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.
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