# Vi Hart: How 0.999 repeating = 1!

Submitted by: 5cats 5 years ago in
81

Proof #8 made my brainz explode!
81
Female 258
I`m able to identify all the Lords except the first, second, and fifth. Who are they?
Male 17
She must spend thousands on sharpies.
Male 328
@MechBFP

If humans made programs that could treat infinite numbers like they should be treated then we`d be gods. The only thing your examples prove are that programs can`t calculate infinitely.
Male 719
She shows a lot of interesting tricks, but really, she only points to the real mathematical proof that 1 = .9...

Basically, in the proof, you start by assuming that they are not equal. So, if we assume that x = 0.9..., then 1 - x = a, for some real number a > 0. Then, equivalently, 1 - a = x.

Then, you pick a number b that is easy to work with that is less than a. Since b < a, 1 - b > x.

But then, based on the choice of b, it is trivial to show that 1 - b < x.

Since this is an obvious contradiction, it means that our assumption that 1 != x is false, and so 1 = x = 0.9...
Male 4,004
Um, she proved that 1=1 and that .999repeating is .999repeating... She would sneak in a -.999repeating to a subtraction rather than a -1...

1/3 is as close as we can get to 33.333333333_%, but it`s not dead on.

I don`t like her explanation, her mathematics only work in her weird way here, not in my mind.
If you have .9999repeating, you are lacking one itty-bitty fraction missing to complete the 1, even if it is intifitismally lesser
Male 7
tedgp... Were you ever taught how to do long division in school? I mean seriously? We`re not using a calculator here and letting it round off. Divide 1 by 3, and you get .3 and a remainder of .1, divide that by 3 and get .03 and a remainder of .01... and you can keep going infinitely and still get that remainder. That`s what defines a repeating number. That`s what happens when you divide one into 3 parts, and that by definition is what 1/3 is. It`s really not that hard to understand.
Male 977
This biatch is ridiculously clever.
Male 3,285
@mahe4 you need to learn to read. 0.33333 repeating is STILL not 1/3 no matter what you do to it. It`s close but it still isn`t 1/3
Male 40,764
April Fools Joke?
But... which video is the joke?
Oh dear me...
Male 40,764
Zeno Of Elea (for @tatripp!)

Don`t forget: the `number` .3333_ isn`t a "real thing" it`s just a representation OF a real thing.

Take 9 marbles, (Z) and divide them into 3 equal groups (Y).
Each Y = 1/3 of Z. If you fiddle around with it enough, like the video shows, you end up with 3 times .3333_ = 1 Why? Because in this case .3333_ is not "imaginary, it is ONE marble! But the math is the same no matter what you do.

It doesn`t work for computer language because izt kbloc wangum! (see what I did there?)
Male 1,196
how can we move if there are infinite mid points between any given point. my head a splode
Male 735
.333 doesn`t equal 1/3, 1/3 equals .333! oh wait i don`t think that works...aw titties i don`t know
Male 40,764
But @LillianDulci... Zeno of Elea!!!

Really, you make good points, and I`m NOT smart enough to refute them. I`ll just let Vi`s video do the talking. And Zeno, him too.
Male 429
it works because it works. unless you can point out a specific flaw in each proof, you have no argument to give us.
Female 155
drat math.
Female 2,674
5Cats, but it uses the infinity mark, which means there`s no exact value just like with infinity. You can`t subtract infinity - infinity, it just don`t make sense, and I think the same goes for .999... The difference with things like pi and 1/3 is that the infinity is implied but we`re using exact values anyway (pi is exactly pi and 1/3 is exactly 1/3). If you change 1/3 to .333... then it becomes slightly different than just using 1/3
Male 40,764
@LillianDulci: .999_ = .999_, otherwise there wouldn`t be the "infinity" mark on both of them.

Just like Pi = Pi! We DO KNOW that an infinitely repeating number equals itself.

There`s rules for rational numbers, irrational numbers, imaginary numbers & etc.

