condennnsa
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1+2+3+... = -1/12 ?
So I've been browsing around and found this youtube video: http://www.youtube.com/watch?v=w-I6XTVZXww
It comes from Numberphile , a highly respected channel making interesting videos on mathematics.
what do you think?
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DraconicAcid
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It's not actually the sum, but Reinmann function, or something like that. You can't add a bunch of positive natural numbers and get a negative
number.
Please remember: "Filtrate" is not a verb.
Write up your lab reports the way your instructor wants them, not the way your ex-instructor wants them.
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bfesser
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<a href="http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%C2%B7_%C2%B7_%C2%B7" target="_blank">1 + 2 + 3 + 4 + ⋯</a> <img
src="../scipics/_wiki.png" />
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blargish
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Numberphile is awesome!
They made a pretty interesting video about Grandi's Series a while back.
http://www.youtube.com/watch?v=PCu_BNNI5x4
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Illusionist
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Mathematics are awesome.
I am currently attending pre-uni so i am definitely going to ask my integral calculus teacher about this summation.
I don't see yet how adding all those positive numbers can give a negative sum.
[Edited on 13-4-2014 by Illusionist]
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ElizabethGreene
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Note: I haven't watched the video, just sharing interesting trivia.
Back when the signed int datatype in C was only 8 bits, a pretty common error was to stuff too much in it which flipped it into a negative number.
i.e. the output from
#include <stdio.h>
main () {
for(int i=0;i++;1) {
printf("(d) \n");
}
}
This prints out the following.
1
2
3
....
125
126
127
-128
-127
....
-2
-1
(crash)
Adding up all of these numbers would add up to -128.
The reason why is that this particular datatype used 7 bits to store the numeric data, and the final (most significant) bit was used to store the sign
information. Adding 1 to 127 flipped the sign but and magically turned it into a negative number.
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smaerd
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I also have seen this and found it a bit befuddling. Supposedly they have used this 'trick' in the development of String Theory. Kinda weird.
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