• GaryPonderosa@lemmy.world
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    1 year ago

    I’m not great at high-level maths like that, but can infinities be sized different in a way that makes a comparison of quantity valid?

    • MikeHfuhruhurr@beehaw.org
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      1 year ago

      Yes! There’s actually two facets to consider:

      1. Infinities can be countable or uncountable:

        • The set of integers is a countable infinity. This is pretty obvious, since you can easily count from one member to the next.

        • The set of irrational numbers is an uncountable infinity. This is because if I give you one member, you can’t give me an objectively “next” one. There’s infinitely many choices.

          Example: I say what’s the next member of the set of irrational numbers after 1.05? Well, there’s 1.050001, 1.056, etc.

      2. Can a member of an infinite set be mapped to a corresponding member of another infinite set? And if so, how?

        Spoiler, there are three different ways: surjective, injective, and bijective.

      In this situation, the sets are both countable. QA can open bug #1, bug #2, etc. It’s also - for now - at least a surjective mapping of Starfield bugs -> Skyrim bugs. Because they’re both countable, for each bug in Starfield you can find at least one bug in Skyrim (because it’s a known bigger set at the moment).

      But we don’t know more than that right now.