## Posts

Showing posts from January, 2018

### Contrapositive, contradiction and construction: common proof methods

In this post we will talk about three different, all very common, ways of making proofs: contrapositive, contradiction and construction.

Construction:
A good example of a proof by construction is the proof that every function $f: \mathbb{R}\to\mathbb{R}$ can be decomposed into a sum $f(x) = O(x) + E(x)$ where $O(x)$ is an odd function and $E(x)$ is an even function, i.e.
$$\begin{cases}O(-x) = -O(x)\\ E(-x) = E(x)\end{cases}\ \forall x \in \mathbb{R}$$