Logic & Proof – 1

To get a taste of logical thinking and the idea of proof, we will take a proof by Euclid, from number theory. This is considered the first proof in the field of math.

In number theory, we will take up Euclid's proof that √2 is not a rational number. He uses an argument which in today's language is called a "proof by contradiction". Euclid assumes that √2 can be expressed as a rational number and then shows that this assumption leads to a contradiction of the original assumption. Let us study this proof presented in a standardized format.