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Surprisingly George Cantor claims there is an infinite-2 which is greater than infinity-1.

Isn’t infinity enough innumerable? Then how can there be two kinds of infinite, where one "infinity" is greater than the second "infinity".

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

This is where the understanding of the continuum hypothesis begins

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MORE IDEAS ON THIS

Those all sets are just one set of infinite number, and we did arranging those numbers into different set of point of view, so we thought we were dealing with something different increasingly at different stage of infniity.

It’s just a set. Only they did interchange in between numbers, so i...

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What is the method for measuring that something that is innumerable can challenge another that is also innumerable?

I will give an example before going into the formal method, so that we can see the weird of the continuum hypothesis in this case.

It’s like between hot water & ice wa...

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When you point to the number one, you are actually pointing to something that exists.

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 ...

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You have to relate math on reality. if you reject this, try with small step. consider a number must be related to a thing, otherwise we're dealing with nonsense. although someday someone accept math explaining other dimention, or relativity, still it has to do with things. there is nothing simple...

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A series of numbers is always uncountable, so how can there be a series of numbers that is more uncountable than the one that was previously uncountable?

How to measure one thing than the other when both are equal? Thus the method was found which became the root of this problem. Some have o...

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They thought there were points that couldn’t be connected (marked by a red cross) one to one (bijective) from left to right (from the member of the...

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How can, according to George Cantor’s version, formally determine that there is an infinite series of numbers that is more infinite than another infinite?

Simply by making a relationship (connecting in) between each member of the two sets.

So, if the members of the two sets can be c...

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Actually, whether we are trying to do cantor’s diagonal, or multiplying power set of aleph-null, but it’s actually we are doing on the same numbers as whole numbers, as one infinity.

Although you can create multiple infinities, still we are doing on the same range.

- It’s just that...

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I’m focusing on “overlap”. Cantors diagonal numbers don’t overlap with the ones on the list either. Even and don’t overlap odd either. Since we can order {0,1,3..} and {0,1,2,3,4…} by the time we get to 2 in the second list, we know we will never find it in the first. Both are infinite yet differ...

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The Concept of Infinity in the Continuum Hypothesis

This is not as commonly known, infinite value. But countless in different contexts.

However, the sequence of numbers of any type is always infinite, in the sense it's unreachable.

There are two infinite series of numbers, th...

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It’s like when we button a shirt, so if all buttons are buttoned, it is assumed that the left and right sides are the same length.

But when the buttons don’t fit properly, so you can see that there is a longer side of the shirt. But actually THE LEFT SIDE & RIGHT SIDE IS TOTALLY THE SAME LE...

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So that between the members of the set of integers and the members of the set of real numbers (involving decimals), it can always be paired (connected) one to one (bijective) for all members of the two set of different types of numbers.

This also has confirmed that from the left side to the...

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A single finite number may be related to a banana. two finite numbers may be related to two bananas. more & more numbers may be related to more and more bananas, rocks, books, atom, and so forth. more & more infinites number then, must be related to all of possible things that fill the entire pos...

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Continuum hypothesis is failed, because of these reasons:

If we can do multiple calc on different areas of infinity and that looks like we are doing things differently, or we're dealing with different infinity, but actually we're doing at the same area, the same numbes were used interchange...

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What are the useful outcomes of denying the Continuum Hypothesis?

This opens new perspective of how we think on math.

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How do the integers and ...

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Related collections

More like this

What are the useful outcomes of denying the Continuum Hypothesis?

This opens new perspective of how we think on math.

_____

How do the integers and ...

Continuum hypothesis is failed, because of these reasons:

If we can do multiple calc on different areas of infinity and that looks like we are doing things differently, or we're dealing with different infinity, but actually we're doing at the same area, the same numbes were used interchange...

If an apple was divided continuously uncountably, divided continuously to infinity, then it’s infinite division of finite apple. Is it possible? No.

- But the fact support it. Through observations, it onl...

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