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we also learned that if a divides bc, then a divides bcn ..... 30 minutes of my life gone :/
Believe it or not, that's not inherently obvious. Depending on what structures you're using, if a doesn't divide b, but a does divide bc, it doesn't necessarily divide c.
number theory ... :)
mattrix algebra has quirks in that its .. cant recall. ring, field, group ??
Number theory is an easy example, but you can define a ring with zero divisors, and suddenly, if ab=0, then neither a nor b must be 0.
o.o show me the logic!
teacher did show us at the begining of the year about her thesis work on abstract algebra and made us write up Zmod 12 tables for addition and multiplication
Zmod12 is a nice example. 2*6=0=3*4
No that's not helpful I don't understand zmods lool
2*6 mod 12=0 If you understand modular multiplication, it's what you would imagine Zmod12 would be.
if a not| b; the (a,b)=1; therefore 1 = ax+by multiply each side by c c = acx+bcy a|acx a|bcy , it was given in the thrm that a|bc therefore a | (acx+bcy) a | c
all the 0 mod 12s have no recipricals :)
.... er, no multiplicative inversai
I look at wikipedia and see funny symbols. http://en.wikipedia.org/wiki/Modular_arithmetic I quit this party.
There must be some way out of here, said the joker to the thief. There's too much confusion ... I can't get no relief
Well, if it's coprime to 12 it has a multiplicative inverse....