dude 1.999...999 / 2 = 0.999...9995 so that's never gonna be equal to 0.999...999 so there is one number between 0.999..999. and 1..!!! so what u r saying is wrong........
@ FoldedArt. Yes, it will touch the ground, because as just shown 0.9.. is the exact same as 1. They are two ways of writing the same number. The math disproves the apparent fallacy you've created, not the other way around
I don't mean to try and dispute your proof (it seems logical) but could this just be that our current mathematical system cannot represent the difference? Could an imaginary number represent the difference? It seems like nitpicking, as 0.999... is literally infinitely close to 1, but I am curious.
odd numbers cant exist in time basicaly just a figment our imaginations created ..is what ur gonna say? why is 10 the perfect excuse ? .9 is rounded to ten do to sciencez effect . universe effects a relitive equation . and there is no such thing as a non relitive equation . im a sophmore and i came up with this idea cause it makes sence to me .
ok i have 33.3 x 3 i get 99.99 (bar notation) science and math are the same. at the -23rd power ur at atoms .its a dimensional problem eventualy the deciamal gets so percise we have pieces of quarks size! this effects the relitivity of the problem ex. 1.9999999999999999 a (9)eventualy is so small its relitivity makes it in join with space and time causeing extreame micro change. 23 nines down making a(10) eventualy on the equation completing the rest of it making the answer 2. my (idea) of it.
Thats one of the reason for why the mathematicians use bases of discrete mathematics (discrete analysis) that explains that type of approaches (in fact a sum of infinitesimal terms sometimes is a finite number), and by the way, this is not new at all, a similar reasoning was used in the Zenon´s Paradox (with the exception that in those times they dont know the infinitesimal analysis), well, greetings from Mexico...
but you have to understand that infinity doesn't exist T_T noob, .999 is between .99 and 1 and .9999 is between .999 and 1, and it goes on forever because of infinity which is only a concept of that last nine which there isn't because it goes on forever
@deanmat Precisely demonstrating 1/3 is .333... requires a thorough understanding of real numbers which is usually quite advanced. You can trust it is not in dispute. But more importantly think of .333... not as an infinite number but as a bounded quantity with infinite parts. After all, to walk 12 inches you must first walk 6, and to walk 6 you must first walk 3, and 1.5, and .75, and so on. You must walk an infinite amount of discrete distances, and yet they add up to a finite 12
Saying that 1/3 = .33333... is wrong, even if you carry it out a trillion places, its rounded it off. Write it out completely, till you get tired, then round it off since you are being lazy. Mathematical fact? No. It is a mathematical anomaly. Square peg, round hole.
The rule of continuity do not apply to repeating decimals or they are unable to be known only logically because they are infinite u cannot find the difference because it is impossible to find
@johnchen0213 That's what I thought. Except, that number can't exist. the .999... is infinite. But the .000...1, isn't. As soon as you put a 1 somewhere, it's not infinite. If you think that .000....1 added to .9999 equals 1, then you don't really believe that the nines are infinite.
Good to see, that there are people like zukaka out there who can handle math properly.
0.999... is just another notation for 1. The definition of a decimal representation is that it stands for the limit of a convergent series. In the case of 0.999... this limit happens to be 1.
There are other representations for 1.
for example:
-e^(i*pi) = 1
cos²(x)+sin²(x) = 1 for every real x
and also the Integral from 0 to infinity of e^(-x) dx =1
As hopefully everyone knews: between two different real numbers, there is at least one other different real number between them. (In fact there are uncountably many). So, can anyone who doesn't think that 1 = 0.999... show me a different real number between them?
@maloney670 Yes, you can. 0.999....=9/10+9/100+9/1000+... This is an infinite sum where every next term is equal to the previous one divided by 10. These terms represent geometric series with r=1/10. This sum converges and is equal to finite number. In this case the sum is equal to 1.
To be fair to JakobiaP he is actually right. 1/3 IS NOT equal to 0,33... 1/3 is an irational number and therefore infinite. You can't write it as a rational number. Humans just want to write it as a number as it is easier for humans to understand numbers than it is to understand fractions. So just because you normally write it as a number it doesn't make it more right.
@bolerie Dude, do you at least know which one is rational number and which not?
From wikipedia: The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base.
Problem is, as 0.333... is NOT an adequate approximation to 1/3 3x0.333... is NOT equal to 0.999... and thus 0.999... is NOT equal to 1, it's equal to 0.999... just as 0.333... is equal to 0.333...
@JakobiaP It's not an approximation, it's a different representation. You don't understand the concept of infinity. 0.999... does not have a measurable amount of nines, it has an INFINITE amount of nines.
Any repeating decimal can be converted to some FINITE fractional form not approximately but EXACTLY. In case of 0.9999.... this fraction is just 9/9 =1.
Infinity is not something you can measure. Infinity - 1 = infinity. Infinity times two is not greater than just infinity. It's a property, not a number.
This is the thing most young people don't understand and try to fight this simple fact.
@originalGawwad wow youare just so stupid ! if youwere smart, you would realise that this has nothing to do with infinity, and he just proved in three different ways that 0.999...=1
@808darkhands Your comment is kind of embarassing. If you would understand what infinity and not understanding it has to do with the 1 = 0.999... fact, you would see it too.
Young people who can't grasp that 1 = 0.999... mostly fail to understand just what I commented on. They don't understand infinity and thus think that 0.999... has a finite amount of 9's even when it's explicitly said that it repeats infinitely.
@JakobiaP if you are over 15 it is sad that you still believe that this is wrong, I'm from France so I don't know what calculas is, geez did you even watch this video ??
