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**jackprestonuk** Hi, I've been asked to show the following assertion;

$\displaystyle {|A|}^2 = |A| > 1 \rightarrow 2 \cdot |A| = |A| \wedge {|A|}^{|A|} = 2^{|A|}$

I've managed to show the $\displaystyle 2 \cdot |A| = |A|$ part, but I'm having trouble with the next part, the $\displaystyle {|A|}^{|A|} = 2^{|A|}$. Am I right in thinking that $\displaystyle {|A|}^{|A|}$ is the number of functions $\displaystyle A \rightarrow A$, and is this on the right lines, or am I looking way off?

Any help would be appreciated!