Infinite set

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In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. Some examples are:

• the set of all integers, , is a countably infinite set; and
• the set of all real numbers is an uncountably infinite set.

Counter-example:

• the set of natural numbers less than four, i.e. , is a finite set, not an infinite set.

See also

• Infinity
• Finite set
• Aleph number

 

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