Real Zero is Less than Real One

From ProofWiki
Jump to navigation Jump to search

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

$\blacksquare$


Sources