2. This may seem trivial but it is EXTREMELY important.
At 5:37 you said only Zero and One equal Zero and One, however (arguably but accepted by most experts) any number other than Zero, (or infinity, if that is a number) can have its last digit subtracted by one and have repeating nines added to the end of it and it still equals the same number. (Examples: 1=0.999..., 4.3=4.2999...) This can be proven easily: 1/9=.111... and 9*1/9=9*0.111... this shows that 1=0.999.... Therefore, three is the cardinality of all things equal to zero and one.
xheadgmenx 2 weeks ago
Could you check out my "All are equal" video? Most of the problems people have pointed out have to do with infinity. Thank you.
RichBogatinovski 1 month ago
It is a number... just an imaginary one...
trevosh15 2 months ago
its not a number its an idea
MissspecialK100 4 months ago
@MissspecialK100 all numbers are ideas!
breadology1 2 months ago
infinity is opiset of zero
same every thing opiset of nothing
mosa0564778798 5 months ago
This has been flagged as spam show
Nefret 5 months ago
Comment removed
Nefret 5 months ago
number is easy to define. its a symbol, sometimes used to represent something.
TheAngryCanary 6 months ago
OF COURSE INFINITY IS A NUMBER.
CHUCK NORRIS COUNTED TO INFINITY. TWICE.
KanyeTroll 6 months ago
Infinity doesn't have a point on the complex plane. How is it a number?
Also, n*infinity does not equal infinity if n is negative. Everyone forgets that. Plus, you can state that 0*infinity = any number, since you said that n/infinity = 0 and that means infinity*0 = n.
anticorncob6 7 months ago
@anticorncob6 0*infinity = 0 and n/infinity = 0. simple as that. whether or not infinity is a number, those equations are 100% true.
TpendragonT 7 months ago
@TpendragonT ? By DEFINITION if a/b = c, then b*c = a. Try it on some numbers.
Then if you say n/infinity = 0, then 0*infinity = n.
0*infinity = 0, n/infinity = 0. You can't say both of these are true.
And if 0*infinity = 0, then a finite line has an infinite amount of points, and points are length zero, so that means 0*infinite = finite. As long as you're talking an uncountable infinity, 0*infinity is more then zero.
anticorncob6 7 months ago
@anticorncob6 If you take a number like 87 and divine it by infinity, you will receive .00000... as your answer. That is equal to 0. Now if somehow you could get to the end of this infinitely repeating decimal, and found a number like 2 (which you never would) then of course .000000...2 * infinity = 87. Since .0000... would be equal to 0 (as we all know this is common maths) The two equations before are true.
TpendragonT 7 months ago
@anticorncob6 I agree on infinity NOT being a number, but when you say 0/infinity you are speaking of a vertical asyntote in a x-y cartesian plane, what 0*infinity = n means is that 0*infinity IS 0, IS n and IS infinity. It is the moment of any curve whose tangent line's slope is infinite, and therefore is an indefinite form for any equation because it makes a number equal all numbers. if a number * something = not a number (all numbers), then that something ISN'T a number.
Tunatunatun 5 months ago
@TpendragonT You take the axiom that defines a Field, then a Vector Space like IR "For all a, b in F, both a + b and a * b are in F". Then if a is any element of IR and b is infinity, when you say n/infinity = 0, then infinity * 0 = n, means any number, or all numbers at the same time. 0*infinity is not one number, it's all of them, so it is not in IR, it's IR itself. IR is not a number then it is not in IR but it's a vector subspace of IR. 0*number = 0 , 0*infinity = ALL NUMBERS, not 0.
Tunatunatun 5 months ago
@Tunatunatun orrrrr 0 * anything = 0
TpendragonT 5 months ago
@TpendragonT anything that is a number. 0 * any number = 0. 0 * infinite =/= 0 so infinite isn't a number.
Tunatunatun 5 months ago
The bars are vertical, not horizontal!
Chus1001 8 months ago
infinity is a number coz i can use it in a math question hmm invinity plus invinity 2 infinity.... infinity is a amount not the limit to numbers duh and im 8 ( question how many zeros in infinity 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 zillion billion in 1 infinity just guessing
thefallingangel2011 8 months ago
@thefallingangel2011 If you think there are any "zeros" in infinity, or even that you can find any digit of it at all, you clearly don't understand it. It is precisely this property (it being completely incalculable in any way) that makes it not a number.
scoreunder 8 months ago
@thefallingangel2011 infinity+infinity = infinity. Your argument is in any universe invalid.
Tunatunatun 5 months ago
A number is often defined as a "quantity" or an "amount". Since the value of infiity is not definite (as you said yourself), then infinity is not ONE value, and is thus not a number.
Zero is a number, because it represents a set with no elements in it. As well, @CombatRocks, your argument implies negatives are not numbers as well.
So you think infinity would be prime? Why?
(and btw there is proof that there is no biggest prime number - take whatever value (let's say n) and do n! + 1
PauseToHesitate 8 months ago
infinity is an idea you good sir are stupid
DiduhlyDoo 8 months ago
If infinity is a number, can you obtain infinity without using another infinity? What equation would yield infinity without using infinity? Infinity gives definition to itself, meaning it, by itself, does not exist as a number.
