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
2. The length of a line extended indefinitely.
(1995-03-29)