Proof Methods - Mathematical and Statistical Sciences
Contradiction Proof Example: The √2 is irrational. Pf: BWOC assume that √2 is rational. There exist integers p and q so that √2 = p/q. We may assume that the fraction is reduced, i.e. no integer divides both p and q. 2 = p2/q2 ⇒ 2q2 = p2, so p2 is even. Thus, p is even. Definition: A real number r is rational iff it can be written as r ...
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Higher Geometry - Mathematical & Statistical Sciences
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www-math.ucdenver.edu1) a is an upper bound for B, and 2) a R x for every upper bound x for B. Example: Reals with the usual ordering. B = {x | 5 < x < 7 } 8, 7.5, 11, 7.00001 are all upper bounds of B. 7 is also an upper bound, and 7 ≤ any of the upper bounds, so 7 …
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