ImmortalAcorn 8 months ago
@ImmortalAcorn
log(0) = negative infinity + arbitrary imaginary component
1/0 = number of infinite modulus with arbitrary argument
tan(pi/2) = number of infinite modulus with arbitrary argument
limit of 1/x as x decreases in value tending to 0 = positive infinity
(-1)! = number of infinite modulus with arbitrary argument
Those are some examples of reaching infinity without using it originally.
An example of using infinity without getting it in the result might be:
tanh(positive infinity) = 1
scoreunder 8 months ago
@scoreunder You can't use Tan to prove infinity, Tan uses Sin and Cos, which are equations that don't really have an end. That would be like saying 1+2+3+4+5+...=inf. Also, notice how none of these gave JUST infinity(you get infinity and an arbitrary argument)? They didn't just equal infinity, it had to have a second part to it, because infinity on it's own does not exist as a number, It's a concept. Unless you can find x amount solid numbers that equal exactly infinity...
ImmortalAcorn 8 months ago
@ImmortalAcorn In that case, |1/0| = infinity.
Sin and cos aren't "equations that don't really have an end", they're functions defined by naturally observed phenomena. Solutions of an equation that involve sines and cosines are generally considered to be closed form. You might be referring to the mclauren series for these functions. Note that also I gained positive infinity in the expression that used limits.
scoreunder 8 months ago
@ImmortalAcorn Also I do not think that infinity is a number. Just because it can be gained from operations on numbers does not mean it is a number, in the same way that performing operations on reals does not always mean that the result is real (classic example is (-1)^(1/2) ).
scoreunder 8 months ago
@scoreunder (-1)^(1/2)=i. i is an existent number, it may not be a real number, but it can be reached through logical mathematical means. i does not need another i to make sense. i=(-1)^(1/2), infinity on the other hand = no possible defined equation. i can be achieved by using other real numbers, infinity can only be gotten out of using another infinity. As I said, if you can get infinity using a defined equation(no a/0) without using inf twice(no inf=inf), then inf is a number.
ImmortalAcorn 8 months ago
@ImmortalAcorn Anyway, if you take into account the fact that limits can be taken from any direction to achieve infinity of any argument, please tell me how 1/x at x=0 is undefined.
scoreunder 8 months ago
@scoreunder Limits, can be taken from any direction to achieve infinity. Limit were created for infinity because infinity did not fit into math. Like I said before, all your basically saying is inf=inf. Your adding a limit to give the concept of infinity meaning. Infinity on it's own does not exist as a number. a/0 is an undefined number. Write 1/0=? as 0*?=1, what is ? equal to other than itself? So, what can be done? Easy, we introduce a new concept to make sense of this, limits.
ImmortalAcorn 8 months ago
@ImmortalAcorn
"Infinity on it's own does not exist as a number"
Yes, I said it's not a number - but that doesn't mean it can't be found using numbers!
"Easy, we introduce a new concept to make sense of this, limits."
I take it you have never used limits. The limit of (x^2-1)/(x-1) as x approaches 1 is 2. How do we calculate this without limits? We simplify. Limits are merely a calculation aid.
"Limit were created for infinity because infinity did not fit into math."
Now you're just trolling.
scoreunder 8 months ago
@ImmortalAcorn Also you have still not explained why you think "1/0" is undefined. Among the reals it is clear that it has exactly 2 possible results, negative and positive infinity.
1/(0.00001) = 100000 and 1/(0.0000001) = 10000000. Once the denominator reaches zero, the result is infinitely large (and if you use negatives, an infinitely large negative). What is so hard to understand about this?
scoreunder 8 months ago
@scoreunder No, Here's the thing... 1/(0.00001) = 100000 is true, 1/(0.0000001) = 10000000 is as well. But, we're not using a .00001, or a .0000001, or even an infinitely small number. We are using 0. We are using a 0.000... The 1 at the end will never be reached, which is why .000... is EXACTLY 0. You used a limit saying that as denominator APPROACHED 0, when we are using 0 exactly(meaning there is no 1 at the end). You used a limit, which again is defining inf using another concept.
ImmortalAcorn 8 months ago
@scoreunder Okay then, here's the deal. You keep adding 0s to that 1/0.000xxxx... You inform me when you reach a 1 to make your equation larger than 0.
ImmortalAcorn 8 months ago
@ImmortalAcorn 1/0.000000 (good enough? :P .... kidding!)
Anyway, here's another way of looking at it:
1 / (infinity) = 0
therefore 1 / 0 = infinity
And if you disagree with this, then please tell me: what number is infinitely small (literally endlessly small, be-all-end-all nothing-can-be-smaller-than-this type of small) but not zero? (There is no such number)
This is almost as bad as debating those that say 0.999 recurring is not exactly equal to 1. They are wrong and do not understand math.
scoreunder 8 months ago
@scoreunder No, 1/inf does not equal 0. You are using a limit now. 1/0.000000... will never ever EVER reach a 1 to make the equation true. You are applying a limit and saying instead of using 0, we're using an infinitely small number. 1/0 does not equal inf, 1/"an infinitely small number"="an infinitely large number." Stop using a limit where your constants should go, Your trying to prove infinity exists WITHOUT using a limit or another infinity.
