# Ordering of Squares in Reals

From ProofWiki

## Contents

## Theorem

### Square of Real Number is Positive

Let $x \in \R$.

Then:

- $0 \le x^2$

### Real Number between Zero and One is Greater than Square

Let $x \in \R$.

Let $0 < x < 1$.

Then:

- $0 < x^2 < x$

### Real Number Greater than One is Less than Square

Let $x \in \R$.

Let $x > 1$.

Then:

- $x^2 > x$