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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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This note was uploaded on 12/08/2009 for the course MATH 300 taught by Professor Staff during the Spring '08 term at University of Washington.
 Spring '08
 Staff
 Math

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