ImmortalAcorn 8 months ago
@ImmortalAcorn So far you've rejected limits because they don't support your mathematical worldview and you have accused me of applying limits where I have not. You still have not answered the question in my previous comment.
Here's a way of thinking about it:
I have a number, "infinitely small". It is not equal to zero.
Thus, there is a number between this number and zero as they are not equal.
There is not, otherwise it contradicts the "infinitely small" property - thus they are equal.
scoreunder 8 months ago
@scoreunder "There is not, otherwise it contradicts the "infinitely small" property - thus they are equal." rephrase -> "This contradicts the statement that the number was "infinitely small" - thus they are equal."
scoreunder 8 months ago
@scoreunder Rejected limits? Not even, I have simply asked you to prove infinity as a NUMBER(math) but you've only proven it as a concept(not math). What sense does it make to say 1/"a number that grows without bounds, eternally"=0. Infinity is not a number, it's a concept. You cannot have 1/concept=0, you can however have a "1/x equals 0, as x approaches a number with no bounds(infinity)". Your using a concept as a number, can you divide 1 by a concept?
ImmortalAcorn 8 months ago
@ImmortalAcorn Numbers are all concepts. You can multiply matrices by each other, and they are not numbers - now, please answer this (and stop avoiding!):
Premise 1: I have an infinitely small number that is not equal to zero.
Premise 2: All numbers that are not equal have an infinite amount of numbers between them.
Conclusion 1: From P1. and P2., the infinitely small number is not the closest possible number to zero - thus it is EITHER not infinitely small OR it is equal to zero.
Do you agree?
scoreunder 8 months ago
@ImmortalAcorn OH! How could I forget:
log(log(log(0))) = positive infinity
scoreunder 8 months ago
Comment removed
ImmortalAcorn 8 months ago
@scoreunder 1/0, log(0) and so on yield an undefined result. Therefor, they more or less equal nothing. If you were to create a concept to give meaning to these nothing numbers at the end of the equation, then obviously, you would get this concept because that's why it was made. log(log(log(0)))=nothing=inf. In order to prove infinity, you need an equation that will give infinity without also giving an undefined number. I can get any other number with a defined equation, so why not infinity?
ImmortalAcorn 8 months ago
@ImmortalAcorn "1/0, log(0) and so on yield an undefined result." No - 1/0 is infinity of arbitrary/unknown argument, (thus |1/0| is infinity) and log(0) is infinity plus an imaginary component. No result is undefined -- 0/0 is undefined UNLESS it is part of a continuous function where limits can be taken to find the value.
I received in my email (not in the comments box though, hmm..) a comment from you stating that 1/0 does not exist... by whose standards?
scoreunder 8 months ago
@ImmortalAcorn I can prove that 1/0 exists: 1/2 is the proportion of something you can share equally between 2 people. 1/1 is the proportion of something you can share with only yourself. And of course, if you're sharing with nobody, you can "give" nobody whatever you're sharing an infinite amount of times and you will still have it.
scoreunder 8 months ago
I don't think most mathematicians care whether infinity is a number or not. You can define terms to mean whatever you like of course, and it's not clear what advantage there is in deciding either way.
Actually most mathematicians don't talk about "numbers" because that's too vague a term. They'll say suppose z is a complex number, or a real number, or an integer, or a rational number, or a natural number. But the term "number is not usually defined or used in isolation, as it's vague.
MistyGothis 9 months ago
Your basic premise is wrong - neither zero nor infinity are 'numbers'. They are concepts - they have no numeric value. Numbers have measurable values - otherwise they are not numbers!
CombatRocks 9 months ago
Plus you have the mathematical knowledge of a first grader.
MasterGhostKnight 9 months ago
Mathematicians are not wrong. Mathematicians are the ultimate arbitrers, this isn't a question of semantics. If you say that infinity is a number, it is notsimply your opinion, you are just wrong. The same way if you say that 1=2, it is not a matter of opinion, you are just wrong.
MasterGhostKnight 9 months ago
infinite x infinite = infinite2. DUN DUN DUN.
ChristopherMedia 10 months ago
“In some sense, the mathematical analysis is nothing else
than a symphony about the topic of infinity.”
MegaDarthraider 10 months ago
If you type: 2^infinity > infinity
into Wolfram Alpha (a free online algebraic calculator that can work with infinity, complex numbers etc) it says False. I am kind of confused, it says 2^infinity = infinity
docopoper 10 months ago
@docopoper Infinity is the concept of endlessness.
By asking if "2^infinity = infinity", you're asking the question: If I endlessly increase the power by which I raise two, does the value also endlessly increase?
In the same way, 2^-infinity = 0 -- if you endlessly increase the negative power by which you raise two, the value will constantly get closer and closer to 0.
scoreunder 8 months ago
@scoreunder
The main thing that confused me was the contradiction between this video and Wolfram Alpha.
I understand that 2^(-infinity) = 0 ; That is intuitive - I actually would have thought that 2^infinity = infinity ; And that is why I was confused by the inconsistencies between this video and W|A.
