My point is that, while I agree with what you've said about infinity (and thank you), I don't think that this definition is complete. Infinity cannot be just a property of sets or of numbers or whatever, but the consequence of a generating rule. It says that a set defined by at least one generating rule is an infinite set. Long story short: This puts mathematical induction on the par with reasoning by induction, doesn't it?
But "property" is a noun, and we understand and use it as such. Objects have properties, which, among other things, are adjectives which describe them. When we speak of redness, we can understand the property as that which applies to all objects that are red, yet we can subtract (or abstract) the objects until we have "redness". "Infinity", if it is a property, could be made into a noun and, as any noun, it has properties too.
@bobbutnot I present no opinion in this video. I am telling you what it is. Infinity is a singular concept and is not limited except by its conceptual confines.
infinity in ways is just an idea any number that can be added subtracted and well ANY KINDA NUMBER so if any number is infinity than 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 etc are all numbers of infinity
the simplest proof that there is neither a largest nor smallest number, and therefore prove the existence of infinity and negative infinity, is as follows.
Define a largest number, N, and a smallest number, n.
N+1 is obviously greater than N, showing that there is no greatest number. This proves the existence of infinity.
n-1 is obviously less than n, showing that there is no smallest number. This proves the existence of negative infinity.
On the subject of cardinality, I know that the set of rational numbers has the same cardinality as the set of natural numbers, and that the set of irrational numbers has a different cardinality because it is not 'countable'.
Is there a system for measuring different cardinalities?
@chaOsMastaGuru: I don't think there is a mechanistic way of measuring them. I was meaning to look into this to be sure, but have been busy with other things.
Whether or not there is a set with a cardinality between countable and the reals is apparently either an open question or an independent axiom (its one or the other, and this is known, I just haven't done the research to know which it is.)
This defies my own intuition for the following reason:
If A is the smallest infinity (countable) and P(x) is the power set of any set x, then *I* imagined that A, P(A), P(P(A)), P(P(P(A))), ... would be a "tightest possible" enumeration of infinities. However the comment above makes it clear that this is probably not right. I.e., the set of reals, C, is probably such that: C < P(A).
If you pursue this and find an answer, I would appreciate being pointed in the right direction. :)
Is there really such thing as a negative infinity, because it would seem like by now is would be nothing because it would take forever to grow small and find something that is infinitely small.
I don't get it... If an infinite set can't have a larger and a smaller number at the same time, then how about a set that contains real numbers let's say from 1 to 2?
Look up the concept of a "power set" and "bijections". The power set of N={1,2,3,...} cannot be put into a bijection with N. In this sense we differentiate the *kinds* of infinity, and we say that the cardinality of the power set of N is larger than that of N.
Google-plex factored is 2 to the power google times 5 to the power of google. That has as much meaning as any other factorization. Making infinity equal to zero doesn't make sense even in projective spaces.
Thank you for taking your time to educate people, we appreciate the video. I could hear it just fine but did have to turn the volume up a bit; such might be a problem for others. Your explanations were clear and easy to follow, and interesting.
Infinite can apply to an abstract set in a sensible and well defined way. When philosophers or "spiritual" people try to use the word it becomes meaningless. It leads people to say nonsensical things like "god is infinite" without any realization that there are *MANY* kinds of infinite (some "larger" than ohers).
How does Turing's halting problem relate to this? Do infinite processes count as infinite if it is impossible to determine whether or not the process is really infinite in the sense of satisfiability?
"We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about 'and'."- sir Arthur Eddington.
You cannot define an absolutly abstract concept like infinity using the cold hard mechanisms of mathematics. However you can use it to explain what infinity isn't for eternity.
I liked your video btw! Id assume you're a lecturer in your spare time? :p
you have me utterly lost, haha, im a really an utter novice with this stuff, unfortunatley im one of those novices that feels the need to blurt his thoughts on things. I shall take a look at those suggestions though, who knows i might learn something.
ok utter stab in the dark here, but arent measurements also infinite? therefor everything in existence is in fact infinite due to that fact that everything in existence can be measured and broken down into smaller properties, i.e a measurement refined or a particle into atoms an atom into a quasar, a quasar into who knows. So theoretically nothing can be finite and everything is in fact infinite therefor it cannot be defined or explained as it doesnt really exist without a finite comparison?
Even if it's is a continuum, trying to pull off a Banach-Tarski still wouldn't work in the real world. You can't apply the axiom of choice to real life, making it hard to chop things into non-measurable pieces.
How do you know what you can or cannot do in a "real world" that manifests a real continuum? The axiom of choice would either be part of that real world or it wouldn't.
That's the point behind my comment -- we live in a very restricted real world in which those things can't happen.
so do you believe that space (the absence of matter) is infinite considering it is technically nothing, and you can't really have an end nor a beginning to nothing?
Space is technically not nothing -- it has structure. It just happens to have no content. Whether or not real space (as in the one we live in) is actually finite or not depends on its geometry, which I am not an expert on (I.e., go ask an astrophysicist.) I don't think its relevant since its locally finite (i.e., the stuff in it exists only to some limits.)
No. Zero is a number, infinity is not. *Empty* is to numbers as atheism is to religion.
There are an infinite quantity of possible numbers, just as there are infinite *possible* religions. We only see a realized finite set of religions just as the human race has only encountered a finite set of specific individual numbers.
Think of infinity as the boundary, not as a participant.
0 is a number and it definitely exists in the same sense and class that 1, 2 or 3 exists. Infinity is not a number at all, but a description for sets of numbers.
Think of it this way: Actual instances and realizations (concrete things) are finite. But the scope of possibilities for things that we can think of abstractly in our mind is infinite (that's not strictly true, but can be thought of in an ideal sense.)
Do you (websnarf) believe that an infinite time can exist before now?
I want to see how you apply your knowledge on infinity on such a philosophical question - bearing in mind that time flows in one direction only. Many Thanks. Great Video.
I see nothing in the science of physics that suggests that there has not been or could not be an infinite amount of time before now.
As I am not a comsmologist, my understanding of this is not especially deeply justified. But the philosophers position is far lest credible.
Nevertheless, if a race car a track has not reverse gear, does that mean the race track does not have an infinite path that it traces out backwards? A direction does not presuppose a start.
Ignoring the Big Bang and time relativity and such: The universe being eternally old would mean exactly that "given any time T in the past, the universe existed at time T." The worry seems to be that something took infinitely long to get to NOW. This isn't a real problem, I don't think, as the time difference between any prior event, and NOW, is finite. I don't find this inherently philosophically troubling (though the actual evidence says it's false).
What i like about yr video is how u explain that numbers and mathematics is basically just a human term to atleast try and explain infinity and time. Without humans infinity would only be what it was no questions asked , we give things words to try and explain certain media and give that thing purpose. Think about this, eternity and infinity are finite words given by finite matter created by the infinite, but if the infinite has found time to do this then has it really been infinite?
That's an interesting perspective, but not really what I was driving at. By today's standards infinity is a precise definition and it is readily understood by finite people. Much of mathematics is, essentially, the study of infinity.
Concepts like eternity and the overly mysterious kind of perspective people have for concepts like infinity ignore or are basically in absence of the modern understanding. Mysteriousness is for mysteries; infinity is only slightly mysterious.
but because we live in a finite world, it is impossible to say infinity even exists. every time you explain what infinity is, you become wrong and discover finite
infinity might as well not exist because it doesn't exist for us
And how useful is "what you think" going to be if you get no buy in, and future generations forget whatever it is you thought? The explanation I have given here is one that is aligned with the core definitions used in modern mathematics. It works and its the one that will be there for as long as humans care to know about mathematics.
