# 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

$\blacksquare$