It is equivalent to many statements which are not intuitive such as “Every set can be well ordered.” How, for example, would you well order the reals?
• With it you can derive non-intuitive results, such as the existence of a discontinuous additive function, the existence of a non-measurable set of reals, and the Banach-Tarski Paradox (see the next section of the sci.math FAQ). • It is nonconstructive – it conjures up a set without providing any sort of procedure for its construction.
