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doesnot exist as inverse only possible for one-one function

y=|x| ?
inverse of this will not be a function

inverse exist x=|y| but its not a function

mod is not 1-1 function

modulus is a many-one function hence it's inverse not possible

c= a mod b
= -> corresponds to

whats and how ?
\(Abs^{-1}(y) = ((y,y),(y,-y))\)

if i have y=x mod 7, how would i find its inverse ?

The Abs is of course |x| not the algebraic coincidence of names.

i eas talking about remainder

like 5 mod 2 is 1

if modulus is with only number then it is one-one and inverse will exist

x = sgn(x) .|x|

and a , the action that should not be asked but anyway received :)

but i didn't understand....

thx oh exalted one !

Learn about Ideals even if you dont have them :)
http://en.wikipedia.org/wiki/Ideal_(ring_theory)

MEdals, Medals gentleman for the wondering scholar ....! Keep them falling !

hmmm...didn't study ideals, i'll go through them, thanks

Everybody that did - pls gratify

yes, i wrote somewhere in between
= -> correcponds to

If that was the question I would not solve it - but it was not!

so for example solve \( 5\equiv x\text{ mod } 3\)

No uniqueness - only an IDEAL OF ANSWERS

there are many (or infinite ?) values of x in 5=x mod 3 ??

Yes - they form an IDEAL

ideals live in arbitrary rings, and are not necessary for understanding elementary number theory

Anyway the set pf answers here IS an Ideal.

http://en.wikipedia.org/wiki/Modular_arithmetic

because of those ... i cannot get the reference

only last one i couldn't get

Just ggle "elementary remainder group theory"