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Axiom of choice

Anonymous Sat 10 Aug 08:25:20 2019 No.10877501 View Reply Original Report

Quoted By: >>10877547

When we say "let $x \in X$ " are we using the axiom of choice?

Anonymous

Anonymous Sat 10 Aug 2019 09:01:21 No.10877547 Report

Quoted By: >>10877556

>>10877501
No.
It happens when |X|>1 and you say let x_1, x_2, ... be in X with no formula/rule based on n that specifies what x_n is.
You have to be making infinitely many unspecified choices.

Anonymous

Anonymous Sat 10 Aug 2019 09:11:57 No.10877556 Report

Quoted By:

>>10877547
I'll just add that x_1, x_2,.. requires only axiom of countable choice. you can also have x_ indexed by some continuous parameter or worse.

Anonymous

Anonymous Sat 10 Aug 2019 09:55:40 No.10877602 Report

Quoted By: >>10877619

I don't get the answer but thank anyway.

Anonymous

Anonymous Sat 10 Aug 2019 10:04:02 No.10877619 Report

Quoted By: >>10877634

>>10877602
What don't you get?

Anonymous

Anonymous Sat 10 Aug 2019 10:18:30 No.10877634 Report

Quoted By: >>10877643

>>10877619
>|X|>1

Anonymous

Anonymous Sat 10 Aug 2019 10:31:52 No.10877643 Report

Quoted By: >>10877645

>>10877634
If X only has one element then x_n is guaranteed to be that element for all n.

Anonymous

Anonymous Sat 10 Aug 2019 10:33:56 No.10877645 Report

Quoted By:

>>10877643
>If X only has one element
This.
Thanks.

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