Question

Show that A=B
A = {1,2,3}
B ={n|n∈Z+ and n^2<10}

Answer 1

Let $A =\{1,2,3\}$ and $B =\{ n\in \mathbb Z_+\ |\ n^2<10\}$.

Let us solve the inequality $n^2<10$ for $n\in \mathbb Z_+$. It followst that $|n|<\sqrt{10}$ and therefore,$n\in(-\sqrt{10},\sqrt{10})\cap\mathbb Z_+=\{1,2,3\}.$ It follows that $A=B.$