Comment on Jeopardy wall calendar pretending that the coastline paradox doesn't exist

• BetterDev@programming.dev ⁨2⁩ ⁨months⁩ ago

  Exactly! It is unintuitive, but there are as many infinite elements of the set of all real numbers between 0 and 1, as there are in the set between 0 and 100.

  I hope this demonstrates what the people here arguing for the paradox are saying, to the people who are arguing that one is obviously longer.

  Just because something is obvious, doesn’t make it true :)

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  • almost1337@lemmy.zip ⁨2⁩ ⁨months⁩ ago

    And then aleph numbers get thrown into the conversation

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  • theunknownmuncher@lemmy.world ⁨2⁩ ⁨months⁩ ago

    Alright, I concede. I did it wrong but still ended up with the right answer. There are other responses in this thread with correct explanation for why Asia has more coastline

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    • BetterDev@programming.dev ⁨2⁩ ⁨months⁩ ago

      Yeah, if you use an arbitrary standardized measuring stick, the problem goes away, as it is no longer infinite.

      Still a fun throught experiment to demonstrate how unintuitive infinities are!

      Anyway, major kudos to you for engaging with this thread in good faith! Its so rare these days, I barely venture to comment anymore. Respect.

      … and thank you for the opportunity to share a weird math fact!

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      • theunknownmuncher@lemmy.world ⁨2⁩ ⁨months⁩ ago

        Hmm I’ve consulted a mathematician that I know, and they say thay cardinality isn’t really the same as “size”, but comparing the two infinite sets of the same cardinality is basically meaningless because even though one set is sorta kinda “bigger” than the other set

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  • BetterDev@programming.dev ⁨2⁩ ⁨months⁩ ago

    And it may very well be true, but we can’t prove it mathematically.

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