@808darkhands I've watched this video, and I'm from Sweden so knowing calculus is quite world wide, and I've watched the video and I still hold what I've learnt true
@808darkhands Well, the evidence is refuted by some mathematicians and has been studied for ages, and no solid proof has been found until the age of the computer, and they are according to some insufficient
@808darkhands but there is still a fallacy with adding and subtracting irrational numbers. I'm majoring in math and computer science. It is enough to demonstrate using logic, but if math isn't perfect, then using mathematical tricks aren't either. It still doesn't formally prove anything
If you move the decimal point to the left there is always one less digit on the right side of the number. Since infinity - 1 is an impossible and implausible concept, so is the entire thing. Please correct me if I'm wrong..?
@Crysis2isOnline You corrected your self. There is not infinity - 1 as infinity is not a number. It is a property of a number and you can't perform any calculations on a property.
9.999... still repeats to infinity. It doesn't matter if you multiply it by 10^10000, the decimal still repeats.
Infinity is something WITH OUT a limit. Naturally infinity in math has no limit either.
maybe i am wrong and 1/3=0.(3) is not a math aproximation...can you do a vido with a small experiment for me?:
take a 10 meter string and divide it in 3 equal strings...and if that strings will have 3 meter exactly than i am a stupid:)...the strings will have 3.3333... and at some point one of them will be 0.000001 longer than the others....
skipping last number is not proff that 1=0.999... It's simple match. If you skip last number in every 0.333... Obviously it's going to by less than 1.0
the second proof is the best one I think (and the one i used to proove it in year 8 at school...). Come on people it clearly is (!) right. Every number that has an infinite number of numbers after the comma, which is repeated (very important) can be written as a fraction. It seems that 0.999... (the 9 is repeated) can be written as 1 (which is a fraction, e.g.: 1=2/2). pi does not have a repeated sequence after the comma, that's why it cannot be written as a fraction...
It is not true if you dont put in the concept of ∞. Infinity actually WILL change the value of the number, therefore 0.999...=1 (I dont 100% agree with it, though)
i see your logic, and i can't find anything wrong with your proofs so i am obligated to believe that 0.999... is infact 1. BUT than again 4.999... is infact 5. and lets say oh, 8.333... is infact 8.4
very wierd indeed... but i do find it very fascinating
@ettoment2 fortunately, mathematics is not about people's opinions, certainly not the ones from people who don't the finer details of positional number systems and what the real numbers are :)
1/3 is not equal to 0.(333) ..when you dive it, it will allways ramain that 0.(000)1 at the end...is just a math just rounds the number to be easy understandeble....
if you want to be 100% correct you need to write it like this: 1=0.999+0,001 and this brakes your theory....
@fragglet its just a math convetion to aproximate a divison if the remainder repeats... if you do the division by hand at one point you will say ok i will not continue cuz it repeats, and you stop dividing it...that dosent meant that 0.000000000001 just disapears...its just a amproximation
No, it isn't. 0.333 would be an approximation. 0.333... is not. The ellipsis indicates that it's an infinitely recurring series.
Again, as I said in my previous comment, it is not an approximation and there is no "remainder". If you think that, you've misunderstood what the notation means.
That's the problem with infinity. At some point you have to artificially end the notation. Since 0.999...is infinite, working it out to a finite number of decimal places introduces an error into the equation. Any infinite number worked out to a finite number of decimals is not completely accurate, and that is why the number appears to equal to 1 when in fact it is merely infinitely close to 1.
Oh, and I'm 12 years old, and they haven't given me a level in maths yet, but when I took a test with my teacher, he explained that there are only 5%-10% of people in the world that are better than me (At any age). Pretty good for a 12 year old.
You made a mistake on the last one. The closest decimal to 1 is 1.000 repeating until you reach the end, where there would have to be a 1. Since this has no finish whatsoever (It is infinite), Therefore there cannot be a 1 on the end, as it would signify that there is a lower number. You have made a paradox before you have even reached the sums.
that's true only with an error aproximed at a given N after the 0. , so you could find a number that fall between 0,9... and 1 for a given error. if you are gonna draw it in a grapich, the limit would prove thet actually 0,9... is not 1, infact what you are gonna draw is gonna go as near as you want ( the given error) but NEVER, EVER touching it, in other words, thet are not equals.
The assumption that .999... = 1 is based on the assumption that 1/3 = 0.333...
Please prove 1/3 = 0.333...
Unfortunately even with the concept of infinite repeating decimal you will never reach the true number. The only way to acurately identify one third is as 1/3. The logic that 0.999... = 1 would also imply that through exponential decay you will reach zero. By the given "theory" there must be a number between, then there should also be a number between zero and y=a(1-r)^x right?
@madamerouge123 maybe, but 1/3 APPROX 0.3333.... with 333 going on infinity and beyaond... problem is that 1/3 = 0.333... is wrong.. its 1/3 APROX 0.33 theres a definition he's lacking... but at some point at the end of the .333(that will never end) so you have to check the whole line. not just some..
@lebqzz Dude, that has nothing to with I said. Also, 1/3=0.333... It's not the same as saying pi is 3.14. There is a contradiction in your sentence. You say the end, but then you say there is no end. What do you mean the whole line? What line are you talking about?
In my oppinion, this is not a good solvation for the problem, because, if x is not=1 , then if you multiply a number with 0,99... for example 2, you will end in a bigger number than 1. Except, if you are multipliing a number that is smaller than 1, but in that case you will end in a smaller number than 0,99... like 0,5*0,999 is smaller than 0,5 ;)
it's not, this is how i worked it out. 1/3+1/3+1/3=3/3 NOT CORRECT. 1/3+1/3+1/3=3/9 so it is not a whole. I know this isn't mathematically correct, but in my head it's wrong x
I know this may have been mentioned before (I don't wanna scroll through all the comments), but I thought that 0.333... was an approximation. It's like dividing by x, when x approaches infinity.
