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# review3 - lems and similar problems 4 Theorems to know Be...

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THINGS TO KNOW FOR EXAM 3 1. Definitions (1) equal cardinality (222) (2) denumerable (223) (3) countable (223) (4) uncountable (223) (5) countably inﬁnite (223) (6) restriction of functions (237) (7) prime number (245) (8) composite number (245) (9) Division algorithm (247) (10) remainder (247) (11) quotient (247) (12) greatest common divisor (250) (13) linear combination (250) (14) relatively prime (255) (15) canonical factorization (257) 2. Skills you should have (1) Know how to prove that a set is de- numerable. (2) Know how to prove that a set is un- countable. (3) Know examples of ﬁnite, denumerable, and uncountable sets. (4) Be able to use the Schr¨ oder-Bernstein theorem to compare cardinalities of sets. (5) Prove theorems about divisibility, primes, and GCD. (6) Compute quotients and remainders in the division algorithm. (7) Compute GCD with Euclidean algo- rithm. (8) Compute canonical factorizations. 3. Problems Be able to do all assigned homework prob-
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Unformatted text preview: lems, and similar problems. 4. Theorems to know Be able to prove the theorems indicated by a • below. (1) • Theorem 10.1 (2) • Result 10.2 (3) Theorem 10.3 (This is SWAT) (4) • Result 10.4 (5) • Result 10.5 (6) Result 10.6 (7) Result 10.7 (8) • Theorem 10.8 (the book’s proof is not as nice) (9) • Theorem 10.9 (10) • Cor. 10.10 (11) • Theorem 10.11 (12) • Theorem 10.12 (13) Theorem 10.13 (14) • Theorem 10.14 (15) • Theorem 10.15 (16) Theorem 10.18 (17) • Theorem 11.2 (18) Theorem 11.3 (19) • Theorem 11.4 (The division algorithm-the book’s proof is not as nice) (20) Corollary 11.5 (21) Theorem 11.7 (22) Theorem 11.8 (23) • Lemma 11.9 (24) Theorem 11.12 (25) • Theorem 11.13 (26) • Corollary 11.14 (27) Corollary 11.15 (28) • Theorem 11.16 (29) Theorem 11.17 (30) • Theorem 11.22 1...
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## This note was uploaded on 03/08/2011 for the course MATH 334 taught by Professor Smith during the Spring '11 term at Vanderbilt.

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