Template:AoC

Include this template at (or near) the bottom of any page which depends, either directly or indirectly, on the Axiom of Choice.

Usage:
 *  

or:
 *  

where  proof  is the ProofWiki page name of a proof which itself depends on the AoC.

If you want this to apply to just one of the proofs of a given theorem, then there exists an optional second parameter which is a number (usually 3 or 4) determining the level of heading that the text of this template appears at. The default is 2 (standard heading) when the template itself is used so as to apply to the entire page.

Note: The current implementation is that only level 4 is available in this context.

Inclusion of this template will result in the page being added to the Axiom of Choice category, and the following being added to the page:

Axiom of Choice
This theorem depends on the Axiom of Choice, by way of (link to proof name).

Because of some of its bewilderingly paradoxical implications, the Axiom of Choice is considered to be controversial.

Most mathematicians are convinced of its truth and insist that it should be unilaterally accepted.

However, others consider its implications so counter-intuitive and nonsensical that they adopt the philosophical position that it cannot be true.

This depends on the Axiom of Choice.

Because of some of its bewilderingly paradoxical implications, the Axiom of Choice is considered to be controversial.

Most mathematicians are convinced of its truth and insist that it should nowadays be generally accepted.

However, others consider its implications so counter-intuitive and nonsensical that they adopt the philosophical position that it cannot be true.