# Ordering of Squares in Reals

## Theorem

### Square of Real Number is Non-Negative

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:

$x^2 > x$