1 + 2 + 3 + 4 + 5 + ... = -1/12

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19 Jan 2014 04:46 - 19 Jan 2014 04:46 #133822 by Lykeios Little Raven
Replied by Lykeios Little Raven on topic 1 + 2 + 3 + 4 + 5 + ... = -1/12

Br. John wrote: Maybe OMNI will throw us a bone and make copies for everybody.

It already has. ;) Love ya brotherXsisterS
“Now I do not know whether I was then a man dreaming I was a butterfly, or whether I am now a butterfly, dreaming I am a man.” -Zhuangzi

“Though, as the crusade presses on, I find myself altogether incapable of staying here in saftey while others shed their blood for such a noble and just cause. For surely must the Almighty be with us even in the sundering of our nation. Our fight is for freedom, for liberty, and for all the principles upon which that aforementioned nation was built.” - Patrick “Madman of Galway” O'Dell
Last edit: 19 Jan 2014 04:46 by Lykeios Little Raven.

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20 Jan 2014 05:43 - 20 Jan 2014 05:47 #134001 by ren
Replied by ren on topic 1 + 2 + 3 + 4 + 5 + ... = -1/12

Br. John wrote: They show here there are not more numbers between 0 through 2 than there are between 0 through 1; they're the same. But there are more numbers between 0 through 1 than there are of all positive integers. 1,2,3,4,5 ... .


He doesn't prove that. What he discusses is "counting infinity". Natural numbers are countable. real numbers (except for the infinite "few" that are naturals) are not countable.

In fact, all the real numbers between 0 and 1 (which have a decimal representation) can have an "equivalent" natural number... that's how computers actually "write" numbers (in memory). And the notation is generally shorter:

0.00165432 has 23456100

if you take any real, the same can be done:

345.6789 becomes 9876543

For sumbers with no decimal representation it's a bit complicated because there is to my knowledge no way in maths to represent an infinite natural number. But in programming it is possible.
Convictions are more dangerous foes of truth than lies.
Last edit: 20 Jan 2014 05:47 by ren.

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20 Jan 2014 12:33 #134024 by Gisteron
Replied by Gisteron on topic 1 + 2 + 3 + 4 + 5 + ... = -1/12
http://www.youtube.com/watch?v=v-pyuaThp-c
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