It takes more than that. Its an analytical topic. Fortunately, its not that difficult; if you can understand my video, you can understand the basics of infinity.
So how can you say the context is finite when it contains some properties which are finite and some which are infinite? I do not see how the fact that the longest path to travel in the circle is infinite shows that infinity is a property of this road, rather it just seems like we're applying something ourselves (the notion of travelling on this road) to introduce infinity to this finite context.
The point of the infinite paths on a finite track example is to respond to those who think infinity is unfathomable; as if there were no way for finite beings to conceive of it.
Nice video. I didn't quite understand how the example at the end shows infinity being present in a finite context. What do you mean by context? As there is no restriction on the distance you can travel, it is infinite in that context. However it may be finite in the context of say that you cant travel off the road (limiting the area of travel), the radius of the circle etc.
Infinity cannot be defined. To define something is to set limits on it which is why it is called deFINing it. An infinite set of discrite things is a potential or relative infinite only. Calling the Christian concept meaningless supports the Christian case actually.
Red can be defined and excludes anything contrary to redness. Colors are qualities inhering in substances and there are only a finite number of substances as there are only a finite number of red things as experience shows.
Calling the Christian concept meaningless supports our case as it shows that a non-Christian worldview cannot cope with the Infinite.
So if someone else decides to count all the shapes that can be made from those atoms, and thus discover a count higher than your estimation of infinite, then where does that leave your opinion?
first off an atom is not the smallest unit of existence, saying that you say that electrons, protons, and neutrons, don't exist. but even if you say these are the smallest unit your still wrong as quarks are smaller still, and even if you some how manage to count all the quarks existence there are still particals that are different from quarks and atoms all together because there are theoretical partials like gravitons and photons
That doesn't really make any sense at all. What if there is a finite amount of matter in existence? Why does one's will to count correlate with finity?
That's not quite correct. If you consider a/x, and let x approach 0 from the right then the limit is +infinity. However, if you let x approach 0 from the left, then the limit is -infinity. Therefore, the limit as x approaches 0 of a/x does not exist. So, we can't really define a/0 to be either of +infinity or -infinity. This is the real reason for why a/0 is said to be undefined.
That's a mathematical colloquialism. It can make sense in a projective space but then you aren't technically using "numbers". Technically, a/0 is just undefined.
Even in calculus you write lim{x->+inf} a/x = +inf which you can see is including plenty of other mathematical machinery. Consider x->-inf, for example. The "=inf" part only makes sense when you write things like "lim" in which case we are not bounding ourselves just to numbers.
Uhm i think it was my brother who used my account by mistake if u want to talk to him his username is notjames1 sorry if i caused you inconvienience(if that is how you spell it):D
I think that ppl maby didn't have so much trouble with what infinity was, but why its infinit-ness had to be prooven. It might come from the widest-known method(dont have any idea if thats the right word) for finding primes: Take 2 as the first prime cross off every 2nd number, take 3 as the next prime cross off every 3rd and so on.
And how does mathematics define the Infinite One? Which number is that "1"? Can it represent infinity if that 1 has no qualitative or quantitative limit or dimension? To close oneself in a field (be it maths, philosophy or theology) is silly and quite limited, and that's the basic mistake which takes out the authority from any of the "specialists" to prove anything such as the nature of atheism or religion, for example.
The mathematical definition of infinite is "not finite". A very detailed complex of necessary results follows from that definition alone, which this video just gives you a basic taste of.
It means that whatever other point of view you have on infinity must either be consistent with these results or choose a different definition or else be inconsistent/irrational. This has nothing to do with being a specialist or closed in one field.
I like the notion that infinity is an adjective and not a noun. but I look at infinity as a verb and not a noun at all. that infinity is a prcess of continuousness. i think man (mathematicians) have it confused with the finite. i look at infinity as the process of always going one step further.
You are probably correct with your logic. I mean maybe man just can't see the forest through the trees when it comes to non-finite things. Being that we are creatures encapsulated in a finite amount of time and everything in our perspective is based off of observation, hence we are unable to observe infinity so we can not appreciate or place it's value.
I don't know if anyone has posted this yet, but there is another definition of an infinite set. Any set which contains a proper subset of the same cardinality is an infinite set.
Cardinality is the measure of the number of elements in a set. If a set is finite with n elements, we say that the cardinality of the set is n. If no such n exists for a set S, and the set is not empty, then we can find an injection f:N --> S. Since we can construct a bijection g:N\{1} --> N, we can construct a map k:S\{f(1)} --> S that gives a bijection induced by g(f). This way this def. agrees with the one you used but isn't a definition by negation.
Sorry, this comment wasn't really aimed at you as I agreed with most everything you said in your video, I just noticed a lot of comments below of people saying they didn't like the 'not' definition so I was giving an alternative. A lot of people say infinity may not be used as a noun on here also, which isn't true, as in the extended reals, surreals and projective spaces.
here another clumsy analogy for you: if you watch a film over and over again is the film itself infinite? If you drive on the same race track over and over again is the track itself infinite?
it all works only if you look at it as an abstract concept. i guess 'path' is probably defined in such (an abstract) way in mathematics. and that's what i was trying to say before. i doubt that infinity exists. it just a word for the fact that we have reached our borders of knowledge, reception or whatever. another word for unimaginable, like we say (outer or maybe even inner) space is infinite. is it? how should we know?
I didn't mean infinity is not an adjective. Infinity can't be a number because it doesn't stop to be one. I meant the definition of infinity from set theory produces paradoxes.One of my favorite paradoxes is Hilbert's Hotel. Try and look it up.
Your questions are interesting to me. They are the starting points to understanding the properties of infinity. For instance that 'race track' thing touches on the distinction between potential and actual infinity. Try reading about George Cantor or Kurt Godel. They were both major mathematicians who went crazy working on infinity.
btw. there should be opportunites to see actual infinity if such a thing exists. first one should be you standing between mirrors but probably this fails because you're in the way of your own image or the angle you need can't be reached. i don't know. second one would be to film yourself live on tv. holding the camera at the screen (which shows you filming yourself, with a camera filming yourself and so on). a well known glitch or bug in many computergames (overlapping objects) also.
i guess what you can see there is the typical pattern of fractals forming a new pattern out of existing parts and details of another structure (kaleidoscope). third maybe the feedback of a microphone. all this fails at some point due to a certain amount of imperfection. ...now i am spamming the board i guess.
since you don't have black hair you can't be me, so everything that's not me is you. that doesn't tell me anything about you. your hair could be blonde, brown whatever. definitions like that don't describe the object they just exclude certain details being part of it.
"not" definitions are actually a valid form of logical arguments called disjunctive syllogisms. Your analogy is an example of a faulty analogy because it distorts the formal structure of what your arguing against. Also, in a clumsy way, your analogy kind of supports Websnarf. "...your hair could be blonde, brown, whatever." Yes, that's what infinity is.
if you look at it this way it could be anything. just because it is unknown to us doesn't mean that it can't be measured or described in better manner than by this "trick". you might as well just say i know crap about it. so this video actually describes what infinity NOT is, not what it is, like the title suggests. hey great, i might add something here: infinity is also NOT a toaster, NOT a car, NOT a tuna salad. so what IS infinity?
You clearly did not watch the video all the way through or else you did not understand it. Infinity is an *adjective*. So its to be compared to worsd like warm, red, and smelly, not toaster, car or salad.
you are right. i didn't thought that it can be used as an adjective too (in the sense of infinite quantity). does that change my point or weaken my argument if we go for the words you chose?
