Theorems – Squares

The theorems of squares are derived from the theorems in Axioms for Real Numbers as interpreted for Wave Numbers.

1. For every a, a² ≥ 0
2. a² = 0 if and only if a = 0
3. a² > 0 if a ≠ 0
4. (^–a)² = ^–a*^–a = a*a =    a²
5. R1 and R2:  (a^-1)² = 1^{^}/a²
6. R3: (a^-1)² = 1‡a^‡a/a²
7. R1 and R2:  if a² = b², then a = b or a = ^–b
8. R3: if a² = b², then a = b
9. If  a < b ⇒ a² < b²

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