If you read the "Uploaders' Comments" then you will notice that he reinforced this by stating:
2^infinity > infinity ;"since you cannot demonstrate a one-one correspondence between these sets."
docopoper 8 months ago
@docopoper He is wrong ;)
scoreunder 8 months ago
@scoreunder
lol, I hope we get an argument on his behalf from someone...
docopoper 8 months ago
@docopoper I don't think anyone will follow on with the argument because I don't really think anyone else believes there's no 'real' way to get infinity from an expression without using infinity in the first place. ;)
scoreunder 8 months ago
@scoreunder I believe what the other dude was saying is that when you say 1/0 = infinite you're wrong because 1/0 isn't defined. Lim x->0 1/x = infinite and that is true. There is a difference of saying a limit than just the ecuation. When you use limits ( lim x-> c f(x) = L ), you don't care about what f(c) is, although most of the time f(c) = L, if f is not defined at c L still exists. When you take lim x->0 1/x = infinite and say 1/0 = infinite, you're just misusing the concept of limits.
Tunatunatun 5 months ago
in my opinion you choose previously the definition of number in the way "infinite" would fit in it. we can give a lot of definitions, some that include infinite, some that don't.if we choose to say, in addition to your definition "you can obtain any real number A by adding 1 to another real number B", this is necessary, even if not enough, to define "number". but wich number B+1 is equal to infinity, if for hypotesis you can't use infinite as B?(that would be circular!). sorry for bad english :)
1991ganjalf 10 months ago
Excuse me, but you should have taken some Allegra (120mg) prior to making this video to have avoided having to inject so many sniffles throughout your project. Oh, the math, yeah, infinity is a very large number. Or, it is something ABOUT numbers. Sniffle, sniffle...
allegrobas 11 months ago
infinite is not a number silly rabbit, it's a concept, so you can't add one to infinite, or have you already figured this out from all the responces.
sonicsoul0 11 months ago
"Infinity is the cardinality of the set of natural numbers" <- This is where you go wrong, logically, from what I can see. The natural numbers aren't a set. Or, if you argue that they are a set, you've pushed the original problem of including infinity in the definition of "number" over onto including it in the definition of a "set", which is a term that even more heavily suggests finity.
Bobstew68 1 year ago
why human beings are so shameless to lie? "Why Infinity is a number ". Definition of number is something that can be measure, it is defined and finite, therefore infinite, and zero are no included in the concept. Dont be fooled because they are into the number line, they are numbers. Zero is the point of reference, to measure something, and infinite is a simbol that stand for a number which cannot be reach but exist. Good understanding needs few words.
xchris1800 1 year ago
At least up to 5:44, your argument is based on the cardinality of a set. Seeing your definition of cardinality at 1:08, take note of the portion "is the number of". By your comparison at 5:44, you are assuming infinity to be a number by saying it is the cardinality of the set of integers.
This is not any different than if someone wants to prove trigonometry with calculus.
Therefore, although your argument is interesting, it is not convincing enough to me to be compared to finite numbers.
4EverTrying 1 year ago 2
You definition of number is wrong. Ordinal numbers don't express equality.
qtheplatypus 1 year ago
well it is known that you are dumb retarted homo and infinite is already known as a number in most peoples minds BITCH SLAP!!!
eppic29 1 year ago
The definition of a number is an label describing "finite." Does in-finite describe finite? Math has setup rules that allow infinity to work as a number...what rules do numbers have? Count to infinity for me real fast...infinity can be counted. Infinity works as a number as long as I follow your rules? But using your rules, I should prove you wrong? These rules need to be changed. If X is a number between 1.0 and .999...and 1.0-X=.999...you say1.0-X=0 i say x was zero! and ask what was x4u?
strongmf 1 year ago
Almost everything in mathematics is based on definitions because it is an invented construct, used as a language to make it easier for us to work on real world problems. Some things are left undefined because not every one can agree on one. The thing is, you will believe what you want. There are areas with different sets of definitions and rules. Your desire to count Inf as a number is allowable within your definition, but one agrees to THEIRs when working with them so one can communicate.
JillPKitten 1 year ago
"You can't divide by zero." - WRONG!
It is NOT impossible, it's just UNDEFINED!
It's undefined because the operation is liable to more than one interpretation, and without knowing more about its use (knowing the equation as opposed to a single operation of div0,) you can't determine what the result should be.
e.g.: 4 states: 0 div 0 = 0 (typical) or 1, N div 0 = 0 or inf (typical)
Each true but if you can't map the function, then you can't determine which is correct.
UNDEFINED!
JillPKitten 1 year ago
"You can't divide by zero." -- WRONG!!!
Not to say if I agree or disagree whether inf is a number, but you have invalidated your argument with that false statement as part of its basis.
[these posts just don't have enough character space] see my next post.
JillPKitten 1 year ago
and what is infinite + 1 ? infinite and one or infinite?
Jon58004 1 year ago
@Jon58004 (infinite + 1) = (infinite) because there is a one-one correspondence between those sets. that is the definition of "equals".
For the same reason (infinite) * (infinite) = (infinite).
