power of 9

I learned a nifty, i mean really NIFTY trick in accounting class last night. ohh.. and by the way, kev, I got new respect for your 'business' degree. this accounting stuff is crazy! I thought senior engineering class was hard, these acocuntants go to EXTREME measures of 1940's style book keeping to keep from using a negative sign. and i'm not just talking aobut using parenthesis to designate negative, i'm talking about these guys hate negative!

ok..... have you guys heard of the divisible by 9 trick? turns out if you are summing two columns and the numbers dont' equal, if the difference is evenly divisble by 9, then you transposed some numbers.

I know you can't officially prove anything by example, but i'll give you an example
123 213
34 34
56 56
77 77
-- --
290 380

dif=90
90/9 = 10

I played around with it a bunch in class and i can't quite figure out why it works. jen, see if you can puts your sets class to work and prove it for us!

--palegreenhorse---
yup topology was useful because it taught me to write better proofs. =) click on the image to see the full proof (a simple one and a generalized on that shows any two numbers switched, they don't have to be adjacent). sorry 'bout the quality... is a really nice pdf, but didn't take the time to convert to a higher quality png or something, just used print screen.