Exercise 13 (Homework 1).
(induction proof)
Easy induction
Let f: {\mathbb N} \rightarrow \mathbb N be a function such that f(x+y) = f(x)+f(y) for any x, y \in \mathbb N. Prove that for any x \in \mathbb N, f(x) = f(1) \cdot x.
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Easy induction
Let f: {\mathbb N} \rightarrow \mathbb N be a function such that f(x+y) = f(x)+f(y) for any x, y \in \mathbb N. Prove that for any x \in \mathbb N, f(x) = f(1) \cdot x.