The question is: prove that there is a bijection between sets A and B for all $n_{1}, n_{2}\in \mathbb N_{> 0}$ and for all $k_{1}, k_{2}\in \mathbb{Z}$

$A = \left\{ {n_{1}q + k_{1}} \mid q\in \mathbb{Z}\right\}$,

$B = \left\{ {n_{2}q + k_{2}} \mid q\in \mathbb{Z}\right\}$

Any help to define the function between both sets is appreciated !!

  • 2
    $\begingroup$ What are your thoughts so far? Have you tried some candidates? $\endgroup$ – T. Eskin May 1 '14 at 23:35

HINT: Try to find a bijection of $A$ with $\Bbb Z$, for a concrete pair of $n,k$ (for example $n=2$ and $k=1$). Then try to see how that would generalize to a bijection between $A$ and $B$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.