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.

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


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