However, (2 raised to the power of infinite) is greater than (infinite), since you cannot demonstrate a one-one correspondence between these sets.
neotropic9 1 year ago
@neotropic9 thanks
Jon58004 1 year ago
@neotropic9 why not
Whitefire240 1 year ago
@neotropic9 except you can.
2^0 with 0,
2^1 with 1,
2^2 with 2, etc.
Whitefire240 1 year ago
@neotropic9
inf*inf =inf?
If so that would mean inf/ inf = inf as well? Well, the answer you could provide is, 0/0 is not zero...but it could be zero!! based on ur premises n/inf = 0 therefore 0/0 = (n/inf)/(n/inf) = inf/inf...treating inf as a number is not my problem, Euler used to do that, but its ur definition of inf as a number...inf has ranks just like u said 2^inf is something bigger thn inf, but like wise 2*inf/inf =2 if both inf's are of the same rank. I ran out of characters...
Vindignatio 11 months ago
So, while we can play as inf as a number, and practically, Euler did and people normally do, we cant define it as a num, including ur reasoning of the cardinality of a set containing infinite elements (which is self reference), because either a. Inf is not in Natural numbers, so then there exists a set containing both Inf and N, which is not equal to the set N, but N is a subset of this set, therefore its cardinality must be greater. if inf is of N why not R? what set does it belong to?
Vindignatio 11 months ago
@neotropic9 Infinity is not a number. It's a term to describe the last number, but numbers go on forever, hence inifnity.
Zekezan88 6 months ago
@Jon58004
You're an idiot. It doesn't matter, add or multiply any number by infinity and you still get an infinity.
RUL1S88 7 months ago
here is a questin for u, what is infinite minus infinute
Jon58004 1 year ago
stop SNIFFLING!
GroovingPict 1 year ago
I think infinity is an idea rathter than a physical being. What is inf-inf or inf/inf ?
x -> inf, when x -> inf and 1/x -> 0, when x -> inf but when you multiply them with eachother it's x times 1/x (which is x/x) = 1 so if x=inf and 1/inf = 0 then Inf times 0 = 1.
So I say that infinity is NOT a number, it's a concept or an idea that we mark with the "fallen eight"
Zhaggysfaction 1 year ago
Interesting argument, but ultimately arbitrary and unimportant to most mathematicians who know the concepts of all numbers and are rightfully unconcerned with verbal definitions. Leave the words to the writers and sophists, it is the knowledge of the concepts of zero and infinity and aleph null, 1, 2 that are important.
iFreeThinker 1 year ago
If you define infinity as a number, then you can not do math with it. Mathematics is based on the principle of equality (inequality is an attempt to discribe qualities of two no equal functions). If you introduce the number infinity, equality breaks down. 2+infinitiy is greater than infinity but it is also equal to infinity which gives contradiction. To solve this problem you would need to define an infinite number of infinites, and then define an infinite number of those. It is a number.
yyttr4 1 year ago
how long is the universe?
Iskander299 1 year ago
Is it true that 1/∞>0?
Is it also also true that nth (n) <∞?
If that's the case, then couldn't you say
1/∞=0.000...1, saying that the 0's are infinite? That would then mean that 1/∞≠0
I'm a 9th grader taking Algebra 2, so be gentle!
AnAmericanComposer 1 year ago
how is 2^inf greater than inf. how can anything be grater than inf
joraiffe 1 year ago
I don't think it is an number, because of its property is too different from the other numbers, I mean for example take limits, with infinity you are able to sum a geometric series to an EXACT sum whereas you can never do that if you treat it as a number, now since you say infity is a number, it must be the biggest number, but as it is constant the geometric must sum to something but not exact.
1001014 1 year ago
I dont see the point. I thought you wanted to show that infinity is an element of N but all you did is define the word "number" in a way that infinity obviously fits it. Thats like saying infinity is a pink elephant by defining pink elephant as the cardinality of N. (So infinity also isnt prime (nor is it not prime) because prime numbers are defined on N (or Z).)
hfhsfkshfkshfksfhsks 1 year ago
is infinity a prime number ?
TechnoMulen 1 year ago 15
@TechnoMulen I suppose it has to be.
neotropic9 1 year ago
@neotropic9
i think not
because as we all see primenumbers quickly rise in the size of the number
and there is so few of them at high numbers it seems impossible at some point to find more and why should that number be a primenumber anyways..
calling something the number infinity is like saying " the edge of the universe"
wich is ever expanding as you reach towards it
we just have a word for it for the human brain to comprehend it..
sorry for my bad english...
TechnoMulen 1 year ago
@neotropic9 It can be, depending on a specified integer above n that you specify.
jjovereats 1 year ago
@neotropic9 I thought you just said infinity*infinity=infinity though...?
ImmortalAcorn 8 months ago
@neotropic9 Except when it's expressed as lim_x->inf 2^x
scoreunder 8 months ago
@TechnoMulen Since the chances of a number being prime reach closer and closer to zero among ever larger integers, infinity would be composite; Divisible by every prime number an infinite amount of times.
759009946576 1 year ago
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759009946576 1 year ago
This has been flagged as spam show
And with an infinite amount of divisors; All finite integers divide infinity.
