COMPSCI 70 Chapter Notes - Chapter 10: Continuum Hypothesis, Bijection, Natural Number

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3:16 pm cardinality - a property of a set that represents its size A property between two sets: the cardinality of set a is equal to the cardinality of set b (i. e. ) if there exists a function that is a bijection. If there exists an injective function , then. A set is countable if it has a bijection with the natural numbers (if the elements in the set can be ordered according to the natural numbers) The bijection can be either to or from the natural numbers (one implies the other) If there exists a bijection or , then is countable. A set is countable if all its elements can be enumerated. Each element in a countable set can be assigned a natural number (it is like counting the set even though it can be an infi nite set) A set is countable if a pattern can be generated that assigns the natural numbers to the pattern in order.

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