There exists a map $f: \Bbb Z\rightarrow \Bbb Q $ such that $f$ is
A. Bijective and increasing
B. Onto and decreasing
C. Bijective and satisfies $f(n)\ge 0$ if $n\le 0$
D. Has uncountable images
Now option D. is absurd . Option C. is given to be the correct answer.I was thinking since both sets are countable bijection is obvious. Now why cannot be increasing ? I could map $0$ to $0$ and the negative integers to the negative rationals and positive integers to the positive rationals. And if increasing would be possible just interchanging signs would give the decreasing map. So none is possible but why?