759009946576 1 year ago
@TechnoMulen Yes, infinity is Prime #19
19 squared is 361 of which means the end and the begining and infinite in this way
PhuQuangLe111 6 months ago
how can it b a number? any number u can think of or arrive at - add 1 to it. then add 1 again. then keep doing that - for infinity. it never ends, so u can never count up to it, or down to it for that matter cause u get negative scales of counts too.
unless ur changing what number means, to mean something else instead. but then u lose the concept of infinity being endless, which is its point.
randomlaughingman 1 year ago
I agree with you here. Even though it is not based on solid proof rather than a lot of evidence (in my opinion). If you divide by 0 the result is of an infinite magnitude.
The most basic way of dividing is to see, how many times you need to add up the divider to reach the dividend. The dividend is 6 and the divider is 2. 2 + 2 + 2 = 6 or rather 2 * 3 = 6. You add 2 to itself 3 times to get 6. Let's say now the dividend is 1 and the divider is 0. 0 + 0 + 0 + 0 + 0 + ... is what?
MajorNr01 1 year ago
@MajorNr01 Basically you would sit there adding 0 to itself for an infinite amount of time, you add it up infinite times which is the result of the calculation. This is very close to a philosophical question i guess but for me it works pretty well.
Also some thoughts i had about the power of a number, concerning the sign. If you invert one number's power's sign you basically turn the number around the point. What i mean is that you have an infinite amount of numbers on each side of the point.
MajorNr01 1 year ago
@MajorNr01 All numbers between 1 and 0 (i dont say between 0 and 1 because i want to point out the direction) and between 1 and infinity. Now if you have a very high number its closer to infinity, the greater it is. In the same way if you divide 1 by that number (number^(-1)), the greater it is, the closer the result is to 0. So i think you can say that also 0 is an infinity. An infinity on the other side of the point in a number.
MajorNr01 1 year ago
@MajorNr01 Or rather the infinity for numbers with a negative power. And if you say 0 is a number then i guess you have to call infinity a number, at least if you are agreeing with my comparison of 0 and infinity.
MajorNr01 1 year ago
@MajorNr01 Btw i made a little mistake because im german: I said power instead of exponent one or two times because i suck at distinguishing between those two terms.
MajorNr01 1 year ago
@MajorNr01 So now we can divide by 0 which gets us infinity as the result, the same way you get 0 when dividing by infinity. So if you divide a number that is not equal to 0 and not equal to infinity then you get the oposite "infinity" (dividing by 0 you get infinity and dividing by infinity you get 0).
The last problem is when multiplying the two numbers. 0 * infinity = ?.
You can basically say e.g.: 1 / 0 = infinity , 1 / infinity = 0. But also: 2 / 0 = infinity , 2 / infinity = 0
MajorNr01 1 year ago
@MajorNr01 and 3 / 0 = infinity , 3 / infinity = 0 and so on. So i guess the term 0 * infinity is equal to any finite number. So the solution set of x = 0 * infinity contains an infinite amount of numbers.
MajorNr01 1 year ago
@MajorNr01 One last comment: If you divide by 0 (i.e. add 0 to itself until you reach e.g. 1) the only problem that gets in the way is time. You need an infinite amount of time to execute that action. Now remember that in mathematics time does NOT exist. So such an action is executable in mathematics.
MajorNr01 1 year ago
@MajorNr01 And finally: I think i could have messed up some mathematical terms because i can speak english pretty well but mathematical terms are something different :D
MajorNr01 1 year ago
@MajorNr01 we still havent been able to generalized or axiomized let alone particularized and exceptionalized the theory of infinities.. qualitatively speaking.. it is plausible but quantitatively undecidable. This video is somewhat updated although it lacks the mathematical rigour what most amatuer and professional mathematicians alike use to obtain or describe mathematical systems for both pure and applied.
PatrickLars 1 year ago
@PatrickLars - what r u looking 4? things like infinty squared can't actually exist, that'd only be useful to describe something like 2 infinite universes somehow combining with one another, to denote the amount of infinite universes that combined. but infinity is already endless, it can't get more endless.
randomlaughingman 1 year ago
@randomlaughingman no my friend, that is not how we interpret mathematics, you see some mathematicians are not satisfied with that kind of answer, my position here is neutral, but.. beware of those mathematicians who are obsessed with infinities.. those guys are nuts.. based from my experience.
PatrickLars 1 year ago
@PatrickLars - u don't interpret it how?
i got an answer elsewhere yesterday about a different way of seeing infinity, so fair enough - that's them calling something else infinity, or distinguishing it from the usual meaning (that it doesn't end, and that's it) by prefixes in description.
but i'm not sure what bit of my comment ur saying isn't how maths is interpreted.
randomlaughingman 1 year ago
@randomlaughingman to be honest, its not my specialization.. im more interested in combinatorics, theory of sets and the theory of categories.. so I cant fill you with all the details, search those "nuts" and ask them, but we all have agreed on one thing.. there are lots of mathematical problems that are still undecidable.
PatrickLars 1 year ago
@PatrickLars - u should like Donald E. Knuths kinda recent tome on combinatronics then, if u haven't picked it up already. art of computer programming volume 0, i think it's called. there's 4 of them.
i find it difficult to get into, as i didn't even do higher maths...but it's a damn good read once it clicks, i haven't had the chance to read the whole thing. but yeah i'm into sets etc too, database and search & patterning reasons. just an interest.
randomlaughingman 1 year ago
@randomlaughingman thanks for that information, Donald E. Knuths? sounds familiar to me, but anyways thanks again.