@Wasserrauschen It is only an approximation if you cut it off at any point before "infinity." However, if you understand that 0.333... is a repeating decimal--in other words, it never ends--then it exactly equals 1/3
@CousinoMacul Hello, i am new in this topic. Your last proof has made me to believe in that, but 0,333... in my oppinion is not equal with 1/3, because no matter, how many times. you write down number"3" if you want to do the operation 1/3, you will alway have 1 as rest. So you could write down the number "3" infinite times, it wont be equal to 1/3. Please correct me if im not correct, and sorry for my english, i am hungarian
equal means ''the same as'' wich means that, if you multiply/divide it will be the same number no matter what... 1*2 = 2 and 0.99999 to infinity * 2 =1.9999.... plus .....-1
also, 0.33333.... * 3 = 1 since 1/3 * 3 = 1 and 1/3 and 0.3333333333........ is the same
@1thing11 Just because it doesn't look like what you expect an integer to look like, doesn't mean that it isn't one. 0.999... is in fact an integer, a whole number, and a natural number since it is equal to 1. It is merely another representation of that number.
@CousinoMacul x=0.999...has infinite 9s behind the decimal point. However, 10x, which is 9.999...has (∞-1) 9s behind the decimal point. Hence, 10x-x does not equals to 9.
@1thing11 (∞-1)??? What exactly is that? A repeating decimal remains a repeating decimal no matter what power of 10 you scale it by. Another way to look at it is to go back to the definition of infinity, which is a quantity so great that no matter how much you subtract from it, it remains unchanged (think of a bottomless pit: no matter how far down you fall, it's still bottomless below you). So 10x-x does indeed equal 9.
the mass of an electron is 9,10938188 × 10-²², or 0,000000000000000000000910938188;okay, if you substitute this 8 for a nine changes completly the mass, in other words, the electron is no more a electron.
one more thing: 9,10938188 × 10-²² , the 10-²² is 10 twenty two times, what happens if you make 21? changes completly. this proof the math contains errors, is a shame...
@felijrbr The mass of the electron is not 'infinite'. 0.999... goes on continuously, in other words, there's an infinite number of '9's behind the '0.'. Hence these are 2 different cases.
@PeachJam Too bad you never studied math seriously enough to realize you are completely wrong in many aspects... math is precise. I'm not just copying you, everything in that sentence applies to you.
@inginerul1987 According to set theory the natural numbers are forming a countable set. If you agree, then there are countably many 9's in 0.999... (as many 9's as there are natural numbers), the math operation is finished and 0.999... is a number. If you disagree, then you can treat 0.999... as an unfinished math operation, and 0.999... = 1 is nonsensical (neither equal nor less than 1).
@daviddahl83 99.999% chance to not be born means you had (1-.99999)*100 percent chance to be born. Which is .001% chance to be born, a positive chance. However, 99.99....% chance would be (1-.999...)*100 which is (0)*100 which is 0 percent chance to be born.
dude 1.999...999 / 2 = 0.999...9995 so that's never gonna be equal to 0.999...999 so there is one number between 0.999..999. and 1..!!! so what u r saying is wrong........
6drnikolas 7 hours ago
But if 0,999... never actually hits 1, it's not the same right?
If you take a rope that's 0,999... long and you hang it from a cliff thats 1 long, it won't touch the ground.
FoldedArt 2 days ago
@ FoldedArt. Yes, it will touch the ground, because as just shown 0.9.. is the exact same as 1. They are two ways of writing the same number. The math disproves the apparent fallacy you've created, not the other way around
AlexeiDmitri 7 hours ago
mind=blown
andyman8253 2 days ago
I don't mean to try and dispute your proof (it seems logical) but could this just be that our current mathematical system cannot represent the difference? Could an imaginary number represent the difference? It seems like nitpicking, as 0.999... is literally infinitely close to 1, but I am curious.
SelectHawk 4 days ago
This has been flagged as spam show
If 0.999999999.... never ends, then it never makes 1 !
maloney670 4 days ago
If 0.999999999.... never ends, then it never makes 1 !
maloney670 4 days ago
i spose they say 0.333 is as close to 1/3 as you gan get, so technically, 1=1
Of coarse 1=1, it's like saying, if 1 doesn't equal 1, then is an apple a banana?
what the fuck!?!?!?!? 1 equals 1 dumbass-san
jackvids7 4 days ago
1/3 = 0.333
1/3x3=0.999
1/3x3=3/3
3/3=1
0.999=1
wtf?? It works
jackvids7 4 days ago
1.99/2=0.995 ||| 0.995(2)=1.99
truehate101 5 days ago
i want to believe u but infinite doesn't equal infinite+1, darn close though
truehate101 5 days ago
odd numbers cant exist in time basicaly just a figment our imaginations created ..is what ur gonna say? why is 10 the perfect excuse ? .9 is rounded to ten do to sciencez effect . universe effects a relitive equation . and there is no such thing as a non relitive equation . im a sophmore and i came up with this idea cause it makes sence to me .
XxKenManxX 1 week ago
ok i have 33.3 x 3 i get 99.99 (bar notation) science and math are the same. at the -23rd power ur at atoms .its a dimensional problem eventualy the deciamal gets so percise we have pieces of quarks size! this effects the relitivity of the problem ex. 1.9999999999999999 a (9)eventualy is so small its relitivity makes it in join with space and time causeing extreame micro change. 23 nines down making a(10) eventualy on the equation completing the rest of it making the answer 2. my (idea) of it.
XxKenManxX 1 week ago
but if i hold up 1 finger do I have a 0.9999999999..... finger?
StarFingerzTeam01 1 week ago
Thats one of the reason for why the mathematicians use bases of discrete mathematics (discrete analysis) that explains that type of approaches (in fact a sum of infinitesimal terms sometimes is a finite number), and by the way, this is not new at all, a similar reasoning was used in the Zenon´s Paradox (with the exception that in those times they dont know the infinitesimal analysis), well, greetings from Mexico...
