Unformatted text preview: . On the other hand, assume a 2 + b 2 = 0. If a 6 = 0 and b 6 = 0, then a 2 > 0 and b 2 > (Thm. 2.1.8). By the Ordering Properties, it follows that a 2 + b 2 > 0. Thus, we don’t have that both are nonzero. If either a 6 = 0 or b 6 = 0 but not both, then say without loss that a 6 = 0 but b = 0. Then a 2 + b 2 = a 2 + 0 2 = a 2 + 0 = a 2 > 0. This again is not possible. The only remaining case is when a = 0 and b = 0, which we showed satisﬁes the desired result. 1...
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 Spring '10
 MetCalfe
 Calculus, Logic, Irrational number, Ordering Properties

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