PatrickLars 1 year ago
@PatrickLars - yeah, i like his books also cause he really pushes how important ASM is, and that the higher lev languages are too ephemeral (to focus on entirely). i'm totally like that, i can't stand people doing things wrong, how they eradicate proper computing knowledge from the courses etc. so important they learn about the actual ways to talk directly to the hardware.
i mean, i ihad to find out myself exactly how maths and programming are linked. there's no teachers anymore.
randomlaughingman 1 year ago
what i'm more meaning is - either nobody teaches anything properly - i asked so many times at school for them to explain what maths is actually for etc. never got any replies, never any sense out of anyone - or - cause education is now so messed up even more, the good teachers there are, they get forced to do shit that has fuck all to do with their subject, or teaching. it's all gone down the same tubes as false industry has, braindead for the most part.
randomlaughingman 1 year ago
@MajorNr01 - u can 0 to 0 for infinity, u'll only ever get 0
randomlaughingman 1 year ago
@MajorNr01 - that should have read, u can add 0 to 0 for infinity, u'll only ever get 0
randomlaughingman 1 year ago
@MajorNr01 - well u could take an infinite (ie - endless) amount of divisions decimally for example, between 0 and 1, so that ur infinitely approaching zero but never actually hitting 0, because it'll always be almost zero like 0.000000000000000003 etc to potentially an infinite amount of decimal places. so yeah that can work too, as infinity is a concept of endlessness.
randomlaughingman 1 year ago
People who are a mathematician would never call infinity a number... (face palm). Go learn some maths please! From a theoretical computer scientist/mathematician who works in foundation systems around infinity...
Entertainmentwf 1 year ago
Infinity is not a number.... infinity is a concept that could be applied to structure, number, space and more.
Entertainmentwf 1 year ago
do a vid on how 0/0=1. because i proved it does i just dont have enough space in a post to show you.
pivotman64 1 year ago
I know it's popular on the internet to say you can't divide by zero, but one of the first thing you're taught in Calc 1 is that n/0 = ∞ or -∞, depending on the sign of n, assuming n is not 0.
I realize this is a semantic debate, so I applaud you for saying that straight away, and I suppose by the definition given, infinity is indeed a number, but it seems like a very trivial point.
Syynth 1 year ago
Chuck Norris counted to infinity TWICE
imanoob4 1 year ago
Go ahead and call it a number if you want.
It isn't a number though. We are not talking about a number when talking about infinity.
zyzzyzus 1 year ago
Also there was nothing supporting the case of infinity being a number. ∞*0 is indeterminate.
zyzzyzus 1 year ago
Although it is impossible to divide by 0, there is not one number where it is not possible to multiply it by 0.
zyzzyzus 1 year ago
well, if infinity is a number then it should have to end and begin with 9, unless you want to use 0 as a higher number than 9. this 0 would have to have a preceding number attached to give it value because you can not get to infinity but if infinity did exist you could use 0 to get nearer to it but not as a value. eg. 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 and so on, forever. if that might make sense. also i think if you can keep dividing1-0
mikeet00n 1 year ago
@mikeet00n well, who said we needed to us 0 or 1-9 numbers? we desperatly need a subatomic rule for numbers, or basically anything other then physical number set
EIN771 1 year ago
@EIN771 Well, of course you would have to use different kinds of matrices or sets, and yes I think that when we start to divide 1 by half = 0.5 and half it again, and again, and so on, where does it stop because sooner or later you will reach 0
Remember- infinity is a number which you always have to add to and therefore, it can never be reached. So this complication has to be looked at by trying to divide down fractions. Well thats my theory anyway.
mikeet00n 1 year ago
@mikeet00n yes I agree with you there. I think its a similiar to the romans. They didnt have anything to represent "0" and we have no rules to represent maths that dont apply to what we can see and use - if that makes sense
EIN771 1 year ago
Infinity is not a number, it is a set of numbers.
brangelito 1 year ago
@brangelito
"Infinity is not a number, it is a set of numbers."
No, it is the cardinality of a set of "items". Specifically, it is the cardinality of the set of infinite items.
All numbers are cardinalities of a set of items. The number six, for example, is the cardinality of the set of six items. The number infinite, is the cardinality of the set of infinite items.
neotropic9 1 year ago
@neotropic9 I mean, there has to exist an infinite amount of different infinities and zeros for the math to make sense..
brangelito 1 year ago
@brangelito
Ah yes. There are an infinite amount of transfinite numbers. An infinity of infinities. And each one is a number.
But "infinite" -in the sense that there are "infinite numbers"- is the first of the transfinite numbers. Aleph-null, we call it.
neotropic9 1 year ago
infinity maybe is a number, but it is unreachable by anything i guess, blackholes cant even reach it, else they would have sucked up the universe
masterjamie9 1 year ago
0.0 *head explodes*
SleepTight7474 1 year ago
Infinity is Zero
becuase infinity cannot be counted, there for it is Zero.