Wildarchdemon 1 week ago
but you have to understand that infinity doesn't exist T_T noob, .999 is between .99 and 1 and .9999 is between .999 and 1, and it goes on forever because of infinity which is only a concept of that last nine which there isn't because it goes on forever
sicoticclown 1 week ago
0.999... = 1 is wrong since between 0.999... and 1 is 0.000...1.
13plu 1 week ago
.......soooo what your saying is Marty and Doc are still trapped back in 1955???
nighteyes777 1 week ago 8
So, it just means the way we present numbers is not perfect.
matt9741399 1 week ago
The number that is between A and B is; B - 0.0_1 83
leminlyme 1 week ago
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leminlyme 1 week ago
This is correct
0.(insert infinite amount of 9's here) = 1
TheMcDucky 1 week ago
@TheMcDucky but u can never reach infinity, only in theory this is true, but application impossible
sicoticclown 1 week ago
@sicoticclown that is exactly one of the things higher mathematics deal with.
the transition to infinity.
btw, what are numbers if not theoretical concepts?
monsterpsycho 1 week ago
You fail...
TheMcDucky 1 week ago
The main counterargument I keep seeing is that .3333... is just an approximation of 1/3. How do we know this is true?
deanmat 2 weeks ago
@deanmat Precisely demonstrating 1/3 is .333... requires a thorough understanding of real numbers which is usually quite advanced. You can trust it is not in dispute. But more importantly think of .333... not as an infinite number but as a bounded quantity with infinite parts. After all, to walk 12 inches you must first walk 6, and to walk 6 you must first walk 3, and 1.5, and .75, and so on. You must walk an infinite amount of discrete distances, and yet they add up to a finite 12
nerfmyaccount 1 week ago
Ima show my maths teacher this... xD
Thumbs up if you heard the police cars after 9:12!!
1968yearofmetal 2 weeks ago
2 * 0,999... = 1,888...
2 * 1 = 2
jopeteus 2 weeks ago
ok now divide by zero
1134yannick 2 weeks ago
Saying that 1/3 = .33333... is wrong, even if you carry it out a trillion places, its rounded it off. Write it out completely, till you get tired, then round it off since you are being lazy. Mathematical fact? No. It is a mathematical anomaly. Square peg, round hole.
garry7263 2 weeks ago
The rule of continuity do not apply to repeating decimals or they are unable to be known only logically because they are infinite u cannot find the difference because it is impossible to find
Ronbugy9 2 weeks ago
.999.... is not 1! it's obvious that it's missing the .000...1
johnchen0213 2 weeks ago
@johnchen0213 That's what I thought. Except, that number can't exist. the .999... is infinite. But the .000...1, isn't. As soon as you put a 1 somewhere, it's not infinite. If you think that .000....1 added to .9999 equals 1, then you don't really believe that the nines are infinite.
deanmat 2 weeks ago
First fail at 00:44. Sure 1/3 = 0,333.... But 1/3+1/3+1/3 is ALWAYS 1, numerical or not.
Second fail was at 02:32. What your'e trying to prove isn't that 0.999...=1. But rather that 0.999... is infinitely close to one.
Third fail at 04:28.Same thing as in fail nr.2
Fourth fail is at 05:20. Now he proves that 1,999999... is infinitely close to 2.
Fifth fail 08:52. He's saying that 0,999... is = 1 on the basis that's there's nothing in between.
Ever heard about irrational numbers?
TheAdept1302 2 weeks ago
awesome !!!
xuioo 2 weeks ago
Comment removed
Undvorabeinsnickers 2 weeks ago
what about 1.666... like 1/6 of ten
ollieoniel 2 weeks ago
I've done more research on the matter and now I do agree that 0.999... = 1.
qubikroot 2 weeks ago 6
@qubikroot but it's not! HOW?? i've tried it with .7777... and .6666..... using the 10x method. and it works too!
johnchen0213 1 week ago
Good to see, that there are people like zukaka out there who can handle math properly.
0.999... is just another notation for 1. The definition of a decimal representation is that it stands for the limit of a convergent series. In the case of 0.999... this limit happens to be 1.
There are other representations for 1.
for example:
-e^(i*pi) = 1
cos²(x)+sin²(x) = 1 for every real x
and also the Integral from 0 to infinity of e^(-x) dx =1
Simchen 2 weeks ago
A few days ago I already made a few people to shut up. Now i guess there are other ones who deserve the same.
Type geometric series in wikipedia, scroll down and read about repeating decimals.
Or type 0.999.... in wikipedia. There is a separate page devoted to this number.
And then stop guessing what is right and wrong. Istead of this just read and start to believe the truth.
0.9999....=1
zukaka84 2 weeks ago
The fact is we always think 1/3=0.9999..., its not equal !!
tingyu1027tw 2 weeks ago
As hopefully everyone knews: between two different real numbers, there is at least one other different real number between them. (In fact there are uncountably many). So, can anyone who doesn't think that 1 = 0.999... show me a different real number between them?
Simchen 3 weeks ago
@Simchen Of course they cannot show it. But of course they will still say that they are not equal.
zukaka84 2 weeks ago
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qubikroot 3 weeks ago
@qubikroot 1/3 is irrational? Do you know the definition of rational number?
zukaka84 2 weeks ago
Comment removed
qubikroot 3 weeks ago
Screw this; I know that if I have one book and add another to it, I have two books, not 1.999 books. >.<'
OhMyFreakingGoshh 3 weeks ago
@OhMyFreakingGoshh It seems you still don't know everything.
zukaka84 2 weeks ago
@zukaka84 True, but maybe one day I'll be able to join you in know-it-all heaven.
