Logic & Proof – 1

< 29.1 Euclid &amp; Logical Thinking | Topic Index | 29.3 Logic &amp; Proof – 2 >

To get a taste of logical thinking and the idea of proof, we will take 2 proofs by Euclid, one from number theory and another from plane geometry.

In number theory, we will take up Euclid&rsquo;s proof that is not a rational number. He uses an argument which in today&rsquo;s language is called a &ldquo;proof by contradiction&rdquo;. Euclid assumes that 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.

Every step of the argument leads logically to only one conclusion which is next step. This continues till the conclusion is reached. This series of statements is called the proof.

< 29.1 Euclid &amp; Logical Thinking | Topic Index | 29.3 Logic &amp; Proof – 2 >