I thought she was putting out an early April Fools joke on us all! If she did, I got fooled...
Male 2,737
boredom
Female 2,674
I usually like her videos, but not so much this one. I think it only "works" for the same reason that infinity - infinity isn`t 0. When she subtracts .999... from both sides, she doesn`t have any way of knowing that she`s subtracting the same .999... from both sides so it`s not really possible to do so. Just a guess anyway.
Male 5
I have the weirdest boner right now...
Male 256
drat math physics is way cooler and more realer
Male 101
O blah blah blah... That was a really lame one. Her voice is really annoying. And her stick figure pictures are too. Yeah so any number that is a nano or micro away from a whole number is usually just the whole number in most applications anyways since that much variation doesn`t matter unless you are researching electrons or cells... I`m surprised she didn`t talk about limits and put the infinite series talk with summation notation.
Male 25,416
meh...
Male 259
_
NERD
Male 57
@tedgp 0.333 REPEATING
Male 3,285
@lily

If .333 repeating and 1/3 are the same, then 1 and .999 repeating can also be considered the same.

Read what you wrote. They arent the same. 0.33333 is NOT 1/3.
Male 3,285
0.999- can never equal 1. It can come really close but because of a fundamental flaw in the math system it can never truly equal 1.
Male 72
... OWWWW!!! My braaaiiinnn!!!
Male 40,764
[quote]5cats posted something that`s not political and doesn`t suck?[/quote]
I submit lots of variety @LazyMe, idk why many AWESOME non-political offerings are refused, but some so-so political ones get accepted...
... sometimes it`s because multiple people suggest the same thing, eh?
Male 1,832
I really only watch these because her writing in super speed looks so cool.
Male 813
Its interesting, but video`s like this are actually quite harmful (even dangerous) because they teach kids to make assumptions that are 100% wrong. If for example a programmer is writing a program that does a calculation with the fraction 1/3 one trillion times a second and he uses a 32 bit floating point consisting of 0.3333... because he thinks they are the same instead of programming the computer to do the fractional math "human style" (the same type you would do it on paper.. 1/3 + 1/3 = 2/3 using a numerator and denominator), his program will NOT work properly. It will actually become horribly inaccurate quite fast because of the amount of calculations being performed per second. The sad thing is that this has actually happened in advanced engineering design tools a number of times because people are taught stupid things like this.
Female 90
"LilyLily, 1/3 is an exact representation. 0.3333 repeating does not equal 1/3, it never can, it is simply the easiest way to represent 1/3 so people can understand and learn fractions. In modern engineering/science it is often considered the same because no one needs sig figs that go out to infinity (usually). But to say they are equal is theoretically incorrect."

Hence why I say `can be considered` (ie, assuming this is 100% correct, I don`t claim to be a mathematician by a long shot) :| it`s an interesting theory regardless.
Male 813
LilyLily, 1/3 is an exact representation. 0.3333 repeating does not equal 1/3, it never can, it is simply the easiest way to represent 1/3 so people can understand and learn fractions. In modern engineering/science it is often considered the same because no one needs sig figs that go out to infinity (usually). But to say they are equal is theoretically incorrect.
Male 813
Uh no, 0.999... repeating does not equal 1. Obviously the more 9`s you use the closer it will get to 1, but it will always be some infinitesimally small value less than 1 as you approach infinity.

Depending on the application, like software that does repeated number calculations, making an assumption like this could screw up your program over time.
If you are on a 64 bit OS and need resolution beyond a 64 bit floating point, than sure you could use 1 because it would technically be more accurate in the long run (rounding up). It would still be inaccurate though. However if for example the number is 0.9999 up to 63 bits and then stops, then you would not want to use just 1 because that would cause you to be less accurate than you could have been by using the exact number.
Female 90
--Still finished high school maths and now in uni still take some maths subjects, but that whole sense of wonder and stuff is gone. It`s why I like Vi`s videos, kind of brings that back and shows you the proofs behind these concepts.

No 8 was what got me too

1/3 =.333 repeating

1/3 x 3 = 1
.333repeating x 3= .999 repeating

If .333 repeating and 1/3 are the same, then 1 and .999 repeating can also be considered the same.

