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] 55 points 4 months ago (16 children)

The first lever I see in each group.

[–] [email protected] 19 points 4 months ago* (last edited 4 months ago) (12 children)

It might sound trivial but it is not! Imagine there is a lever at every point on the real number line; easy enough right? you might pick the lever at 0 as your “first” lever. Now imagine in another cluster I remove all the integer levers. You might say, pick the lever at 0.5. Now I remove all rational levers. You say, pick sqrt(2). Now I remove all algebraic numbers. On and on…

If we keep playing this game, can you keep coming up with which lever to pick indefinitely (as long as I haven’t removed all the levers)? If you think you can, that means you believe in the Axiom of Countable Choice.

Believing the axiom of countable choice is still not sufficient for this meme. Because now there are uncountably many clusters, meaning we can’t simply play the pick-a-lever game step-by-step; you have to pick levers continuously at every instant in time.