hartnn
  • hartnn
inverse of mod function? like y= x mod p, 1=5 mod 2 how do i get 5 from {1,2}
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
doesnot exist as inverse only possible for one-one function
anonymous
  • anonymous
y=|x| ? inverse of this will not be a function
anonymous
  • anonymous
inverse exist x=|y| but its not a function

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ganeshie8
  • ganeshie8
mod is not 1-1 function
anonymous
  • anonymous
modulus is a many-one function hence it's inverse not possible
hartnn
  • hartnn
c= a mod b = -> corresponds to
anonymous
  • anonymous
NO PROBLEMAS SENIOUR @hartnn ! Let B be the set of ordered pairs of pairs-of-numbers, in other words pairs of points in the plane: \[ b \in B \,\,\iff b=(P_1, P_2) \] then the inverse function of \[Abs^{-1}(y) = ((y,y),(y,-y)) \] and a medal , naturally. forgive my humbleness...
hartnn
  • hartnn
whats and how ? \(Abs^{-1}(y) = ((y,y),(y,-y))\)
hartnn
  • hartnn
if i have y=x mod 7, how would i find its inverse ?
anonymous
  • anonymous
The Abs is of course |x| not the algebraic coincidence of names.
hartnn
  • hartnn
i eas talking about remainder
hartnn
  • hartnn
like 5 mod 2 is 1
anonymous
  • anonymous
if modulus is with only number then it is one-one and inverse will exist
anonymous
  • anonymous
x = sgn(x) .|x|
anonymous
  • anonymous
Anyway also for remainder possible to invert \[ mod:\,r_{Ideal} \rightarrow r \\ mod^{-1}: r \rightarrow r_{Ideal}\]
anonymous
  • anonymous
and a , the action that should not be asked but anyway received :)
hartnn
  • hartnn
but i didn't understand....
anonymous
  • anonymous
thx oh exalted one !
anonymous
  • anonymous
Learn about Ideals even if you dont have them :) http://en.wikipedia.org/wiki/Ideal_(ring_theory)
anonymous
  • anonymous
MEdals, Medals gentleman for the wondering scholar ....! Keep them falling !
hartnn
  • hartnn
hmmm...didn't study ideals, i'll go through them, thanks
anonymous
  • anonymous
Everybody that did - pls gratify
anonymous
  • anonymous
i think the question is maybe something different, are you asking how do you solve \[x\equiv y (mod n)\] for \(y\) if you know \(x\) ?
hartnn
  • hartnn
yes, i wrote somewhere in between = -> correcponds to
anonymous
  • anonymous
If that was the question I would not solve it - but it was not!
anonymous
  • anonymous
so for example solve \( 5\equiv x\text{ mod } 3\)
anonymous
  • anonymous
No uniqueness - only an IDEAL OF ANSWERS
hartnn
  • hartnn
there are many (or infinite ?) values of x in 5=x mod 3 ??
anonymous
  • anonymous
Yes - they form an IDEAL
anonymous
  • anonymous
ideals live in arbitrary rings, and are not necessary for understanding elementary number theory
anonymous
  • anonymous
Anyway the set pf answers here IS an Ideal.
anonymous
  • anonymous
By the way the only proper way to make equivalence necessary for "REMAINDER CALCULUS" is bu using ideals. Elementary - well yes.
hartnn
  • hartnn
ok, thank you @Mikael i'll go through IDEALS and ask u if i have any doubts. thanks to @satellite73 also :)
anonymous
  • anonymous
Firstly is the "cyclical group". It will give you the applications. Only then that. This takes you further
hartnn
  • hartnn
any good reference for such things(other than wikipedia) where these things are explained in lucid manner ?
anonymous
  • anonymous
http://en.wikipedia.org/wiki/Modular_arithmetic
anonymous
  • anonymous
1 mathdl.maa.org/images/upload_library/22/Polya/Brenton.pdf en.wikipedia.org/wiki/Elementary_group_theory math.uc.edu/~hodgestj/Abstract%20Algebra/GroupTheory512.pdf www.rowan.edu/.../Some%20Elementary%20Group%20Theory.pdf
hartnn
  • hartnn
because of those ... i cannot get the reference
hartnn
  • hartnn
only last one i couldn't get
anonymous
  • anonymous
Just ggle "elementary remainder group theory"

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