(On a side note, it`s good how she shoes multiple proofs and explanations too, thats a good teaching strategy, we use similar with primary kids, showing multiple proofs and such since we all learn in different ways)

LONG POST OUT.

(TL;DR enjoyment)
Female 90
Actually I also remember we also did something similar to that video of Vis with the flowers and such for the Fibonacci sequence outside with random flowers and stuff we found (and some stuff the teacher bought in) though still a mathematical proof I guess, counting the numbers and such, seeing it in the natural world shown us that this stupid thing we needed to learn actually does exist, and is not just a human made concept. Was an awesome feeling, especially since I had a huge interest in biology and the natural world, so I found it fascinating when usually I would HATE maths with a passion.

Since a lot of other stuff we learnt would build off these basic theories we had explored and proven in non mathematical ways we really got it an the theory behind it.

He was the best teacher. I had him for year 7 and 8, but in year 9 we had some guy with a thick accent and terrible teaching skills, and I understood nothing.--
Female 90
I`m not even going to get into it because it blows my mind how maths works (I like vi`s videos very much actually)

Dave
One of my yr 7 teachers game me an explanation about maths that sticks with me still. It was something like maths is a theory "Hey guys I have something to explain all this and it seems to fit, lets try it out" and future theories and discoveries may prove that wrong or right. Most maths has been proven `right` that many times over since we first started this concept of numbers that it`s basically concrete. He also liked to show us non mathematical proofs, which I liked a lot (I loved the theory behind it, but I could never really grasp it so seeing it in action without all the equations/ie a non maths proof really made it click in my head). I remember him showing us a non mathematical proof or Pythagorean theory using triangle tiles, essentially proving Pythagorean theory without numbers. It was awesome.
Male 10,440
5cats posted something that`s not political and doesn`t suck? I didn`t predict this. The streak is broken! Somehow 5cats is becoming more sane, maybe.
Male 40,764
@Langer: Aaag! Why did I click that??? (lolz!)

Also: I`m sure he says `whore` and `bored` randomly in place of `four`...
Male 40,764
@LuckyDave: Proof #8: 1/3 = .333_ (repeating)
1/3 + 1/3 + 1/3 = 1
Get it? Substitute .333_ with 1/3 (because they`re equal) and presto! .999_ = 1

Proof! Math-wise.

[quote] and you should be able to find another number til infinity that`s closer...[/quote]
You need to understand Zeno of Elea better... he`s my favorite philosopher!
Male 3,332
I <3 V <3
Male 3,482
@LuckyDave

People said the same things about imaginary numbers at first, but now they`re essential to many of our daily routines.

You "make up" numbers when "normal" numbers just won`t cut it.
Male 675
So, let me get this straight, the whole point of math is to invent numbers? Great, here`s my number: Ghet. It is a whole number and it goes in between six and seven. Don`t think that`s possible? I`ll invent a math system called FART (an acronym meaning For All Retarded Tarts) and it will work. At least that`s the idea I`m getting here.
Bear with me for a second and let me try and reason something here. The basic concept I`m getting here is that using infinity, a number she herself says is imaginary and doesn`t exist, proves that .9999~ mathematically equals 1 because nothing comes closer to 1 than .9999~ and you should be able to find another number til infinity that`s closer... I`ll let you pick that one apart from there.
By the way, they`re 95% sure the Higgs Boson particle doesn`t exist. Meaning we`d have to pretty much reinvent physics as we know it and these "split octonians" wouldn`t explain jack anymore. Guess they`ll have to "invent" more numbers...
Male 77
So she proves that 0.999... is not a real number and cannot = 1 and claims that as proof that it does??
epic facepalm time
Male 39,931

`cause it rounds up.

DUH !
Male 3,648
I love the Lord of the Flies reference that I doubt many people will get.
Male 399
<clickie> -_-
Male 319
WITCH!
Male 40,764
Link: Vi Hart: How 0.999 repeating = 1! [Rate Link] - Proof #8 made my brainz explode!