Monday 28 October 2013

elementary set theory - Show a bijection between sets

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 !!

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