Introduction We have learned that is irrational and thousands of sites on the internet will show you the proof that is irrational. In this post, we show that is irrational. This is a prerequisite for the next post which will show that is irrational. You will probably argue that since is irrational and is irrational, […]

Continue reading…

# Numbers

## The Transitivity of Whole Numbers

Introduction The less than relation is an order relation of real numbers. In this post, however, to prove one of its properties, we limit it to the set of whole numbers. In the set of whole numbers, is less than , or in symbol, if and only if there exists a whole number such that . For […]

Continue reading…

## Proof that Square Root of Three is Irrational

Introduction In The Intuitive Proof of the Infinitude of Primes, I showed you a proof strategy called proof by contradiction. In this post, we use this strategy to prove that is irrational. In proof by contradiction, if the statement P is true, you have to assume the contrary, and then find a contradiction somewhere. Note […]

Continue reading…