Minus One is Less than Zero

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Theorem

$-1 < 0$


Proof

\(\displaystyle 0\) \(<\) \(\displaystyle 1\) Real Zero is Less than Real One
\(\displaystyle \leadsto \ \ \) \(\displaystyle -0\) \(>\) \(\displaystyle -1\) Order of Real Numbers is Dual of Order of their Negatives
\(\displaystyle \leadsto \ \ \) \(\displaystyle 0\) \(>\) \(\displaystyle -1\) Negative of Real Zero equals Zero
\(\displaystyle \leadsto \ \ \) \(\displaystyle -1\) \(<\) \(\displaystyle 0\) Definition of Dual Ordering

$\blacksquare$


Sources