OhMyFreakingGoshh 2 weeks ago
0.999.... is not one, it is just infinitely close
maloney670 3 weeks ago
@maloney670 There is a rift in the mathematic community over that sadly, as it's allmost infinitely (no pun indented) hard to prove
JakobiaP 3 weeks ago
Lol, can you add an infinity of decimals and get 1 ? can you times an infinity of decimals by 10 ?
maloney670 3 weeks ago
@maloney670 you can't. that's the fault in the argument
spdyeric 2 weeks ago
@maloney670 Yes, you can. 0.999....=9/10+9/100+9/1000+... This is an infinite sum where every next term is equal to the previous one divided by 10. These terms represent geometric series with r=1/10. This sum converges and is equal to finite number. In this case the sum is equal to 1.
zukaka84 2 weeks ago
To be fair to JakobiaP he is actually right. 1/3 IS NOT equal to 0,33... 1/3 is an irational number and therefore infinite. You can't write it as a rational number. Humans just want to write it as a number as it is easier for humans to understand numbers than it is to understand fractions. So just because you normally write it as a number it doesn't make it more right.
bolerie 3 weeks ago
@bolerie Dude, do you at least know which one is rational number and which not?
From wikipedia: The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base.
zukaka84 2 weeks ago
A number that is rounded to another number is NOT equal to that number
JakobiaP 3 weeks ago
@JakobiaP There is no any rounding here.
zukaka84 2 weeks ago
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rodasnepervilo 3 weeks ago
fuk u and fuk maths so what 0.999..equal 1
fadyboi 3 weeks ago
This is stupid.... 1=1 and 0.999 doesn't = 1 it = 0.999
maloney670 3 weeks ago
@maloney670 Maybe you will also say: This is stupid 5/10=5/10 and 1/2 doesn't = 5/10.
zukaka84 3 weeks ago
@zukaka84 And you are ignorant to compare incomparable mathematical concepts
JakobiaP 3 weeks ago
@zukaka84 Fractions are in a different number system I think, and work a bit different, you have equivalents. He is talking about (1)
maloney670 3 weeks ago
Problem is, as 0.333... is NOT an adequate approximation to 1/3 3x0.333... is NOT equal to 0.999... and thus 0.999... is NOT equal to 1, it's equal to 0.999... just as 0.333... is equal to 0.333...
JakobiaP 3 weeks ago
@JakobiaP It's not an approximation, it's a different representation. You don't understand the concept of infinity. 0.999... does not have a measurable amount of nines, it has an INFINITE amount of nines.
originalGawwad 3 weeks ago
@originalGawwad And you have studied calculus then? If you claim that you understand and I don't? Or are you better at this than my lecturers?
JakobiaP 3 weeks ago
for |r|<1, a+ar+ar^2+ar^3+....=a/(1-r)
A repeating decimal can be thought of as a geometric series whose r=1/10. For example:
0.7777....=7/10+7/100+7/1000+....=(7/10)/(1-1/10)=7/9
0.12341234....=1234/10000+1234/10000000+....=(1234/10000)/(1-1/10000)=1234/9999
0.9999....=9/10+9/100+9/1000+....=(9/10)/(1-9/10)=9/9=1
Any repeating decimal can be converted to some FINITE fractional form not approximately but EXACTLY. In case of 0.9999.... this fraction is just 9/9 =1.
The end of the story.
zukaka84 3 weeks ago
Infinity is not something you can measure. Infinity - 1 = infinity. Infinity times two is not greater than just infinity. It's a property, not a number.
This is the thing most young people don't understand and try to fight this simple fact.
Just wait till you get to imaginary numbers.
originalGawwad 4 weeks ago
@originalGawwad wow youare just so stupid ! if youwere smart, you would realise that this has nothing to do with infinity, and he just proved in three different ways that 0.999...=1
if you think he's wrong, find the mistake
808darkhands 3 weeks ago
@808darkhands Your comment is kind of embarassing. If you would understand what infinity and not understanding it has to do with the 1 = 0.999... fact, you would see it too.
Young people who can't grasp that 1 = 0.999... mostly fail to understand just what I commented on. They don't understand infinity and thus think that 0.999... has a finite amount of 9's even when it's explicitly said that it repeats infinitely.
originalGawwad 3 weeks ago
@originalGawwad dude his guy is right, 1=0.999.. is TRUE; it doesn't seem to me like you know that
808darkhands 3 weeks ago
@808darkhands 1=0.999... is a fallacy, study calculus
JakobiaP 3 weeks ago
@JakobiaP lol you are stupid, he just proved to you that it's true
808darkhands 3 weeks ago
@808darkhands Have you studied calc? Do you have an education? If the answer is no, get one and come back.
JakobiaP 3 weeks ago
@JakobiaP if you are over 15 it is sad that you still believe that this is wrong, I'm from France so I don't know what calculas is, geez did you even watch this video ??
808darkhands 3 weeks ago
@808darkhands I've watched this video, and I'm from Sweden so knowing calculus is quite world wide, and I've watched the video and I still hold what I've learnt true
JakobiaP 3 weeks ago
@JakobiaP well what you think is wrong IT HAS BEEN PROVEN for heaven's sake
808darkhands 3 weeks ago
@808darkhands Well, the evidence is refuted by some mathematicians and has been studied for ages, and no solid proof has been found until the age of the computer, and they are according to some insufficient
JakobiaP 3 weeks ago
@JakobiaP so you think there's a mistake in this demonstration, go ahead find the mistake
808darkhands 3 weeks ago
@808darkhands I have not stated that there are any direct mistakes, just that what the author is presenting are not evidence for the claim 1=0.999...
