Solutions Algebra

Let [ n ] be the set { 1,2,3,..,n }. Show that for any set X there is a bijective function {{X

Question: Let $\left[ n \right]$ be the set $\left\{ 1,2,3,..,n \right\}$ . Show that for any set X there is a bijective function

{{X}^{\left[ n \right]}}\to \underbrace{X\times X\times ...\times X}_{\text{n times}}

where ${{X}^{\left[ n \right]}}$ is the set of all functions from [n] to X.

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