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Unformatted text preview: Math 5020 Homework 3 due Friday, March 4 1. Prove that (a, b) = (c, d) iﬀ a = c and b = d. 2. Determine whether each of the following statements is true or false. If it is true, give a proof; if it is false, give a counterexample. (a) If x is a transitive set and a ∈ x, then a is transitive. (b) If x is a transitive set and y ⊆ x, then y is transitive. 3. Show that an ordinal α is a limit ordinal iﬀ for every β < α, β + 1 < α. 4. Without assuming the Axiom of Inﬁnity, prove the following: (a) Any inductive set contains all ﬁnite ordinals. (b) If there exists an inductive set then ω is a set. ...
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This note was uploaded on 04/11/2011 for the course MATH 5020 taught by Professor Staff during the Spring '11 term at North Texas.
 Spring '11
 staff
 Math, Set Theory

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