User talk:Dntflme

Hello,

I noticed an error in the statement of the Axiom of Choice(AC). My suggested corrections are italicized.

The first suggested correction is as follows:

Let X be a non-empty collection of non-empty sets. Then we can choose a member from each set in that collection.

As stated from Wikipedia, X could very well be empty since the empty set is a collection of non-empty sets (vacuously).

The second correction is as follows:

There exists a function f defined on X such that for each non-empty set S in X, f(S) is an element of S.

Thank you.

Axiom of choice From Wikipedia, the free encyclopedia.

In mathematics, the axiom of choice is an axiom in set theory. It was formulated about a century ago by Ernst Zermelo, and was quite controversial at the time. It states the following:

   Let X be a collection of non-empty sets. Then we can choose a member from each set in that collection.

Stated more formally:

   There exists a function f defined on X such that for each set S in X, f(S) is an element of S.