Proof -There Are The Same Number of Rational Numbers as Natural Numbers

Описание к видео Proof -There Are The Same Number of Rational Numbers as Natural Numbers

First we discuss how to compare the cardinalities (sizes) of two infinite sets. Then, we outline Cantors counterintuitive 1874 proof of the fact that the cardinality of (number of elements in) the infinite set of Natural Numbers (1, 2, 3, ) is exactly equal to the cardinality of the apparently much larger infinite set of Rational Numbers (all numbers of the form p/q where p is an integer and q is a natural number). Since the set of Rational numbers include, as a proper subset, the entire set of Natural Numbers in the form 1/1, 2/1, 3/1, , this is a surprising result, and an insight into the nature of infinite sets.

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