/sci/ - Science & Math » Thread #11439624

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Anonymous Wed 04 Mar 16:38:49 2020 No.11439624 View Reply Original Report

Quoted By: >>11439628 >>11439634

Why do you need the axiom of choice to well order the reals? I mean, if the subset is like (0,1) you can just pick some number say 0.5 to be the least element. Or with (0, infinity), just pick like 42. For any subset it's possible to just pick some element.

Anonymous

Anonymous Wed 04 Mar 2020 16:43:07 No.11439628 Report

Quoted By:

>>11439624
>For any subset it's possible to just pick some element.
Nonempty, sure. You don't need the axiom of choice to show that for any nonempty subset, you can pick an element.
The thing is you want a consistent way to assign an element for ALL subsets. It's not enough to know that you can do it for any given subset.

Anonymous

Anonymous Wed 04 Mar 2020 16:45:35 No.11439634 Report

Quoted By:

>>11439624
first of all, you need to do it consistently. for example (0,1) is a subset of (0,infty) therefore the least element of (0,infty) must be smaller than the least element of (0,1). but even if this wasn't necessary, you're right that you would need to select an element out of every subset of the reals. but this is LITERALLY what axiom of choice does for you.

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