# Existence of a bijective function

There exists a bijective function that when expressed as a subset of the Cartesian product has exactly 10,000 elements.

I think to the solution is: let $$A=\{1,2,3,...,10000\}$$ and $$B=\{2,3,4,...,10001\}$$ then if i define $$f:A \rightarrow B$$ like $$f(n)=n+1$$ is clear than $$f$$ is a bijection and $$|f|=10,000$$ but im not sure. Every suggestion or hint i will very grateful.

• Seems fine. Any bijection between sets of cardinality $10000$ should work. The identity function on $\{1, 2, \ldots, 10000\}$ would also work, for example. Apr 20 at 4:42