Every vector space has a basis.
<-> The Cartesian product of any nonempty family of nonempty sets is nonempty.
<-> If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.
<-> Every set can be well-ordered. Consequently, every cardinal has an initial ordinal.
Unknown "Sexy Officer" - 16 years, 7 months, 12 days ago