Science Memes

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Tough Trolly Choices (mander.xyz)

submitted 4 months ago by [email protected] to c/[email protected]

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[–] [email protected] 5 points 4 months ago* (last edited 4 months ago) (1 children)

It seems to me that, since the set of real numbers has a total ordering, I could fairly trivially construct some choice function like "the element closest to 0" that will work no matter how many elements you remove, without needing any fancy axioms.

I don't know what to do if the set is unordered though.

[–] [email protected] 10 points 4 months ago (1 children)

If I give you the entire real line except the point at zero, what will you pick? Whatever you decide on, there will always be a number closer to zero then that.

[–] [email protected] 3 points 4 months ago

I guess I can pick another number x to be closest to but it has the same problem unless I can guarantee it's in the set. And successfully picking a number in the set is the problem to begin with! Foiled again!