Chapter 2 - Countable and Uncountable Sets

# Chapter 2 - Countable and Uncountable Sets - Chapter 2...

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Chapter 2 – Countable and Uncountable Sets Equivalence and Cardinality Pg 18 We say that two sets A and B are equivalent (A~B) if there is a one-to-one correspondence between them. Equivalence you need: (1)one-to-one and (2)onto. A function f from A to B is called one-to-one (injective) if whenever f(a) = f(b), then a = b. No element of B is the image of more than one element of A A function f from A to B is called onto (surjective) if for all b in B there is an a in A such that f(a) = b. All elements in B are used. Bijective is when both one-to-one and onto. Equivalent sets have the same cardinality (number of elements). A is called finite if A = { } or if A is equivalent to the set {1, 2, … n} for some n ϵ N, otherwise A is infinite . An infinite set A is said to be countable (or countably infinite ) if A is equivalent to N. Pg 19 Countable Sets – either countably infinite or finite. Well Ordered

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## This note was uploaded on 11/10/2011 for the course MATH 511 taught by Professor Higdon during the Spring '11 term at Oregon State.

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Chapter 2 - Countable and Uncountable Sets - Chapter 2...

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