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Unformatted text preview: Q , this is equivalent to: Let x > 0. Given any ε (no matter how small), ∃ y ∈ Q such that 0 < xy < ε . These are also true for R . A basic idea of analysis: a < b = ⇒ ∃ c ∈ ( a,b ) ∩ R . 26 Math 413 Preliminaries I.e., a < c < b and c ∈ R . Question 4. What does this mean? ∀ ε > , | a-b | < ε 1.4 Axiom of Choice Given a sequence of nonempty sets A 1 ,A 2 ,... , the product Q ∞ k =1 A k is nonempty....
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- Fall '11
- nonempty sets A1, b2 ≤ a2, OBVIOUS note