I gain a self-consistent definition which makes mathematics a viable and productive endeavor. Anything less an I become ignorant of any kind of accurate mathematical reasoning.
Llazyoli, I was saying you were illogical. There's a difference between "Infinity is a set that is not finite" and "I am a person that is not you." The former's a disjunctive syllogism and the latter is affirming the consequent. But again you might have touched on something, albeit clumsily. The paradox of set theory is, the set that contains all sets. Websnarf didn't talk about that yet.
|Z| = |N| = |Q|. If you don't understand this, then you have to accept that you don't understand infinity, and should probably not be coming to any conclusions about connections that thinking about it makes for you.
Mathematicians disagree, stoic. The cardinality (size) of the integers is the same as the cardinality of the naturals which is the same as the size of the rationals. It's counter-intuitive, to be sure. Have you looked up Cantor's method of diagonalization?
would it be possible to *see* infinity? an example would be pointing a camera at a screen on which its own images are being displayed. would that be an actual observation of infinity? but then we can only observe finite objects, can't we?
more closer rather would be saying it's infinity in *action*
Well, infinity is an abstract concept. You can't really see infinity unless you are looking at things abstractly. So on the racetrack you can try to *see* the longest path that you can travel. But you are still restricted by your visual input and mental visualization abilities by their inherent finiteness. "Seeing infinity" has to be something that happens totally inside your mind.
another problem is that you would have to wait an infinate amount of time before looking. so basically, no. you cant se infinity, but looking into space is kinda close :)
although you could use a camera that does not absorb other wavelengths of electromagnetic radiation and look at these, this is stretching the definition of truly 'seeing'
in order to 'see' infinity in this situation would be to have the photons going exactly adjacent to the two mirrors and have the mirrors exactly parallel (this is hard enough in itself). this would mean that to view infinity the position of your camera would need to be in the path of the photons. you would therefore require an invisible camera so that your camera did not inhibit these photons, unfortunatly this would mean that your camera would not be able to generate an image.
I'm not sure what one means by "finite context". But since you're trying to address a typical misunderstanding, perhaps it is necessary to be a little vague. A better example might be a straight line AB:
"What is the maximum time a car take to drive from A to B?". Obviously 't_max' is unbounded (no circles required).
Another thing (more important to your post) is this notion of adjective vs noun. While it is true that "infinite" is an adjective, the word "infinity" is a legal noun. I think you are saying that there is no such thing as "infinity" only because it is a noun and that mathematical objects (sets let's say), having only "properties", even though they are nouns in themselves, can never actually be "the object called infiniy" since "infinity" can not be precisely defined. Is that your idea here?
Inifinity as a noun has no meaning in mathematics. But philosophers or common-folk can't let go of it. There's nothing I can do about that. But that doesn't make the word meaningful. If mathematics doesn't endorse the noun meaning, then you are stuck trying to define a mathematical idea in a non-mathematical way. Essentially that means the word as a noun has no rigor and is ultimately vacuous.
Well I've done quite a bit of math in my time and I'm not certain that "infinity" as an object (perhaps of varying powers) cannot be rigorously defined. It seems, as certain as anything else, that infinitesimals (which are essentially "infinities") can be regarded as solid mathematical numbers however obeying different algebraic rules. Archimedes axoim is *still* an axiom... (to his credit).
And... (sorry to bore you :)) "can not be precisely defined" is supposedly illustrated by the definition of something being NOT some other thing. That is, I could define non-dogs as being "NOT dogs" but I cannot say that since cats are non-dogs that all non-dogs are necessarily cats (cats being analogous to "infinity").
websnarf, PLEASE do your promised vid on Zeno's paradoxes. Specifically the arrow and the target. Because every solution that I've found on the web is not only beyond my skill set to judge, but not universally accepted. Or have I missed THE solution? And please explain at what scale common sense breaks down about having to go halfway before going the whole way.
Problem: the race car does not exist "within" the race track, it is over and above. Thus you have not contained infinite within finite. If you bound the infinite it is no longer infinite, your explanation always leaves an unbounded set for the infinite to exist. You have confused channeling with bounding.
Do you have one shred of support for this outlandish claim? Can you explain to me what an atheist church, priest, bible, dogma, prayer or commandment is?
That's nice that you disagree with it, but you're wrong (belief that there is no god is called "strong atheism" which is a subset of ordinary atheism). Are there any other straight forward facts, like 2+2=4 for example, that you disagree with that you care to share with us?
To be fair, that's not a straight forward fact, is it? What you call "strong atheism", many other people would call "atheism", as well "weak atheism" is also called "agnosticism" by some. Ah, the beauty of language!
The kind of atheism you talk about, which is a firm conviction in the fact that there is no god, I think you'll find almost no-one who call themself an atheist in this category. There will be some who have an irrational reason for being atheist, such as a desire to not go to hell, but most I've met have actually thought about it and are the kind of people who don't experience religious faith-like certainty at all.
That's what *EVERYONE* who understands atheism means by atheism. Look up weak and strong atheism on wikipedia. The semantic difference is an important one. Strong atheism is just, logically, a narrower definition, that falls under general atheism.
Ohhhhhh! look at that! can't make an argument so you attack the person. Saying "your wrong" is not proof, nice try. Strong atheism is not a sub-set, it is a set. More over a in Greek means No, theism is believe in God, thus a theism is the no god belief. It is a definite declaration such as, you have no hat. It is a positive statement of the impossibly of God.
We are discussing the definition, and since I and many other atheists self-identify according to this definition, then that's just what it is. If ellhow wants to make up new definitions, then he cannot use them in exposition where I am part of the audience, or else he gets called out as being wrong. The rest of your post above is unintelligible, so I can't address it.
I watched this video looking for things to argue with and found nothing. You really did that well. I guess the real problem I had with infinity was when people talked about it as though it were a noun. I never realized it was an adjective. Have you done/Are you thinking about doing one on Cantor's idea of the transfinite?
umm.. i'm not good at all at maths but what i've heard about Infinity is that once u get to a high enough number, it starts all over again, back to unit 1, or something like that. jsut what i've heard.
Galileo concluded that the ideas of less, equal, and greater applied only to finite sets, and did not make sense when applied to infinite sets. In the nineteenth century, Cantor, using the same methods, showed that while Galileo's result was correct as applied to the whole numbers and even the rational numbers, the general conclusion did not follow: some infinite sets are larger than others, in that they cannot be put into one-to-one correspondence.
infinity is not a number yet one infinity can be greater than another. like the set of numbers between 1 and 2 is greater than the set of all natural numbers
Our finite minds cannot comprehend the infinite. We have a vague concept of it that we can wonder about. Even our wonderful imagination, and logic is limited. There are things that we will never figure out, no matter what we try to do to make it fit in our limited logical minds.
Well dont know if i agree with the atheism/religion analogy but it was a good video. It didnt anwser my question if an infinity can exist other than in theory but good explanation on how math thinks of it.
Whether it can actually exist at all (i.e., is time infinite?) is not something I am qualified to definitively answer. Quantum theory seems to suggest that it does not exist for objects or space. However, the value of the abstract cannot be underestimated; its the framework in which we build things that we don't know will work until we actually make them.
I was under the impression that .9999 never equals 1; does your "essentially yes" just describe the behavior of, for instance, .9999 approaching 1? But would there not still be an infinitesimal difference between .999... and 1, rendering it not equal?
1-.99=.01, 1-.9999=.0001, etc... as .9999 approaches 1, it's still bounded by a difference that approaches an infinitesimally small number (1-.99999999=.00000001), thus this difference, however small, is still a deviation from the actual whole of 1; by this example, I would say that .9999 does not equal 1.
