review3 - lems, and similar problems. 4. Theorems to know...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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-
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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 books 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 books 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...
View Full Document

Ask a homework question - tutors are online