On 27/07/2015 10:19 AM, scott wrote:
> s= 1+2+3+4+5+6+...
>
> s = -1/12
>
> Crazy huh?

If you think that's mad, watch this:

   10 + 4 = 2

   2 / 5 = 10

Wait, whaaat?!

Well now, let's try that again. If the time is currently 10 PM, then 
what time will it be in 4 hours' time? Hint: not 14 PM.

In "normal" arithmetic, claiming that 10 + 4 = 2 is just flat wrong. But 
change your definitions (say, to agree that after counting past 12 we go 
back to 1 again), and suddenly this makes a whole lot of sense, and is 
"useful" in that billions of people do this exact type of calculation 
all over the world every single day. It doesn't get much more 
"practical" than that.

To convince yourself that 2 / 5 = 10, start at 12 o'clock, and keep 
adding on 5 hours until you land on 2 o'clock. I promise you, it takes 
10 steps to do this. Hence, 5 * 10 = 2, and therefore surely 2 / 5 = 10.

This latter type of shenanigans is mostly used in cryptography and 
number theory, but does also pop up in places like error-correcting 
codes. (If you've ever tried to scan a bar code or play a CD, you care 
about error-correcting codes.)

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