I don't follow your reasoning. Can you please pick a specific number *greater* than 0 but less than this infinitesimal, so I can have some idea of why you think this number is a positive number, but not zero?
The concept infinity has no impact on humans, life or existence as a wholefor that matter. Everything that we believe to be real begins and ends in one way or another. Your race track model is flawed. Not only is the track finite you forget to factor in the veihicle. A car cannot mechanically operate indefinitly. Then add the fuel limitation. The only way to establish an infinity construct is to use an infinite constant as an element thus you're using the word to define itself.
Saying infinity has no impact on humans is the same as saying that abstract ideas don't have impact on humans. Ask yourself this, without the abstract notion of infinity, how do the car engineers know that by improving the car's engine, fuel efficiency, etc that the car can even go any further than it did before? How do they know that there is even any more path to drive on?
The have empirical proof. The path is not infinite the path is point A to point b. Not to mention the main factors that inhibit eternal automobiles are friction and faith in internal combustion as a necessity for propulsion.imo
"The concept infinity has no impact ..." - That's like saying that Calculus has no impact on humans. The concept of infinity is fundamental to Calculus and Calculus is fundamental to practically every technical or scientific discipline we have.
You do have the basic idea. Its not calculable by the basic means of counting or simply directly measuring them -- that's what makes them infinite. I will show in a later lecture that you can *classify* infinities however, and thus be able to put some tractability to them. Some of the comments posted here heavily allude to what I will be talking about.
My point is that, while I agree with what you've said about infinity (and thank you), I don't think that this definition is complete. Infinity cannot be just a property of sets or of numbers or whatever, but the consequence of a generating rule. It says that a set defined by at least one generating rule is an infinite set. Long story short: This puts mathematical induction on the par with reasoning by induction, doesn't it?
catincaf 3 months ago
But "property" is a noun, and we understand and use it as such. Objects have properties, which, among other things, are adjectives which describe them. When we speak of redness, we can understand the property as that which applies to all objects that are red, yet we can subtract (or abstract) the objects until we have "redness". "Infinity", if it is a property, could be made into a noun and, as any noun, it has properties too.
catincaf 3 months ago
infinity is opiset of zero
same every thing opiset of nothing
mosa0564778798 4 months ago
i feel like you are saying infinity is actually very limited in your opinion !?
bobbutnot 5 months ago
@bobbutnot I present no opinion in this video. I am telling you what it is. Infinity is a singular concept and is not limited except by its conceptual confines.
websnarf 5 months ago
infinity in ways is just an idea any number that can be added subtracted and well ANY KINDA NUMBER so if any number is infinity than 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 etc are all numbers of infinity
TotalGameMaster 1 year ago
Aren't parts of the universe that are far enough away receding from us faster than the speed of light due to the expansion of the universe itself?
ananiasacts 1 year ago
@ananiasacts : Yes that is correct. Though I did not know that at the time I made this video. If I said otherwise, it was a mistake out of ignorance.
websnarf 1 year ago
@websnarf Your comment is a good example of infinity in reality :)
DJxSGGxNeo 3 months ago
the simplest proof that there is neither a largest nor smallest number, and therefore prove the existence of infinity and negative infinity, is as follows.
Define a largest number, N, and a smallest number, n.
N+1 is obviously greater than N, showing that there is no greatest number. This proves the existence of infinity.
n-1 is obviously less than n, showing that there is no smallest number. This proves the existence of negative infinity.
mathgeek11 1 year ago
@mathgeek11 I really love this comment, even though it's ancient...lol
mrice102888 2 months ago
real projective plane yp
affablegiraffable 1 year ago
infinitys like a dog chasing after its tail. Never gona catch it and it just gives you a headache to try.
sparkycorry 1 year ago
On the subject of cardinality, I know that the set of rational numbers has the same cardinality as the set of natural numbers, and that the set of irrational numbers has a different cardinality because it is not 'countable'.
Is there a system for measuring different cardinalities?
chaOsMastaGuru 1 year ago
@chaOsMastaGuru: I don't think there is a mechanistic way of measuring them. I was meaning to look into this to be sure, but have been busy with other things.
Whether or not there is a set with a cardinality between countable and the reals is apparently either an open question or an independent axiom (its one or the other, and this is known, I just haven't done the research to know which it is.)
websnarf 1 year ago
This defies my own intuition for the following reason:
If A is the smallest infinity (countable) and P(x) is the power set of any set x, then *I* imagined that A, P(A), P(P(A)), P(P(P(A))), ... would be a "tightest possible" enumeration of infinities. However the comment above makes it clear that this is probably not right. I.e., the set of reals, C, is probably such that: C < P(A).
If you pursue this and find an answer, I would appreciate being pointed in the right direction. :)
websnarf 1 year ago
0:55 I don't believe the answer is nothing! I think it's Usain Bolt! haha
bendavis575 1 year ago
Is there really such thing as a negative infinity, because it would seem like by now is would be nothing because it would take forever to grow small and find something that is infinitely small.
mqg96 1 year ago
'There is nothing stopping you at any point' 16:04...
Until you run out of gas
But thanks for the lecture, very informative
DinoPedia 2 years ago
I don't get it... If an infinite set can't have a larger and a smaller number at the same time, then how about a set that contains real numbers let's say from 1 to 2?
phmx 2 years ago
An infinite set of *integers* cannot have a largest and smallest element.
websnarf 2 years ago
How can there be "larger" infinites?
cool2bwichu 2 years ago
Look up the concept of a "power set" and "bijections". The power set of N={1,2,3,...} cannot be put into a bijection with N. In this sense we differentiate the *kinds* of infinity, and we say that the cardinality of the power set of N is larger than that of N.
websnarf 2 years ago
what about multiples of 2 exponentialy?
angie4josh 2 years ago
There are an infinite set of such numbers.
websnarf 2 years ago
thats not what i ment.
think of it like this, what do you get when goggleplex is factored? Numbers will then meen nothing at all. "Infinity" may as well equal zero.
angie4josh 2 years ago
Google-plex factored is 2 to the power google times 5 to the power of google. That has as much meaning as any other factorization. Making infinity equal to zero doesn't make sense even in projective spaces.
websnarf 2 years ago
nice.
jojojojo123098 2 years ago
just get the largest number and add 1 therefore its impossible
samurai4321cheesey 2 years ago
Interesting stuff!
Vektruscen 2 years ago
Thank you for taking your time to educate people, we appreciate the video. I could hear it just fine but did have to turn the volume up a bit; such might be a problem for others. Your explanations were clear and easy to follow, and interesting.
semasiologistics 2 years ago
talk louder dude... it's really hard to hear you...
4ynep 2 years ago
so... Infinity is an adjective, not a noun unless in concept.?
pxgblftn 2 years ago
Infinite can apply to an abstract set in a sensible and well defined way. When philosophers or "spiritual" people try to use the word it becomes meaningless. It leads people to say nonsensical things like "god is infinite" without any realization that there are *MANY* kinds of infinite (some "larger" than ohers).
websnarf 2 years ago
How does Turing's halting problem relate to this? Do infinite processes count as infinite if it is impossible to determine whether or not the process is really infinite in the sense of satisfiability?
Ormaaj 3 years ago
"We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about 'and'."- sir Arthur Eddington.
You cannot define an absolutly abstract concept like infinity using the cold hard mechanisms of mathematics. However you can use it to explain what infinity isn't for eternity.
I liked your video btw! Id assume you're a lecturer in your spare time? :p
k0sha 3 years ago
but infinity only exists in mathematics....
spike0804 2 years ago
planks constant? banach-tarski paradox?
