Let $A$ and $B$ be the two sets, such that $|A|=|B|$. There is a one to one function from $f:A\to B$.
Which of the following must be true about function $f$ ?
- $f$ is an onto function.
- $f$ has an inverse.
According to me, both are false if $A$ and $B$ are countable infinite set of Natural numbers.
So suppose, If there exists a function $f(i) = i^2$.
Well, in this case onto not possible which implies bijection not possible, hence no inverse possible .
But, I need some confirmation for my try .