JakobiaP 3 weeks ago
@JakobiaP then you don't know how math works, I'm done arguing
808darkhands 3 weeks ago
@808darkhands I know how empiric study of mathematics in an scientific context, and the authors "proof" is based on assumptions to far stretched
JakobiaP 3 weeks ago
@808darkhands The "mistake" and I am pretty sure the poster knows this too, is that 10x-x would not equal 9.
spdyeric 2 weeks ago
@spdyeric yes it would 10(0.999...)=9.999... 9.999...-0.999...=9
come on thats easy, and even if that was wrnog, theres still two other demonstrations :p
808darkhands 2 weeks ago
@808darkhands but there is still a fallacy with adding and subtracting irrational numbers. I'm majoring in math and computer science. It is enough to demonstrate using logic, but if math isn't perfect, then using mathematical tricks aren't either. It still doesn't formally prove anything
spdyeric 2 weeks ago
@spdyeric .999... is not irrational it is 9/9.
sinbien336 2 weeks ago
This is perfectly true. From a Mathematician.
JSM44677 4 weeks ago 3
x = 0.9r
10x therefore = MATHS ERROR.
If you move the decimal point to the left there is always one less digit on the right side of the number. Since infinity - 1 is an impossible and implausible concept, so is the entire thing. Please correct me if I'm wrong..?
Crysis2isOnline 1 month ago
@Crysis2isOnline You corrected your self. There is not infinity - 1 as infinity is not a number. It is a property of a number and you can't perform any calculations on a property.
9.999... still repeats to infinity. It doesn't matter if you multiply it by 10^10000, the decimal still repeats.
Infinity is something WITH OUT a limit. Naturally infinity in math has no limit either.
What ever you do, infinity is always infinity.
originalGawwad 3 weeks ago
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sinbien336 2 weeks ago
0.999...=1 it repeats it to infinity but it dosent make it 1
0.333...... repeats to infinity, i cant turn it to 0.4 like 0.333....+ 0.333... = 0.8?
Grievith 1 month ago
@Grievith Why do you want to make 0.333... equal to 0.4? 0.333...=1/3 and 0.999...=1/1
You don't have enough logical sense.
zukaka84 4 weeks ago
@zukaka84 i guess not, i was drunk i didint understand either but i still say 0,999 is not 1
Grievith 3 weeks ago
@Grievith You are still drunk :)
zukaka84 3 weeks ago
@zukaka84 i agree
Grievith 3 weeks ago
@Grievith Thats correct. But 0.(9) is. :P
gwani 3 weeks ago
Every real number is the limit of a sequence,
so the 1 is the limit (unique) of the sequence S1 = 9 / 10, s2 = 99/100, 999/1000 = S3, S4 = 9999/10000 ... (infinitely)
gogogino 1 month ago
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For second Proof :
9.(9)-0.9(9)
this is the substruction genious ;) when multiplied by 10 the number shrinks by 1 decimal.
P.S. you're future John Nash bro :D
snakerocket1992 1 month ago
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snakerocket1992 1 month ago
maybe i am wrong and 1/3=0.(3) is not a math aproximation...can you do a vido with a small experiment for me?:
take a 10 meter string and divide it in 3 equal strings...and if that strings will have 3 meter exactly than i am a stupid:)...the strings will have 3.3333... and at some point one of them will be 0.000001 longer than the others....
TicaSimplyME 1 month ago
@TicaSimplyME You do not understand the concept of infinity. It has no real life examples, it is a theory and an agreement.
originalGawwad 4 weeks ago
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Simple, if you think about it this way, 1 is actually a new number, when we talk about .XXX
mm... how to explain it... OH YEAH decimals !!!
well 0-9 what are they ? units
but 10 itz a new number the last unit number actually is 9.999999
same thing happen here, tahst why 0 after all is still a number
leonardo989 1 month ago
@leonardo989 like the Computers 1bite = 8 bits right ? so 1kb = 1024bites
so tahts how this should be here, 10 should actually be 9.99999990
got it ?
this is to get the math more precisely but nobody cares about that small numbers >.<
but after all that means all taht we have learn and the result we have given, they are all wrong XD
leonardo989 1 month ago
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leonardo989 1 month ago
My mind just exploded, but before it fully finishes exploding..
(.999...)/(.999...)=.999...
I don't think that I can say that's true in anyway..
And 1/1=.999...
This idea doesn't work except in certain scenarios.
TheElitebumbershoot 1 month ago
skipping last number is not proff that 1=0.999... It's simple match. If you skip last number in every 0.333... Obviously it's going to by less than 1.0
Ormusn2o 1 month ago
the second proof is the best one I think (and the one i used to proove it in year 8 at school...). Come on people it clearly is (!) right. Every number that has an infinite number of numbers after the comma, which is repeated (very important) can be written as a fraction. It seems that 0.999... (the 9 is repeated) can be written as 1 (which is a fraction, e.g.: 1=2/2). pi does not have a repeated sequence after the comma, that's why it cannot be written as a fraction...
whatshisnamegain1 1 month ago
It is not true if you dont put in the concept of ∞. Infinity actually WILL change the value of the number, therefore 0.999...=1 (I dont 100% agree with it, though)
derek19062 1 month ago
i made one mistake it is 8.39999... is infact 8.4 still very wierd as how 2 numbers are the same... mind blowing!
teunybc 1 month ago
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teunybc 1 month ago
i see your logic, and i can't find anything wrong with your proofs so i am obligated to believe that 0.999... is infact 1. BUT than again 4.999... is infact 5. and lets say oh, 8.333... is infact 8.4
very wierd indeed... but i do find it very fascinating
teunybc 1 month ago
@teunybc 8.3333... in not 8.4. But 8.3999...=8.4
zukaka84 1 month ago
Actually you can save yourselves time by remembering a basic mathematical logic:
2 numbers are the same if their substraction value equals zero.
