18a-CardinalityII

# 18a-CardinalityII - Cardinality Introduction Discrete...

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Cardinality Discrete Mathematics

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Discrete Mathematics - Cardinality 18-2 Previous Lecture Cardinality of sets and bijections Comparing cardinalities Countable and uncoutable sets
Discrete Mathematics - Cardinality 18-3 How to Count Elements in a Set How many elements are in a set? Easy for finite sets, just count the elements. Sets A and B (finite or infinite) have the same cardinality if and only if there is a bijection from A to B

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Discrete Mathematics - Cardinality 18-4 Countable and Uncountable A set A is said to be countable if | A | | N | This is because an injective function from A to N can be viewed as assigning numbers to the elements of A, thus counting them Sets that are not countable are called uncountable Countable sets: finite sets any subset of N a b c 1 2 3
Discrete Mathematics - Cardinality 18-5 More Countable Sets The set of all integers is countable 0 1 2 3 4 5 6 7 8 3 -3 -2 -1 0 1 2 In other words we can make a list of all integers 0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, …

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## This note was uploaded on 12/12/2010 for the course MACM 201 taught by Professor Marnimishna during the Fall '09 term at Simon Fraser.

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18a-CardinalityII - Cardinality Introduction Discrete...

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