1. Bigger than any natural number. There are various formal set definitions in set theory: a set X is infinite if
(i) There is a bijection between X and a proper subset of X.
(ii) There is an injection from the set N of natural numbers to X.
(iii) There is an injection from each natural number n to X.
These definitions are not necessarily equivalent unless we accept the Axiom of Choice.
2. The length of a line extended indefinitely.
See also infinite loop, infinite set.