countable set
Quick Summary
In mathematics, a countable set is a set whose elements can be put into a one-to-one correspondence with the set of positive integers. This means that even if the set is infinite, its elements can be listed in an order, even if that list never ends. Examples of countable sets include the set of all whole numbers, all even numbers, and all fractions.12
Sets that cannot be paired off with the integers are called uncountable, and they are considered larger than countable sets. The size of infinite sets is indicated by cardinal numbers, symbolized by the Hebrew letter aleph (āµ).3
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mathematicsCantorā¦of all rational numbers, is countable in the sense that there is a one-to-one correspondence between the integers and the members of each of these sets by means of which for any member of the set of algebraic numbers (or rationals), no matter how large, there is always a uniqueā¦
Read Moreā¦of all rational numbers, is countable in the sense that there is a one-to-one correspondence between the integers and the members of each of these sets by means of which for any member of the set of algebraic numbers (or rationals), no matter how large, there is always a uniqueā¦
Read More- set theoryCardinality and transfinite numbers
ā¦of this cardinality are called denumerable), and āµ (aleph) is sometimes used for that of the set of real numbers. Then n < āµ0 for each n ā ā and āµ0 < āµ.
Read Moreā¦of this cardinality are called denumerable), and āµ (aleph) is sometimes used for that of the set of real numbers. Then n < āµ0 for each n ā ā and āµ0 < āµ.
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