:S
you have me utterly lost, haha, im a really an utter novice with this stuff, unfortunatley im one of those novices that feels the need to blurt his thoughts on things. I shall take a look at those suggestions though, who knows i might learn something.
kangaroobin 3 years ago
ok utter stab in the dark here, but arent measurements also infinite? therefor everything in existence is in fact infinite due to that fact that everything in existence can be measured and broken down into smaller properties, i.e a measurement refined or a particle into atoms an atom into a quasar, a quasar into who knows. So theoretically nothing can be finite and everything is in fact infinite therefor it cannot be defined or explained as it doesnt really exist without a finite comparison?
kangaroobin 3 years ago
Measurement is not infinite. That's the whole point of plank's constant. The real world is quantized in at least the spacial dimensions.
There is actually a real problem with any real universe being made up of a continuum. Look up the Banach-Tarski paradox for a real head spinner.
websnarf 3 years ago
Even if it's is a continuum, trying to pull off a Banach-Tarski still wouldn't work in the real world. You can't apply the axiom of choice to real life, making it hard to chop things into non-measurable pieces.
abyaly 3 years ago
How do you know what you can or cannot do in a "real world" that manifests a real continuum? The axiom of choice would either be part of that real world or it wouldn't.
That's the point behind my comment -- we live in a very restricted real world in which those things can't happen.
websnarf 3 years ago
It doesn't follow from that that the spacial dimensions can't be homeomorphic to R. By itself, this assumption doesn't cause the paradox.
If we supposed the axiom of choice could be used to cut up objects in real life, we aren't necessarily able to preform the needed (wacky) rotation.
And the object we chop up in this way has to be a continuum as well. (Correct me if I'm wrong on this one)
We need all of those to happen to pull it off in the real world.
abyaly 3 years ago
so do you believe that space (the absence of matter) is infinite considering it is technically nothing, and you can't really have an end nor a beginning to nothing?
siik138 3 years ago
Space is technically not nothing -- it has structure. It just happens to have no content. Whether or not real space (as in the one we live in) is actually finite or not depends on its geometry, which I am not an expert on (I.e., go ask an astrophysicist.) I don't think its relevant since its locally finite (i.e., the stuff in it exists only to some limits.)
websnarf 3 years ago
if space is nothing how can it have structure?
ThePlatinumPengwin 3 years ago
I said space is *not* nothing. The fact that it has structure (dimensions, coordinates/orientation) is the evidence I provide for this.
websnarf 2 years ago
Would this be more accurate?
Zero is to numbers as
atheism is to religion.
The reason I ask is because an atheist does not believe in all religions, but no religion.
Religion also doesn't fit.
Numbers are infinite, and there is a finite number of religions.
You can have zero dollars, and you can have a dollar. There is not an infinite amount of dollars. So maybe it could be
Nothing is to something as
atheism is to religion.
raymond18 3 years ago
No. Zero is a number, infinity is not. *Empty* is to numbers as atheism is to religion.
There are an infinite quantity of possible numbers, just as there are infinite *possible* religions. We only see a realized finite set of religions just as the human race has only encountered a finite set of specific individual numbers.
Think of infinity as the boundary, not as a participant.
websnarf 3 years ago
benderboyscott said
"infinity is zero
just as zero makes things into nothing
infinity makes things into everything
we live in a finite world. its impossible to say infinity exists. every time you explain what infinity is, you become wrong and discover finite
infinity might as well not exist because it doesn't exist for us"
zero doesn't exist for us either dude, otherwise nothing would exist. But you do understand the concept of zero.
infinity is just zero the other way.
its zero's opposite.
raymond18 3 years ago
0 is a number and it definitely exists in the same sense and class that 1, 2 or 3 exists. Infinity is not a number at all, but a description for sets of numbers.
Think of it this way: Actual instances and realizations (concrete things) are finite. But the scope of possibilities for things that we can think of abstractly in our mind is infinite (that's not strictly true, but can be thought of in an ideal sense.)
websnarf 3 years ago
Do you (websnarf) believe that an infinite time can exist before now?
I want to see how you apply your knowledge on infinity on such a philosophical question - bearing in mind that time flows in one direction only. Many Thanks. Great Video.
Catz007 3 years ago
I see nothing in the science of physics that suggests that there has not been or could not be an infinite amount of time before now.
As I am not a comsmologist, my understanding of this is not especially deeply justified. But the philosophers position is far lest credible.
Nevertheless, if a race car a track has not reverse gear, does that mean the race track does not have an infinite path that it traces out backwards? A direction does not presuppose a start.
websnarf 3 years ago
Ignoring the Big Bang and time relativity and such: The universe being eternally old would mean exactly that "given any time T in the past, the universe existed at time T." The worry seems to be that something took infinitely long to get to NOW. This isn't a real problem, I don't think, as the time difference between any prior event, and NOW, is finite. I don't find this inherently philosophically troubling (though the actual evidence says it's false).
VeryEvilPettingZoo 3 years ago
What i like about yr video is how u explain that numbers and mathematics is basically just a human term to atleast try and explain infinity and time. Without humans infinity would only be what it was no questions asked , we give things words to try and explain certain media and give that thing purpose. Think about this, eternity and infinity are finite words given by finite matter created by the infinite, but if the infinite has found time to do this then has it really been infinite?
humbug2008 3 years ago
That's an interesting perspective, but not really what I was driving at. By today's standards infinity is a precise definition and it is readily understood by finite people. Much of mathematics is, essentially, the study of infinity.
Concepts like eternity and the overly mysterious kind of perspective people have for concepts like infinity ignore or are basically in absence of the modern understanding. Mysteriousness is for mysteries; infinity is only slightly mysterious.
websnarf 3 years ago
simple way to say it is that it has no such ending!
fligypoo 3 years ago
im going with what i think
infinity is zero
just as zero makes things into nothing
infinity makes things into everything
but because we live in a finite world, it is impossible to say infinity even exists. every time you explain what infinity is, you become wrong and discover finite
infinity might as well not exist because it doesn't exist for us
benderboyscott 3 years ago
And how useful is "what you think" going to be if you get no buy in, and future generations forget whatever it is you thought? The explanation I have given here is one that is aligned with the core definitions used in modern mathematics. It works and its the one that will be there for as long as humans care to know about mathematics.
websnarf 3 years ago
Infinity is what someone sees when he opens his eyes.
marendoo 3 years ago
It takes more than that. Its an analytical topic. Fortunately, its not that difficult; if you can understand my video, you can understand the basics of infinity.
websnarf 3 years ago
So how can you say the context is finite when it contains some properties which are finite and some which are infinite? I do not see how the fact that the longest path to travel in the circle is infinite shows that infinity is a property of this road, rather it just seems like we're applying something ourselves (the notion of travelling on this road) to introduce infinity to this finite context.
KikiManini 3 years ago
The point of the infinite paths on a finite track example is to respond to those who think infinity is unfathomable; as if there were no way for finite beings to conceive of it.
websnarf 3 years ago
Nice video. I didn't quite understand how the example at the end shows infinity being present in a finite context. What do you mean by context? As there is no restriction on the distance you can travel, it is infinite in that context. However it may be finite in the context of say that you cant travel off the road (limiting the area of travel), the radius of the circle etc.
KikiManini 3 years ago
my hypothesis is that infinity is an endless number or amount of space within the universe
Jmf619 3 years ago
Infinity cannot be defined. To define something is to set limits on it which is why it is called deFINing it. An infinite set of discrite things is a potential or relative infinite only. Calling the Christian concept meaningless supports the Christian case actually.
patrissimo 3 years ago
So does that mean a color like "RED" cannot be defined because there is no limit on what sorts of things can be red contained in its definition?