TheKiemaster 1 year ago
infinity is a concept
BMBaccount 1 year ago
numbers represent quantities
infinity represents a quantity
trying to use infinity with other numbers will of course result in problems simply because not all numbers behave alike, zero being a good example
BigGordonLips 1 year ago
My definition of number is a tool used to express the total quantity and such of something in writing or speaking. It can also be used, like you said, to express similar quanitites, but can also be used to find quantities using other quantities (zero is a quantity, infinity is a quantity, they just can't be percieved by the human mind or senses).
Moshikashitenai 1 year ago
i was right. people keep on saying i was wrong and they said infinity was not a number. i sad it was.
infinitylord08 1 year ago
you cannot count to infiniti therefore it should not be a number. also how can 2 to the infinite power be smaller than 2^2^infiniti if infiniti is infinite and therefore continues forever? they should be equal because they are both infinite.
Wigger94 1 year ago
Comment removed
infinitylord08 1 year ago
@Wigger94 you can't count to pi in the sense like one, two, three, four but pi is still consider a number. also you can't count to the square root of negative one.
infinitylord08 1 year ago
I'm not sure if someone already pointed this out, but when you say that infty*n=infty, you should also say that n is positive. Negative values for n ought to give negative infinity.
Danielkwalsh111 1 year ago
However, what you can do is measure how fast something approaches infinity.
y=2t appraoches infinty faster then y=t (t = time, the output [y] equalling the quantity) because at 10 seconds (t=10) we get 20 for y=2t and 10 for y=t. the bigger t is, the bigger the gap between y1 and y2 are. Therefore, we can conclude y=2t approaches infinity faster then y=t.
achilles6822 1 year ago
Finally, i can give you every number >3. If i get rid of every number greater then 3, i am left with 3 numbers (1,2,3). this can be represented by infinty-infinty=3
So, we have three different scenarios infinity-infinty=0, infinity, or 3. which is it? trick question, because infinity isn't a number, and the question is a fallacy because you can't subtract infinity from something, or add to it.
achilles6822 1 year ago
infinty isn't a number, its a direction that a limit can approach.
If we decided to treat infinity as a number, imagine this scenario:
I have a set of all natural numbers > 0. if i were to give you all of the numbers, i would have none left, this can be represented by infinity-infinity=0
I have the same set, but this time i only give you every odd number (infinant amount). This leaves me with all the even numbers (infinite amount). This can be represented by infinity-infinity=infinty
achilles6822 1 year ago
"Mathematicians are not the ultimate arbiters of this issue."
Um, yes they are.
Infinity is a concept. Which is why things /tend/ towards it. It's just notation that:
lim_{x->0} 1/x = \infty
The proper way to read that is as x approaches 0, 1/x approaches infinity. Infinity is unattainable, it can't be nailed down, not a number.
"In fact, there are infinite infinities."
Nope. Cantors "infinite infinites" was left behind by ZF/ZFC axiomatic set theory.
And that's just the first 2:14...
CrispyGreyMatter 1 year ago
Hi, for some reasone i failed to post my coment on youtube.. But i have several things i would like to discuss with you, coz it seems like you are interested in same things as me :) plz answer, hope we can get contact^^
and i just want to say: n/inf=0 is absolutelly wrong.... if we take a random number like 5 instead of n, then: 5/inf=0, then 5=0 x inf, and since n x 0 = 0... you are saying that 5=0 what is wrong :) plz answer^^
Twixmonster1 1 year ago
Here's my ponderance.
Each form of displaying a quantity greater than one hundred thousand is displayed in a word with a latin prefix followed by "llion".
And if numbers are infinite there must be an infinite amount of prefix's. To where does this stop? What is the greatest prefix made?
And then can a quantity be verified for that next region in sequence?
It is in it'self an infinite reoccurance. Take the next step in the process.
OleprechaunO 1 year ago
I am not here to disprove your theory. I think it was well thought out, and well presented.
What I am here to say, is that we delve into another idea.
We are always taught that the numbers are infinite, and never ending.
So one may be willing to argue the ability to prove infinity as a number which may be what people were expecting. But what they need to prove to you as well, is also in words just as you have proved to the community.
To be continued.
OleprechaunO 1 year ago
thank you!!!, i understand alot better now, thank you very much
RTGhy90 1 year ago
people think of infinity the wrong way... dont think of it as the highest number or anything like that, think of it as ANY number, that is infinity
buckeyefan2107 1 year ago
Bullshit, 2^infinity is not greater than infinity. ALTHOUGH, taking the lim of n->infinity, then 2^n > n^2. This may seem trivial but it is EXTREMELY important.
Embrigh 1 year ago
infinite x 2 eqauls
2(infinite) duhhhhhh so obvious now im gonna be famous
maxxxx1112 1 year ago
if infinity is a number
what is the sqrt of it
what is the diffrence between x over infinity and zero.
what is X^infinity
100000000years 1 year ago
@100000000years
sqrt of inf is inf.
x/inf = 0.
x^inf is different depending on x. if x is inf then x^inf is a higher order inf.
neotropic9 1 year ago 4
@neotropic9 and inf - inf is...?
iwantcoolname 1 year ago