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

theunknownmuncher@lemmy.world ⁨13⁩ ⁨hours⁩ ago

• BetterDev@programming.dev ⁨8⁩ ⁨hours⁩ ago

  Its true that not all intinities are equal, but the way we determine which infinities are larger is as follows

  Say you have two infinite sets: A and B A is the set of integers B is the set of positive integers

  Now, based on your argument, Asia has the largest infinite coastline in the same way A contains more numbers than B, right?

  Well that’s not how infinity works. |B| = |A| surprisingly.

  The test you can use to see if one infinity is bigger than another is thus:

  Can you take each element of A, and assign a unique member of B to it? If so, they’re the same order of infinity.

  As an example where you can’t do this, and therefore the infinite sets are truely of different sizes, is the real numbers vs the integers. Go ahead, try to label every real number with an integer, I’ll wait.

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  • Atlas_@lemmy.world ⁨5⁩ ⁨hours⁩ ago

    I’ll label every real number with the integer 1.

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  • theunknownmuncher@lemmy.world ⁨8⁩ ⁨hours⁩ ago

    Go ahead, try to label every real number with an integer, I’ll wait.

    Why would I be trying to do this though? You’ve got the argument backwards.

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    • BetterDev@programming.dev ⁨7⁩ ⁨hours⁩ 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 ⁨5⁩ ⁨hours⁩ ago

        And then aleph numbers get thrown into the conversation

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      • theunknownmuncher@lemmy.world ⁨7⁩ ⁨hours⁩ 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 ⁨7⁩ ⁨hours⁩ ago

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

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