Solution to Compute the number of functions f from the set {0,1,2,...; n} (where n is a … - Sikademy
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Archangel Macsika

Compute the number of functions f from the set {0,1,2,...; n} (where n is a positive integer), to the set {0,1}.

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Let us compute the number of functions f:\{0,1,...,n\}\to\{0,1\}. For each k\in\{0,1,...,n\} for the value f(k) there are two possibility: f(k)=0 or f(k)=1. Since the cardinality of the set \{0,1,...,n\} is n+1, by Multiplication Principle the number of all functions is

\underbrace{2\cdot 2\cdot ...\cdot 2}_{n+1}= 2^{n+1}.


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