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Vi Hart: How 0.999 repeating = 1!

Proof #8 made my brainz explode!

submitted by: 5Cats
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Vi Hart: How 0.999 repeating = 1!. Proof #8 made my brainz explode!
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Hits: 8478 | Favorites: 6 | Emailed: 1 | Rating: 2.5 | Category: Science | Date: 03/31/2012
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Female, 18-29, Eastern US
 259 Posts
Friday, April 6, 2012 11:10:48 PM
I'm able to identify all the Lords except the first, second, and fifth. Who are they?

Male, 18-29, Western US
 17 Posts
Monday, April 2, 2012 9:51:12 AM
She must spend thousands on sharpies.

Male, 18-29, Southern US
 331 Posts
Sunday, April 1, 2012 10:03:34 PM

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, 18-29, Eastern US
 724 Posts
Sunday, April 1, 2012 2:40:08 PM
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, 18-29, Canada
 4012 Posts
Sunday, April 1, 2012 2:14:24 PM
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

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