Sciencemadness Discussion Board

1+2+3+... = -1/12 ?

condennnsa - 20-1-2014 at 08:15

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?

DraconicAcid - 20-1-2014 at 08:29

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.

bfesser - 20-1-2014 at 08:44

<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" />

blargish - 20-1-2014 at 15:45

Numberphile is awesome!

They made a pretty interesting video about Grandi's Series a while back.

http://www.youtube.com/watch?v=PCu_BNNI5x4

Illusionist - 12-4-2014 at 16:25

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]

ElizabethGreene - 12-4-2014 at 19:58

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.

smaerd - 13-4-2014 at 06:09

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.