Ordering of Squares in Reals

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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:

$x^2 > x$