-
Short test:
0.9¯ + x = 1
x = 0.0¯
x=0
=> Both numbers are infact the same.
sooperfukker 1 month ago
PROFESSOR FUENTES
SophistAtheist 1 month ago
@ettoment2 fortunately, mathematics is not about people's opinions, certainly not the ones from people who don't the finer details of positional number systems and what the real numbers are :)
nicuramar 1 month ago
im french ... ça s'appelle arrondire trou duc
greg65400 1 month ago
no.
Aabcyclonix 2 months ago
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1/3 = 0,333...4, then it can do more than 1 (like 1,000...2) but not 1 still. Without with 4, it's infinite, and then still wrong.
almiser 2 months ago
wow, you are great at counting infinite ammount of numbers.
54n141n3n 2 months ago
1/3 is not equal to 0.(333) ..when you dive it, it will allways ramain that 0.(000)1 at the end...is just a math just rounds the number to be easy understandeble....
if you want to be 100% correct you need to write it like this: 1=0.999+0,001 and this brakes your theory....
TicaSimplyME 2 months ago
@TicaSimplyME Incorrect. 1/3 is equal to 0.333... It is not an approximation and there is no remainder.
fragglet 1 month ago
@fragglet its just a math convetion to aproximate a divison if the remainder repeats... if you do the division by hand at one point you will say ok i will not continue cuz it repeats, and you stop dividing it...that dosent meant that 0.000000000001 just disapears...its just a amproximation
TicaSimplyME 1 month ago
@TicaSimplyME "its just a amproximation"
No, it isn't. 0.333 would be an approximation. 0.333... is not. The ellipsis indicates that it's an infinitely recurring series.
Again, as I said in my previous comment, it is not an approximation and there is no "remainder". If you think that, you've misunderstood what the notation means.
fragglet 1 month ago
That's the problem with infinity. At some point you have to artificially end the notation. Since 0.999...is infinite, working it out to a finite number of decimal places introduces an error into the equation. Any infinite number worked out to a finite number of decimals is not completely accurate, and that is why the number appears to equal to 1 when in fact it is merely infinitely close to 1.
jamesbooty 2 months ago
Oh, and I'm 12 years old, and they haven't given me a level in maths yet, but when I took a test with my teacher, he explained that there are only 5%-10% of people in the world that are better than me (At any age). Pretty good for a 12 year old.
InwardsFlow 2 months ago
You made a mistake on the last one. The closest decimal to 1 is 1.000 repeating until you reach the end, where there would have to be a 1. Since this has no finish whatsoever (It is infinite), Therefore there cannot be a 1 on the end, as it would signify that there is a lower number. You have made a paradox before you have even reached the sums.
InwardsFlow 2 months ago
that's true only with an error aproximed at a given N after the 0. , so you could find a number that fall between 0,9... and 1 for a given error. if you are gonna draw it in a grapich, the limit would prove thet actually 0,9... is not 1, infact what you are gonna draw is gonna go as near as you want ( the given error) but NEVER, EVER touching it, in other words, thet are not equals.
powerpoison 2 months ago
@littlemonster2392 LOL please don't comment if you havent taken grade 5 math yet...
ruster1971 2 months ago
i am studying mathematics
it is a fact indeed, but this is not a proof lol
bluecarpet12345 2 months ago
Why do I Always end up on weird videos, after watching minecraft?
MrPepsi305 2 months ago
It's not that hard... 1/3= 0.333... Multiply that by 3, you get: 1=0.999...
Scoala12345 2 months ago
The assumption that .999... = 1 is based on the assumption that 1/3 = 0.333...
Please prove 1/3 = 0.333...
Unfortunately even with the concept of infinite repeating decimal you will never reach the true number. The only way to acurately identify one third is as 1/3. The logic that 0.999... = 1 would also imply that through exponential decay you will reach zero. By the given "theory" there must be a number between, then there should also be a number between zero and y=a(1-r)^x right?
tyty8484 3 months ago
well you are making a crucial mistake.. you are not diving infinite times. GET TO WORK AND PROVE IT.
lebqzz 3 months ago
@lebqzz Why would he dive an infinite number of times? that is both impossible and impractical.
madamerouge123 1 month ago
@madamerouge123 maybe, but 1/3 APPROX 0.3333.... with 333 going on infinity and beyaond... problem is that 1/3 = 0.333... is wrong.. its 1/3 APROX 0.33 theres a definition he's lacking... but at some point at the end of the .333(that will never end) so you have to check the whole line. not just some..
Same as saying pi = 3.14 and not 3.14.......
lebqzz 1 month ago
@lebqzz Dude, that has nothing to with I said. Also, 1/3=0.333... It's not the same as saying pi is 3.14. There is a contradiction in your sentence. You say the end, but then you say there is no end. What do you mean the whole line? What line are you talking about?
madamerouge123 1 month ago
@madamerouge123 lol max
BillycatBoyz1 1 month ago
0.999... < 0.99x < 1
JtheKiwi 3 months ago
@JtheKiwi
In my oppinion, this is not a good solvation for the problem, because, if x is not=1 , then if you multiply a number with 0,99... for example 2, you will end in a bigger number than 1. Except, if you are multipliing a number that is smaller than 1, but in that case you will end in a smaller number than 0,99... like 0,5*0,999 is smaller than 0,5 ;)
ettoment2 1 month ago
@ettoment2 0.99x , x is a number not yet comprehended by your Earth mathematicians
JtheKiwi 1 month ago
I CAN PROVE THIS VERY EASY!!!
so we take the period: 0.(9) \*O.(9)=0.9999*\
by definition 0.(9)=9\9 -->0.(9)=1 so that means that 0.999...=1
PLEASE THUMBS UP SO EVERYONE CAN SEE THIS!
raducu120 3 months ago 2
it's not, this is how i worked it out. 1/3+1/3+1/3=3/3 NOT CORRECT. 1/3+1/3+1/3=3/9 so it is not a whole. I know this isn't mathematically correct, but in my head it's wrong x
littlemonster2392 3 months ago
@littlemonster2392
1/3+1/3+1/3=3/3
Downloadice 3 months ago
@littlemonster2392 to get 3/9 you have to bend the basic rules ;)
a/b+c/d = (a*d+b*c)/(b*d) = 6/9 = 2/3
lebqzz 3 months ago
I know this may have been mentioned before (I don't wanna scroll through all the comments), but I thought that 0.333... was an approximation. It's like dividing by x, when x approaches infinity.
