If a subset of a set is uncountable then the set is uncountable. The following three conditions are equivalent. 1 11 3 Countable Sets Video Youtube 2 There is an injection f. . 1 S is countable. In practise we will often just say countable when we really mean countably in nite when it is clear that the set involved is in nite. Let h1 minA. How do you know if a set is countable. Note that R A T and A is countable. As in the first one and as in the second are quite different. So a proof of countability amounts to providing a function that maps natural numbers to the set and then proving it is surjective. In mathematics a set is countable if it has the same cardinality the number of elements of the set as some subset of the set of natural numbers N 0 1 2 3. S N from S to the natural numbers N 0 1 2 3. Using this concept we may summarize some of our above results as follows for a non-empty set...
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