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, {..., -1, 0, 1, 2, ...}, 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. {0, 1, 2, 3}, is a finite set, not an infinite set.

See also

• Infinity
• Finite set
• Aleph number

Set theory | Cardinal numbers

Nekonečná množina | مجموعه نامتناهی | Ensemble infini | Conjunto infinito | 无限集合