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## Homework Statement

How many functions are there from {1,...,n} to {0,1}? and prove.

## The Attempt at a Solution

For any k in {1,...,n} we can map k to either 0 or 1. So for any k there are two possible images. Since there are n kinds of k (from 1 to n) then there are 2^n possible functions

I'm not sure how to formally prove this, or what kind of proof to use at least.