Unformatted text preview: + β . As (rearranging) z-β < α , there exists a ∈ A such that z-β < a (recall that α = lub A ). As (rearranging) z-a < β , there exists b ∈ B such that z-a < b (recall that β = lub B ). The resulting inequality z < a + b shows that z is not an upper bound of S . (iii) Though nonempty, P need not be bounded above: indeed, A and B may contain arbitrarily large negative numbers. 1...
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- Fall '08
- Empty set, Supremum, upper bound, lub