My textbook states the following proposition: Let $f:R \rightarrow S$ be a ring homomorphism and let $s$ be in the image of $f$. Then $\{r \in R \mid f(r) = s\}$ is in one-to-one correspondence with $\ker(f)$.
What does it mean to have one to one correspondence with $\ker(f)$? Does it mean the set $\{r \in R \mid f(r) = s\}$ and the set $\ker(f)$ have the same cardinality?
Thanks!