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Countability (Mathematics) (view source)
Revision as of 22:54, January 6, 2010
, 22:54, January 6, 2010→Examples of Countable Sets
==Examples of Countable Sets==
==Examples of Countable Sets==
[[Image:Rationals countable.jpg|right|250px|thumb|While some details remain, such as eliminating reducible fractions, this picture shows the idea behind a numbering of all fractions.]]
Obviously, the numbers 1, 2, 3, etc., are countable, but so are all the integers: 0 we call first, 1, second, -1, third, 2, fourth, -2, fifth, 3, sixth, and so on, going outwards. We're sure to hit every integer this way.
Obviously, the numbers 1, 2, 3, etc., are countable, but so are all the integers: 0 we call first, 1, second, -1, third, 2, fourth, -2, fifth, 3, sixth, and so on, going outwards. We're sure to hit every integer this way.
Somewhat surprisingly, the rational numbers are countable as well. See the picture below:
Somewhat surprisingly, the rational numbers, also called fractions, are countable as well. See the picture, right.
==Examples of Uncountable Sets==
==Examples of Uncountable Sets==