Infinity is a property (like RED), and its defined as "not finite".
How can calling a Xian concept meaningless possibly support anything? It supports what I think of Xianity and nothing else.
websnarf 3 years ago
Red can be defined and excludes anything contrary to redness. Colors are qualities inhering in substances and there are only a finite number of substances as there are only a finite number of red things as experience shows.
Calling the Christian concept meaningless supports our case as it shows that a non-Christian worldview cannot cope with the Infinite.
tlingren 3 years ago
Experience cannot show something to be finite or infinite -- because you cannot experience all of the future until it has all happened.
The "Xian concept" of infinity is meaningless in *ANY* world view because it has no specific meaning that is applicable in a universal way.
How can identifying something as insular unaccountable double talk be a support for your case?
websnarf 3 years ago
infinity is the count of every atom(smallest unit of existence) once u have no reason to count anything else u have discovered infinite. My opinion
RocBre011 3 years ago
So if someone else decides to count all the shapes that can be made from those atoms, and thus discover a count higher than your estimation of infinite, then where does that leave your opinion?
websnarf 3 years ago
Good point.
patrissimo 3 years ago
first off an atom is not the smallest unit of existence, saying that you say that electrons, protons, and neutrons, don't exist. but even if you say these are the smallest unit your still wrong as quarks are smaller still, and even if you some how manage to count all the quarks existence there are still particals that are different from quarks and atoms all together because there are theoretical partials like gravitons and photons
romerboy55 3 years ago 2
That doesn't really make any sense at all. What if there is a finite amount of matter in existence? Why does one's will to count correlate with finity?
dhchemistry 3 years ago
Positive infinity is a/0 where 'a' is any finite, positive real valued number, and 'a' does not equal 0. Viceversa for negative infinity
crazymaria12 4 years ago
That's not quite correct. If you consider a/x, and let x approach 0 from the right then the limit is +infinity. However, if you let x approach 0 from the left, then the limit is -infinity. Therefore, the limit as x approaches 0 of a/x does not exist. So, we can't really define a/0 to be either of +infinity or -infinity. This is the real reason for why a/0 is said to be undefined.
MrLazy27 4 years ago
That's a mathematical colloquialism. It can make sense in a projective space but then you aren't technically using "numbers". Technically, a/0 is just undefined.
Even in calculus you write lim{x->+inf} a/x = +inf which you can see is including plenty of other mathematical machinery. Consider x->-inf, for example. The "=inf" part only makes sense when you write things like "lim" in which case we are not bounding ourselves just to numbers.
websnarf 3 years ago
Uhm i think it was my brother who used my account by mistake if u want to talk to him his username is notjames1 sorry if i caused you inconvienience(if that is how you spell it):D
crazymaria12 3 years ago
I think that ppl maby didn't have so much trouble with what infinity was, but why its infinit-ness had to be prooven. It might come from the widest-known method(dont have any idea if thats the right word) for finding primes: Take 2 as the first prime cross off every 2nd number, take 3 as the next prime cross off every 3rd and so on.
LddStyx 4 years ago
this is the worst explanation of anything mathematical ive ever had
nicknack175 4 years ago
And how does mathematics define the Infinite One? Which number is that "1"? Can it represent infinity if that 1 has no qualitative or quantitative limit or dimension? To close oneself in a field (be it maths, philosophy or theology) is silly and quite limited, and that's the basic mistake which takes out the authority from any of the "specialists" to prove anything such as the nature of atheism or religion, for example.
iyours 4 years ago
The mathematical definition of infinite is "not finite". A very detailed complex of necessary results follows from that definition alone, which this video just gives you a basic taste of.
It means that whatever other point of view you have on infinity must either be consistent with these results or choose a different definition or else be inconsistent/irrational. This has nothing to do with being a specialist or closed in one field.
websnarf 4 years ago
capitol wow.
orangeblueandlavenda 4 years ago
I like the notion that infinity is an adjective and not a noun. but I look at infinity as a verb and not a noun at all. that infinity is a prcess of continuousness. i think man (mathematicians) have it confused with the finite. i look at infinity as the process of always going one step further.
cobra5002 4 years ago
You are probably correct with your logic. I mean maybe man just can't see the forest through the trees when it comes to non-finite things. Being that we are creatures encapsulated in a finite amount of time and everything in our perspective is based off of observation, hence we are unable to observe infinity so we can not appreciate or place it's value.
matthewshurt 4 years ago
I don't know if anyone has posted this yet, but there is another definition of an infinite set. Any set which contains a proper subset of the same cardinality is an infinite set.
mbk181 4 years ago
Ok, but that requires that you define cardinality.
websnarf 4 years ago
Cardinality is the measure of the number of elements in a set. If a set is finite with n elements, we say that the cardinality of the set is n. If no such n exists for a set S, and the set is not empty, then we can find an injection f:N --> S. Since we can construct a bijection g:N\{1} --> N, we can construct a map k:S\{f(1)} --> S that gives a bijection induced by g(f). This way this def. agrees with the one you used but isn't a definition by negation.
mbk181 4 years ago
I know what it is, but the point of my lecture is to aim it at regular non-math heads. There is no reason to avoid definitions by negation.
websnarf 4 years ago
Sorry, this comment wasn't really aimed at you as I agreed with most everything you said in your video, I just noticed a lot of comments below of people saying they didn't like the 'not' definition so I was giving an alternative. A lot of people say infinity may not be used as a noun on here also, which isn't true, as in the extended reals, surreals and projective spaces.
mbk181 4 years ago
It seems like it is more of an adjective, anyway.
MrLazy27 4 years ago
here another clumsy analogy for you: if you watch a film over and over again is the film itself infinite? If you drive on the same race track over and over again is the track itself infinite?
llazyoli 4 years ago
it all works only if you look at it as an abstract concept. i guess 'path' is probably defined in such (an abstract) way in mathematics. and that's what i was trying to say before. i doubt that infinity exists. it just a word for the fact that we have reached our borders of knowledge, reception or whatever. another word for unimaginable, like we say (outer or maybe even inner) space is infinite. is it? how should we know?
llazyoli 4 years ago
in other words: i haven't seen anything infinite yet.
llazyoli 4 years ago
I didn't mean infinity is not an adjective. Infinity can't be a number because it doesn't stop to be one. I meant the definition of infinity from set theory produces paradoxes.One of my favorite paradoxes is Hilbert's Hotel. Try and look it up.
ThisSentenceIsFalse 4 years ago
Your questions are interesting to me. They are the starting points to understanding the properties of infinity. For instance that 'race track' thing touches on the distinction between potential and actual infinity. Try reading about George Cantor or Kurt Godel. They were both major mathematicians who went crazy working on infinity.
ThisSentenceIsFalse 4 years ago
ultrafinitism. i'd probably go with that.
llazyoli 4 years ago
btw. there should be opportunites to see actual infinity if such a thing exists. first one should be you standing between mirrors but probably this fails because you're in the way of your own image or the angle you need can't be reached. i don't know. second one would be to film yourself live on tv. holding the camera at the screen (which shows you filming yourself, with a camera filming yourself and so on). a well known glitch or bug in many computergames (overlapping objects) also.
llazyoli 4 years ago
i guess what you can see there is the typical pattern of fractals forming a new pattern out of existing parts and details of another structure (kaleidoscope). third maybe the feedback of a microphone. all this fails at some point due to a certain amount of imperfection. ...now i am spamming the board i guess.
llazyoli 4 years ago
i hate this "not" definitions.
since you don't have black hair you can't be me, so everything that's not me is you. that doesn't tell me anything about you. your hair could be blonde, brown whatever. definitions like that don't describe the object they just exclude certain details being part of it.
llazyoli 4 years ago
"not" definitions are actually a valid form of logical arguments called disjunctive syllogisms. Your analogy is an example of a faulty analogy because it distorts the formal structure of what your arguing against. Also, in a clumsy way, your analogy kind of supports Websnarf. "...your hair could be blonde, brown, whatever." Yes, that's what infinity is.
