Template:AoC

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

Usage
This template can be invoked as:



or:



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

Multiple Proofs
Suppose there are multiple proofs of a theorem being proved.

Suppose that not all of these require the use of AoC.

Then what you do is to invoke AoC on the page containing a proof that uses AoC, outside the onlyinclude tags, but then do not invoke AoC on the parent page.

If you use this option, 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 Examples of Use of 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 in some mathematical circles 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 in some mathematical circles 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.