Wasserrauschen 3 months ago
@Wasserrauschen It is only an approximation if you cut it off at any point before "infinity." However, if you understand that 0.333... is a repeating decimal--in other words, it never ends--then it exactly equals 1/3
CousinoMacul 3 months ago
@CousinoMacul Hello, i am new in this topic. Your last proof has made me to believe in that, but 0,333... in my oppinion is not equal with 1/3, because no matter, how many times. you write down number"3" if you want to do the operation 1/3, you will alway have 1 as rest. So you could write down the number "3" infinite times, it wont be equal to 1/3. Please correct me if im not correct, and sorry for my english, i am hungarian
ettoment2 1 month ago
@CousinoMacul OK UNDERSTAND THIS..
equal means ''the same as'' wich means that, if you multiply/divide it will be the same number no matter what... 1*2 = 2 and 0.99999 to infinity * 2 =1.9999.... plus .....-1
also, 0.33333.... * 3 = 1 since 1/3 * 3 = 1 and 1/3 and 0.3333333333........ is the same
M4TH145spr 4 weeks ago
Isn't 1 a whole number and natural number? But 0.999... belongs to neither of these groups.
1thing11 3 months ago
@1thing11 Just because it doesn't look like what you expect an integer to look like, doesn't mean that it isn't one. 0.999... is in fact an integer, a whole number, and a natural number since it is equal to 1. It is merely another representation of that number.
CousinoMacul 3 months ago
@CousinoMacul x=0.999...has infinite 9s behind the decimal point. However, 10x, which is 9.999...has (∞-1) 9s behind the decimal point. Hence, 10x-x does not equals to 9.
1thing11 3 months ago
@1thing11 (∞-1)??? What exactly is that? A repeating decimal remains a repeating decimal no matter what power of 10 you scale it by. Another way to look at it is to go back to the definition of infinity, which is a quantity so great that no matter how much you subtract from it, it remains unchanged (think of a bottomless pit: no matter how far down you fall, it's still bottomless below you). So 10x-x does indeed equal 9.
CousinoMacul 3 months ago
@CousinoMacul 0.999... is NOT an integer, it's a natural fraction (as it's infinitely repeating)
JakobiaP 3 weeks ago
Ok, to everyone who still can't accept it:
en . wikipedia . org/wiki/0.999...
Dawwe9505 3 months ago
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Dawwe9505 3 months ago
0.899999... = 0.9
1.499999... = 1.5
Jorgo94 3 months ago
The 'has to be a number between them' argument is fucking stupid. I agree with the rest, but that one is dumb.
SteveyKoz 3 months ago
@SteveyKoz How? It makes perfect sense.
madamerouge123 1 month ago
the mass of an electron is 9,10938188 × 10-²², or 0,000000000000000000000910938188;okay, if you substitute this 8 for a nine changes completly the mass, in other words, the electron is no more a electron.
one more thing: 9,10938188 × 10-²² , the 10-²² is 10 twenty two times, what happens if you make 21? changes completly. this proof the math contains errors, is a shame...
felijrbr 3 months ago
@felijrbr WTF?
SixOutOfAHundred 3 months ago
@felijrbr that might be the worst proof ever
Dawwe9505 3 months ago
@felijrbr The mass of the electron is not 'infinite'. 0.999... goes on continuously, in other words, there's an infinite number of '9's behind the '0.'. Hence these are 2 different cases.
94winsonyeap 3 months ago
Too bad you never studied math seriously enough to realize you are completely wrong in many aspects... math is precise.
PeachJam 4 months ago
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@PeachJam Too bad you never studied math seriously enough to realize you are completely wrong in many aspects... math is precise. I'm not just copying you, everything in that sentence applies to you.
madamerouge123 1 month ago
0.(9) cannot be compared with 1 !!!
1 is a number and 0.999999...is an unfinished math operation!
Think!
inginerul1987 5 months ago
@inginerul1987 According to set theory the natural numbers are forming a countable set. If you agree, then there are countably many 9's in 0.999... (as many 9's as there are natural numbers), the math operation is finished and 0.999... is a number. If you disagree, then you can treat 0.999... as an unfinished math operation, and 0.999... = 1 is nonsensical (neither equal nor less than 1).
netzweltler 5 months ago
@inginerul1987 It isn't an unfinished math operation. It is an integer, specifically, 1. Also, please look up math operation and report back.
madamerouge123 1 month ago
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daviddahl83 5 months ago
@daviddahl83 You do realise that 99.999% =/= 99.999.....% ?
COMMANDERZEALOT1 5 months ago
@daviddahl83 You do realise that 99.999% =/= 99.999.....% ?
COMMANDERZEALOT1 5 months ago
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daviddahl83 5 months ago
@daviddahl83 99.999% chance to not be born means you had (1-.99999)*100 percent chance to be born. Which is .001% chance to be born, a positive chance. However, 99.99....% chance would be (1-.999...)*100 which is (0)*100 which is 0 percent chance to be born.
brosephjames 5 months ago
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daviddahl83 5 months ago
@daviddahl83 The guy in the video never claimed that 99.999% = 100%.
anticorncob6 4 months ago