# Real Zero is Less than Real One

## Theorem

The real number $0$ is less than the real number $1$:

$0 < 1$

## Proof

 $\displaystyle 1 \times 1$ $>$ $\displaystyle 0$ Square of Non-Zero Real Number is Strictly Positive $\displaystyle \implies \ \$ $\displaystyle 1$ $>$ $\displaystyle 0$ Real Number Axioms: $\R M3$: Identity $\displaystyle \implies \ \$ $\displaystyle 0$ $<$ $\displaystyle 1$ Definition of Dual Ordering

$\blacksquare$