How an infinity can be bigger than another if they're both infinite? I just don't get it

How an infinity can be bigger than another if they're both infinite? I just don't get it

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  1. 3 weeks ago
    Anonymous

    learn what a bijection is

  2. 3 weeks ago
    Anonymous

    Mathematicians use a private definition of "greater than", which is not how anyone else uses the term.

  3. 3 weeks ago
    Anonymous

    One infinity can have more stuff in it than other. For example there are an infinite number of integers AND an infinite number of even integers, but since there are twice as many integers as there are even integers, the first infinity is twice is big as the second

    • 3 weeks ago
      Anonymous

      Good example. Rationals are even greater in number. N < Z < Q.

      • 3 weeks ago
        Anonymous

        They all have the same cardinality

        • 3 weeks ago
          Anonymous

          So one set can be bigger than another set with the same cardinality

    • 3 weeks ago
      Anonymous

      You are right. Infinities are not bigger than others. Mathematicians redefined the word "bigger" to mean something else completely.

      While this is obviously true, it's not true that N, Z, Q have different cardinalities. In fact, their cardinalities are the same - it's possible to construct a bijection between each pair.
      However, having the same cardinality is not the same as having the same size.

      https://i.imgur.com/3IOhy5y.jpg

      > It's not an empirical claim
      then it’s bullshit and irrelevant. Actual math is based on empirically derived axioms and can theoretically be experimentally verified. The Pythagorean theorem, for example, is falsifiable. So don’t even try to start saying that math is not falsifiable or empirical, because it is, and it certainly can lead to disastrous consequences if you misuse math. But with actual infinities? It makes no difference. Cope and seethe, platonist troony

      I'm pretty sure all mathematical claims are falsifiable. A falsification in this context just means a proof to the contrary, which is always in principle possible given a well-formed mathematical statement (a condition that is algorithmically verifiable).
      What you probably wanted to say is that it doesn't have an computable interpretation, which is true, because you can only encode stuff on a computer that you understand (and mathematicians don't understand infinities).

      this is your brain on scientism

      Axioms are not empirically derived, they are empirically INSPIRED. We still teach the pythagorean theorem in school even though it has been "falsified" by general relativity.

      Axioms are neither empirically derived nor empirically inspired. Axioms are a post-hoc rationalization and compression of a collection of observed mathematical facts. Those facts however, which come prior to the axioms, are often empirically inspired. So many fruitful mathematical conjectures (which later became proofs) were created by observing a natural mathematical pattern by computing examples.

      • 3 weeks ago
        Anonymous

        Which infinite sets are mathematicians confused about?

  4. 3 weeks ago
    Anonymous

    Plane segments of any size contain curves of indefinite length

  5. 3 weeks ago
    Anonymous

    think of the infinite amount of decimals between 0 and 1, then the infinite amount of decimals between 0 and 2. but yeah it's silly and pointless

  6. 3 weeks ago
    Anonymous

    unfalsifiable nonsense that has no practical consequences for society

    • 3 weeks ago
      Anonymous

      It's not an empirical claim. I'm not sure how falsifiability is relevant.

      • 3 weeks ago
        Anonymous

        > It's not an empirical claim
        then it’s bullshit and irrelevant. Actual math is based on empirically derived axioms and can theoretically be experimentally verified. The Pythagorean theorem, for example, is falsifiable. So don’t even try to start saying that math is not falsifiable or empirical, because it is, and it certainly can lead to disastrous consequences if you misuse math. But with actual infinities? It makes no difference. Cope and seethe, platonist troony

        • 3 weeks ago
          Anonymous

          this is your brain on scientism

          Axioms are not empirically derived, they are empirically INSPIRED. We still teach the pythagorean theorem in school even though it has been "falsified" by general relativity.

          • 3 weeks ago
            Anonymous

            homie how the FRICK do you discover math without OBSERVING the world? Axioms are just generalizations based on past experience, it’s not magic. And by the way, here is a pro tip to help make your religion sound a little more reasonable: drop the idea of “bigger” infinities, and instead talk about “denser” infinities. The integers are denser than the evens, the rationals are denser than the integers, and the reals are denser than the rationals. But they’re all infinite so comparing their absolute size is moronic. There, so much better. You’re welcome.

          • 3 weeks ago
            Anonymous

            homie how the FRICK do you discover math without OBSERVING the world? Axioms are just generalizations based on past experience, it’s not magic. And by the way, here is a pro tip to help make your religion sound a little more reasonable: drop the idea of “bigger” infinities, and instead talk about “denser” infinities. The integers are denser than the evens, the rationals are denser than the integers, and the reals are denser than the rationals. But they’re all infinite so comparing their absolute size is moronic. There, so much better. You’re welcome.

            both of you are metaphysically moronic

          • 3 weeks ago
            Anonymous

            >>>/x/

  7. 3 weeks ago
    Anonymous
  8. 3 weeks ago
    Anonymous

    Humans don't have the ability to conceive the infinite to begin with, you're not supposed to "get it"

    These are forces beyond what most humans have the capacity to properly calculate

  9. 3 weeks ago
    Anonymous

    Just think about infinites as rates of change, it naturally lends itself to the idea of different sizes of infinity

  10. 3 weeks ago
    Anonymous

    Infinity isn't "big" to begin with.

    We need a century-long moratorium on use of the word "infinite".

  11. 3 weeks ago
    Anonymous
  12. 3 weeks ago
    Anonymous

    It cannot, endless is a synonym for infinite and there is no 2 sizes of endless
    It's just a larp

    • 3 weeks ago
      Anonymous

      Wrong, "even more endless"

      • 3 weeks ago
        Anonymous

        >muh more nonstop process

  13. 3 weeks ago
    Anonymous

    infinity is a continuum, some are bigger than others.

  14. 3 weeks ago
    Anonymous

    There's basically two concepts.

    The first is correspondence. If all of the elements in one set can be made to uniquely correspond to elements in another set, that other set is either the same size or bigger. As an example, we know that all of the rationals are "countable" because it is possible to establish a 1-1 correspondence between the rationals and the natural numbers.

    The other concept is coverage. If a set "covers" another set in the sense that every element in the inner set is also guaranteed to be within the outer set, we say the outer set is at least as large as the inner set. in this case, we see the rationals cover the integers (because every single is in between two rationals of finite size). In this sense, the rationals can be argued to be larger than the integers, because it not only covers the integers, but has an impossibly large collection of elements between every two integers.

  15. 3 weeks ago
    Anonymous

    Because infinity is not a number, it's a different concept. More like a direction, or a vector with no specified magnitude: "Just keep going that way... forever." Or a vector with infinite magnitude, but that's a circular definition, which is dumb. Don't be dumb.

    Anyway you can still make comparisons: There are infinite integers, but there's twice as many integers as there are odd integers.

    Just don't think it's a number or you'll be like Georg Cantor and you'll go nuts.

  16. 3 weeks ago
    Anonymous

    A line and a plane are both infinite.
    But the plane is bigger when viewed from our higher 3D.

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