Continuum Hypothesis

There are two infinite series of numbers, that's what it means.

  • ...all the stars in the sky are countless, and as countless as the number of hairs on everyone’s head
  • ...or, all the planets that exist are innumerable, and as countless as the number of particles
  • ... more axiomatically, all the incalculable possibilities, are the same as all the changes that exist.

Yet intuitively, the infinite is pretty much weird. Then how many kinds of infinite are more than the previous infinity?

  • ...all the stars in the sky are countless, and as countless as the number of hairs on everyone’s head
  • …or, all the planets that exist are innumerable, and as countless as the number of particles
  • ... more axiomatically, all the incalculable possibilities, are the same as all the changes that exist.
  • ... "which is more characteristic of water, hot water or ice water?"
  1. Take a set of numbers which thoroughly countless a lot.

Well, here’s the weird thing. How to measure that one of the two is more than the other, when both are included as many as innumerable?

  • Boots <---> Men
  • High Heels <---> Women
  • Flip Flops <---> Little Boy

So Cantor formulated a pattern of comparing distances as above and applied it to two sets. Therefore?

  • If the members of two sets can be connected one-to-one, it means that the distance between them is the same length and regardless of how far, the two sets are considered to have the same probability of infinity.
  • However ...
    However, if the members between two sets cannot be connected at all, in the sense that some are not connected, then? There is greater sst of numbers than the other one, so the value of the infinite is greater than the other infinity.

Put simply: there is an infinity that is shorter than another infinity. You see, this reasoning is much more absurd, but forcing it, as this is a mathematical structure.

This is where the continuum hypothesis is weird.

  1. that the reasoning on the continuum hypothesis is absurd
  2. that the reasoning on the continuum of the hypothesis does not characterize mathematical reasoning and does not abrogate the certainty of math

The question is "how wide is the “number 1" you’re pointing at?"

  • ... Of course the number 1 is the area of ​​0 to 0.999999999999999 ...
  • ...Similarly the number 2 is
    area from 0 to 1.999999999999999 ...

Yes, that "Continuum Hypothesis" is FALSE.

That there is no "countless" greater than another “countless”

  • 🧩 If the two things overlap each other perfectly, then they are really just one thing (venn diagram)
  • ​​​​​​🧩 Two infinites overlap each other perfectly, then it's just one thing

We are playing at the same area and there is no bigger infinity, it’s just one infinity.

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