ThisSentenceIsFalse 4 years ago
i never said it wasn't logical. i just wondered what you gained by describing infinity in this way.
llazyoli 4 years ago
if you look at it this way it could be anything. just because it is unknown to us doesn't mean that it can't be measured or described in better manner than by this "trick". you might as well just say i know crap about it. so this video actually describes what infinity NOT is, not what it is, like the title suggests. hey great, i might add something here: infinity is also NOT a toaster, NOT a car, NOT a tuna salad. so what IS infinity?
llazyoli 4 years ago
You clearly did not watch the video all the way through or else you did not understand it. Infinity is an *adjective*. So its to be compared to worsd like warm, red, and smelly, not toaster, car or salad.
websnarf 4 years ago
you are right. i didn't thought that it can be used as an adjective too (in the sense of infinite quantity). does that change my point or weaken my argument if we go for the words you chose?
llazyoli 4 years ago
I gain a self-consistent definition which makes mathematics a viable and productive endeavor. Anything less an I become ignorant of any kind of accurate mathematical reasoning.
websnarf 4 years ago
Llazyoli, I was saying you were illogical. There's a difference between "Infinity is a set that is not finite" and "I am a person that is not you." The former's a disjunctive syllogism and the latter is affirming the consequent. But again you might have touched on something, albeit clumsily. The paradox of set theory is, the set that contains all sets. Websnarf didn't talk about that yet.
ThisSentenceIsFalse 4 years ago
i will have to watch this later
but
I don't care
|Z|is NOT equal to |N|
it may fit the definition okay
but my mind will not accept it and i thought i was retarded but Galileo thinks so too
phew, i'm not alone
infinity is cool though
when i think about the universe i do not put myself and think outwards i try to grasp it all and think inward if need be
thoughts of infinity make clear connections of time and space
TheStoicAgnostic 4 years ago
|Z| = |N| = |Q|. If you don't understand this, then you have to accept that you don't understand infinity, and should probably not be coming to any conclusions about connections that thinking about it makes for you.
websnarf 4 years ago
i definitely understand it
but
you can not honestly say you can't see the awkwardness of it
and dude
relax
TheStoicAgnostic 4 years ago
Its not awkward if you truly understand it. That's kind of the point.
websnarf 4 years ago
arrogance will interfere with your progress
TheStoicAgnostic 4 years ago
Mathematicians disagree, stoic. The cardinality (size) of the integers is the same as the cardinality of the naturals which is the same as the size of the rationals. It's counter-intuitive, to be sure. Have you looked up Cantor's method of diagonalization?
TheFallibleFiend 4 years ago
Then if it is not the case that |Z|=|N|=|Q|,
then it is up to you to prove otherwise.
theorytheorist 4 years ago
would it be possible to *see* infinity? an example would be pointing a camera at a screen on which its own images are being displayed. would that be an actual observation of infinity? but then we can only observe finite objects, can't we?
more closer rather would be saying it's infinity in *action*
TheParanoid 4 years ago
Well, infinity is an abstract concept. You can't really see infinity unless you are looking at things abstractly. So on the racetrack you can try to *see* the longest path that you can travel. But you are still restricted by your visual input and mental visualization abilities by their inherent finiteness. "Seeing infinity" has to be something that happens totally inside your mind.
websnarf 4 years ago
another problem is that you would have to wait an infinate amount of time before looking. so basically, no. you cant se infinity, but looking into space is kinda close :)
will9909 4 years ago
although you could use a camera that does not absorb other wavelengths of electromagnetic radiation and look at these, this is stretching the definition of truly 'seeing'
will9909 4 years ago
in order to 'see' infinity in this situation would be to have the photons going exactly adjacent to the two mirrors and have the mirrors exactly parallel (this is hard enough in itself). this would mean that to view infinity the position of your camera would need to be in the path of the photons. you would therefore require an invisible camera so that your camera did not inhibit these photons, unfortunatly this would mean that your camera would not be able to generate an image.
will9909 4 years ago
Please explain more Alephs other than naught. Thank you.
matttdrum 4 years ago
That riddle reminds me of Wittgenstein's idea of different word games that get entangled.
Newton1692 4 years ago
I'm not sure what one means by "finite context". But since you're trying to address a typical misunderstanding, perhaps it is necessary to be a little vague. A better example might be a straight line AB:
"What is the maximum time a car take to drive from A to B?". Obviously 't_max' is unbounded (no circles required).
alancarre 4 years ago
Nice one. :)
websnarf 4 years ago
Another thing (more important to your post) is this notion of adjective vs noun. While it is true that "infinite" is an adjective, the word "infinity" is a legal noun. I think you are saying that there is no such thing as "infinity" only because it is a noun and that mathematical objects (sets let's say), having only "properties", even though they are nouns in themselves, can never actually be "the object called infiniy" since "infinity" can not be precisely defined. Is that your idea here?
alancarre 4 years ago
Inifinity as a noun has no meaning in mathematics. But philosophers or common-folk can't let go of it. There's nothing I can do about that. But that doesn't make the word meaningful. If mathematics doesn't endorse the noun meaning, then you are stuck trying to define a mathematical idea in a non-mathematical way. Essentially that means the word as a noun has no rigor and is ultimately vacuous.
websnarf 4 years ago
Well I've done quite a bit of math in my time and I'm not certain that "infinity" as an object (perhaps of varying powers) cannot be rigorously defined. It seems, as certain as anything else, that infinitesimals (which are essentially "infinities") can be regarded as solid mathematical numbers however obeying different algebraic rules. Archimedes axoim is *still* an axiom... (to his credit).
alancarre 4 years ago
And... (sorry to bore you :)) "can not be precisely defined" is supposedly illustrated by the definition of something being NOT some other thing. That is, I could define non-dogs as being "NOT dogs" but I cannot say that since cats are non-dogs that all non-dogs are necessarily cats (cats being analogous to "infinity").
alancarre 4 years ago
Aegius,
Wrong! The LIMIT of 1/x, when x approaches 0 = |INFINITY|; the value of 1/0 is UNDEFINED!
Mickeygallo 4 years ago
websnarf, PLEASE do your promised vid on Zeno's paradoxes. Specifically the arrow and the target. Because every solution that I've found on the web is not only beyond my skill set to judge, but not universally accepted. Or have I missed THE solution? And please explain at what scale common sense breaks down about having to go halfway before going the whole way.
MetaBob 4 years ago
SCREW the arrow, I want to know of the collosium, and the object being pulled in one
wackyraul 4 years ago
Very informative. Thanks Websnarf. I'm also curious... how did you come up with your name?
Aedak33 4 years ago
websnarf = to snarf (download en mass) the web. It has nothing to do with thundercats.
websnarf 4 years ago
snarf was that littal cat thing wasent it?
Pooper0101 4 years ago
Problem: the race car does not exist "within" the race track, it is over and above. Thus you have not contained infinite within finite. If you bound the infinite it is no longer infinite, your explanation always leaves an unbounded set for the infinite to exist. You have confused channeling with bounding.
wolfhunter0321 4 years ago
I am not aware of the definitions of "channeling" outside of the "psychic friends network". What exactly are you talking about?
websnarf 4 years ago
websnarf = brains
milnusthegnome 4 years ago
infinity is 69 divided by zero
fiendin281 4 years ago
Anything divided by zero = infinity.
