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Old 10-29-2014, 03:08 PM   #1
tyconger191
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Default The Positive Thread

If you look long and hard enough you will find something that will make you happy. Whether it be a serious relationship or a great hobby.
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Old 10-29-2014, 04:26 PM   #2
seamonkey
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Default Re: The Positive Thread

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 ... = -1/12

OH SNAP. Even the most positive of things is negative.

(I'm so sorry, but teh funniez)
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Old 10-30-2014, 12:52 AM   #3
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Default Re: The Positive Thread

Quote:
Originally Posted by seamonkey View Post
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 ... = -1/12

OH SNAP. Even the most positive of things is negative.

(I'm so sorry, but teh funniez)
Uhm, how in the world is that equal to negative -1.12?
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Old 10-30-2014, 12:08 PM   #4
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Default Re: The Positive Thread

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Originally Posted by REACTOR View Post
Uhm, how in the world is that equal to negative -1.12?
It's a lot of really advanced and complicated math, and I understand about a third of it. I'm just going to drop a wikipedia link and let you sift through it http://en.wikipedia.org/wiki/1_%2B_2..._%2B_%E2%8B%AF

One more thing: this isn't just some random result as part of weird math that has no applicability. This equation literally shows up in quantum mechanics textbooks.
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Old 10-30-2014, 03:52 PM   #5
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Default Re: The Positive Thread

It comes from the same math that makes 1 - 1 + 1 - 1 + 1 - 1 + ... = 1/2.

You then do 1 - 2 + 3 - 4 + 5 - 6 + ... = 2 * (1 - 1 + 1 - 1 + 1 - 1 + ...) = 1/4.

and then you have 1 + 2 + 3 + 4 + 5 + 6 + ... - 1 - 2 + 3 - 4 + 5 - 6 + ... = 4 + 8 + 12 + 16 + ... = 4*(1 + 2 + 3 + 4 + 5 + 6 + ...) => -1/4 = 3*(1 + 2 + 3 + 4 + 5 + 6 + ...) => 1 + 2 + 3 + 4 + 5 + 6 + ... = -1/12.

That's the best I can do in explaining it. This was taken from the numberphile video on the subject, which I can post because youtube.
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Old 10-30-2014, 06:27 PM   #6
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Default Re: The Positive Thread

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Originally Posted by Megadog View Post
It comes from the same math that makes 1 - 1 + 1 - 1 + 1 - 1 + ... = 1/2.

You then do 1 - 2 + 3 - 4 + 5 - 6 + ... = 2 * (1 - 1 + 1 - 1 + 1 - 1 + ...) = 1/4.

and then you have 1 + 2 + 3 + 4 + 5 + 6 + ... - 1 - 2 + 3 - 4 + 5 - 6 + ... = 4 + 8 + 12 + 16 + ... = 4*(1 + 2 + 3 + 4 + 5 + 6 + ...) => -1/4 = 3*(1 + 2 + 3 + 4 + 5 + 6 + ...) => 1 + 2 + 3 + 4 + 5 + 6 + ... = -1/12.

That's the best I can do in explaining it. This was taken from the numberphile video on the subject, which I can post because youtube.
Except that numberphile screwed it up. Adding and multiplying infinite series that diverge isn't something that is allowed.
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Old 10-30-2014, 09:03 PM   #7
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Default Re: The Positive Thread

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Except that numberphile screwed it up. Adding and multiplying infinite series that diverge isn't something that is allowed.
They write it out the same way it's written on wikipedia (s = 1 - 1 + 1... = 1/2). I just didn't want to have to assign variables in an otherwise simple explanation...

EDIT: It mentions that this is not entirely appropriate on the wiki page, and goes on to do other proofs. Still, my attempt was first and foremost to explain why it's possible, and not to give a proof I can't understand.
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Old 10-30-2014, 09:14 PM   #8
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Default Re: The Positive Thread

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Originally Posted by Megadog View Post

EDIT: It mentions that this is not entirely appropriate on the wiki page, and goes on to do other proofs. Still, my attempt was first and foremost to explain why it's possible, and not to give a proof I can't understand.
Fair enough. My only argument was that regardless of assigning variables this proof doesn't hold up because it breaks to rules. But you got that.
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