Unformatted text preview: Thoerem: If X is a ±nite set and there exists a surjection X → S , then S is also ±nite and  S  ≤  X  . 4. Eccles, page 143, Exercise 11.2. 5. Eccles, page 184, Problem 12. 6. If X is a set that contains an uncountable subset, prove that X is uncountable. 7. If X is an uncountable set and A is a countable subset of X , prove that XA is uncountable. 8. Determine whether each of the following sets is empty, Fnite but nonempty, denumerable, or uncountable. No proofs necessary. (a) { 1 /n : n ∈ Z + } . (b) RQ . (c) Z × R . (d) [0 , ∞ ). (e) { x ∈ R : x 2 ∈ Z } . (f) { x ∈ Z : x 2 ∈ RZ } ....
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 Spring '08
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 Math, Eccles, Mathematical Reasoning Assignment, previous homework problems

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