How do I prove the function $\theta$ is injective, surjective, and bijective, if any of these?
2026-04-04 04:37:13.1775277433
Consider the function $θ:\{0,1\}×{\Bbb N}→{\Bbb Z}$ defined as $θ(a,b)=(-1)^{a}b$
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$0$ is not in the range so it is not surjective. Can you see that it is injective? Hint: if $\theta (a,b)=\theta(a',b')$ take absolute value on both sides to prove that $b=b'$ and then prove that $a=a'$.