Comment on 🔔 SHAME 🔔

superfes@lemmy.world ⁨7⁩ ⁨months⁩ ago

• Ephera@lemmy.ml ⁨7⁩ ⁨months⁩ ago

  Might be this?

  en.wikipedia.org/wiki/Absolute_Infinite

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  • Leate_Wonceslace@lemmy.dbzer0.com ⁨7⁩ ⁨months⁩ ago

    these are non-sensical

    Transfinite algebra is a widely-accepted aspect of mathematics.

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    • Klear@sh.itjust.works ⁨7⁩ ⁨months⁩ ago

      ↑Statements dreamed up by the totally Deranged

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  • StructuredPair@lemmy.world ⁨7⁩ ⁨months⁩ ago

    I mean, the Casimir effect was initially derived as the result of two infinite values having a finite difference.

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  • superfes@lemmy.world ⁨7⁩ ⁨months⁩ ago

    Bonkers

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• turkalino@lemmy.yachts ⁨7⁩ ⁨months⁩ ago

  There are different kinds of infinity

  “Countably infinite” means an infinitely-large set of numbers that could be generated by infinitely following an algorithm with a finite number of steps. For example, integers/whole numbers are countably infinite because they could be generated by following this simple algorithm:

  1. Start with the number 1
  2. Add 1 to your number
  3. Repeat step 2

  The set of real numbers, on the other hand, is uncountably infinite because you can have an infinite number of digits after the decimal place. You can’t define a finite generation algorithm like the one above simply because any precision you use wouldn’t cover the full range. In other words, if you wanted to modify the above algorithm, and chose 0.1 as your starting number, your algorithm would miss 0.01. If you chose to start at 0.01, you would miss 0.001, and so on

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  • weker01@feddit.de ⁨7⁩ ⁨months⁩ ago

    That is the way it is often taught but actually both sets are infinite that is have no ends or in other words are not bounded.

    The thing that is confusing to understand is that the question how many there are and how much there is diverges at infinity.

    Our intuition (as finite beings) is broken here. Both sets are infinite but in one is more than in the other. That does not make one set more infinite than the other. You cannot be more unending than to literally have no end.

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    • thesmokingman@programming.dev ⁨7⁩ ⁨months⁩ ago

      This is incorrect. There is not a one-to-one and onto mapping from the natural numbers to the real numbers ergo the sets have a different size. We have defined words to describe this. We can put uncountably many copies of the natural numbers inside of the real numbers so there are arguably infinitely more reals than naturals.

      Granted you have to accept the axiom of choice for any of this.

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      • weker01@feddit.de ⁨7⁩ ⁨months⁩ ago

        I know. I’ve studied this extensively. I am specialized in formal logic and by extension set theory. I’ve worked with and help write actual research papers in this field where this is basic knowledge.

        I’ve never claimed their to be a bijection between the reals and the natural numbers. Please point out what statement I made that is wrong. I would very much like to know.

        Also no you do not have to accept choice for this to be true. ZF is perfectly acceptable to study various infinite sets with differing cardinality.

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