Aegius 4 years ago
Thanks websnarf, now my ears and nose are bleeding.
DeimosSaturn 4 years ago
watch out for a great rabbit shadow puppet here!!!
sixandahalfstrings 4 years ago
atheism is a religion, it's a very concrete belief. I think you should have said agnosticism -- that to me is really not a religion.
ellhow 4 years ago
Do you have one shred of support for this outlandish claim? Can you explain to me what an atheist church, priest, bible, dogma, prayer or commandment is?
websnarf 4 years ago
When I say a "religion" I just mean a belief, not the absence of any belief as you said in the video.
ellhow 4 years ago
Atheism is a lack of belief in god(s). Therefore atheism is not a religion.
websnarf 4 years ago
This is what I am disagreeing with. Aetheism is not a lack of belief in god but a belief that there is no god.
ellhow 4 years ago
That's nice that you disagree with it, but you're wrong (belief that there is no god is called "strong atheism" which is a subset of ordinary atheism). Are there any other straight forward facts, like 2+2=4 for example, that you disagree with that you care to share with us?
websnarf 4 years ago
To be fair, that's not a straight forward fact, is it? What you call "strong atheism", many other people would call "atheism", as well "weak atheism" is also called "agnosticism" by some. Ah, the beauty of language!
yessingno 4 years ago
What an arogant little jab. But if that's what you meant by atheism in your video then it's only semantics.
ellhow 4 years ago
The kind of atheism you talk about, which is a firm conviction in the fact that there is no god, I think you'll find almost no-one who call themself an atheist in this category. There will be some who have an irrational reason for being atheist, such as a desire to not go to hell, but most I've met have actually thought about it and are the kind of people who don't experience religious faith-like certainty at all.
theinquisitor 4 years ago
That's what *EVERYONE* who understands atheism means by atheism. Look up weak and strong atheism on wikipedia. The semantic difference is an important one. Strong atheism is just, logically, a narrower definition, that falls under general atheism.
websnarf 4 years ago
Ohhhhhh! look at that! can't make an argument so you attack the person. Saying "your wrong" is not proof, nice try. Strong atheism is not a sub-set, it is a set. More over a in Greek means No, theism is believe in God, thus a theism is the no god belief. It is a definite declaration such as, you have no hat. It is a positive statement of the impossibly of God.
wolfhunter0321 4 years ago
We are discussing the definition, and since I and many other atheists self-identify according to this definition, then that's just what it is. If ellhow wants to make up new definitions, then he cannot use them in exposition where I am part of the audience, or else he gets called out as being wrong. The rest of your post above is unintelligible, so I can't address it.
websnarf 4 years ago
I watched this video looking for things to argue with and found nothing. You really did that well. I guess the real problem I had with infinity was when people talked about it as though it were a noun. I never realized it was an adjective. Have you done/Are you thinking about doing one on Cantor's idea of the transfinite?
parkingst0nes 4 years ago
umm.. i'm not good at all at maths but what i've heard about Infinity is that once u get to a high enough number, it starts all over again, back to unit 1, or something like that. jsut what i've heard.
AndreLeCoz 4 years ago
Galileo concluded that the ideas of less, equal, and greater applied only to finite sets, and did not make sense when applied to infinite sets. In the nineteenth century, Cantor, using the same methods, showed that while Galileo's result was correct as applied to the whole numbers and even the rational numbers, the general conclusion did not follow: some infinite sets are larger than others, in that they cannot be put into one-to-one correspondence.
ryanwtyler 5 years ago
infinity is not a number yet one infinity can be greater than another. like the set of numbers between 1 and 2 is greater than the set of all natural numbers
ryanwtyler 5 years ago
"Equal," "greater," and "less," are not applicable to infinities. en(dot)wikipedia/(dot)org/wiki/Galileo%27s_paradox
Rowantwig 5 years ago
This video is such a great example - I wish we had you teaching math when i was in high school =)
JDRedstone 5 years ago
Our finite minds cannot comprehend the infinite. We have a vague concept of it that we can wonder about. Even our wonderful imagination, and logic is limited. There are things that we will never figure out, no matter what we try to do to make it fit in our limited logical minds.
LewisTolkienFan01 5 years ago
Well dont know if i agree with the atheism/religion analogy but it was a good video. It didnt anwser my question if an infinity can exist other than in theory but good explanation on how math thinks of it.
peranimo 5 years ago
Whether it can actually exist at all (i.e., is time infinite?) is not something I am qualified to definitively answer. Quantum theory seems to suggest that it does not exist for objects or space. However, the value of the abstract cannot be underestimated; its the framework in which we build things that we don't know will work until we actually make them.
websnarf 5 years ago
Agree there. But think we will never really "build" this thing.
peranimo 5 years ago
The shadow of the moon during a solar eclipse
itzsoez 5 years ago
Does 0.99999.... = 1?
TheDudeOfLife 5 years ago
This will be covered in the next lecture. (The answer is *essentially* yes.)
websnarf 5 years ago
I was under the impression that .9999 never equals 1; does your "essentially yes" just describe the behavior of, for instance, .9999 approaching 1? But would there not still be an infinitesimal difference between .999... and 1, rendering it not equal?
bosphorus 5 years ago
What do you think the value of this infinitesimal difference is?
websnarf 5 years ago
1-.99=.01, 1-.9999=.0001, etc... as .9999 approaches 1, it's still bounded by a difference that approaches an infinitesimally small number (1-.99999999=.00000001), thus this difference, however small, is still a deviation from the actual whole of 1; by this example, I would say that .9999 does not equal 1.
bosphorus 5 years ago
I don't follow your reasoning. Can you please pick a specific number *greater* than 0 but less than this infinitesimal, so I can have some idea of why you think this number is a positive number, but not zero?
websnarf 5 years ago
.(9)*9=9.(9)
9.(9)-.(9)=9
9/9=1 --> .(9)=1
Jacnas 4 years ago
The concept infinity has no impact on humans, life or existence as a wholefor that matter. Everything that we believe to be real begins and ends in one way or another. Your race track model is flawed. Not only is the track finite you forget to factor in the veihicle. A car cannot mechanically operate indefinitly. Then add the fuel limitation. The only way to establish an infinity construct is to use an infinite constant as an element thus you're using the word to define itself.
TheLoadedQuestion 5 years ago
Saying infinity has no impact on humans is the same as saying that abstract ideas don't have impact on humans. Ask yourself this, without the abstract notion of infinity, how do the car engineers know that by improving the car's engine, fuel efficiency, etc that the car can even go any further than it did before? How do they know that there is even any more path to drive on?
websnarf 5 years ago
The have empirical proof. The path is not infinite the path is point A to point b. Not to mention the main factors that inhibit eternal automobiles are friction and faith in internal combustion as a necessity for propulsion.imo
TheLoadedQuestion 5 years ago
"The concept infinity has no impact ..." - That's like saying that Calculus has no impact on humans. The concept of infinity is fundamental to Calculus and Calculus is fundamental to practically every technical or scientific discipline we have.
DavidJGrossman 5 years ago
You do have the basic idea. Its not calculable by the basic means of counting or simply directly measuring them -- that's what makes them infinite. I will show in a later lecture that you can *classify* infinities however, and thus be able to put some tractability to them. Some of the comments posted here heavily allude to what I will be talking about.
websnarf 5 years ago