/sci/ - Science & Math » Thread #14183291

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The Continuum Hypothesis (Solved!)

Anonymous Thu 03 Feb 20:41:41 2022 No.14183291 View Reply Original Report

Quoted By: >>14183293 >>14183316 >>14183336 >>14183750 >>14183765

https://123abcmathematics.blogspot.com/

Check out my blog. In a beautiful 10 step proof I show that the Continuum Hypothesis is false.

Anonymous

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Anonymous Thu 03 Feb 2022 20:42:29 No.14183293 Report

Quoted By:

>>14183291
Call me when it's formalized in lean. Until then, I sleep.

Anonymous

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Anonymous Thu 03 Feb 2022 20:44:21 No.14183303 Report

Quoted By:

Anonymous

Anonymous Thu 03 Feb 2022 20:47:27 No.14183316 Report

Quoted By: >>14183326 >>14183332 >>14183377

>>14183291
> $\mathbb{Q}$ has larger cardinality than $\mathbb{N}$
Dropped

Anonymous

Anonymous Thu 03 Feb 2022 20:49:24 No.14183326 Report

Quoted By: >>14183331 >>14183798

>>14183316
Prove it's not.

Anonymous

Anonymous Thu 03 Feb 2022 20:50:32 No.14183331 Report

Quoted By:

>>14183326
I am 100% certain that he can't

Anonymous

Anonymous Thu 03 Feb 2022 20:50:37 No.14183332 Report

Quoted By:

>>14183316
You're insane.

Anonymous

Anonymous Thu 03 Feb 2022 20:51:05 No.14183336 Report

Quoted By: >>14183734

>>14183291
Why mention your blog if its the same pic.

Why do you post this so often.

Wikipedia tells me you cant prove or disprove this hypothesis in ZFC or something like that.

I understand you have a different definition of cardinality than wikipedia? Can you say more about that?

Anonymous

Anonymous Thu 03 Feb 2022 20:59:10 No.14183377 Report

Quoted By: >>14183397

>>14183316
Check this shit out bro. An element of Q is a pairing {x,y} such that x,y ? N. The probability that x,y are coprime is 6/?^2 so it follows immediately that there are exactly 6N/?^2 more elements in Q than there are in N.

Anonymous

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Anonymous Thu 03 Feb 2022 21:04:29 No.14183397 Report

Quoted By: >>14183413

>>14183377
>there are twice as many even integers as there are integers

Tooker

Tooker Thu 03 Feb 2022 21:07:06 No.14183409 Report

Quoted By: >>14183731

Add me to the screencap

Anonymous

Anonymous Thu 03 Feb 2022 21:08:27 No.14183413 Report

Quoted By: >>14183756

>>14183397
Aye laddy, but you've made me consider a flaw in my proof. The positive elements of Q also have a full negated copy and zero is in Q but not in N. So in fact Q is exactly 12N/?^2+1 times large N.

Anonymous

Anonymous Thu 03 Feb 2022 22:51:58 No.14183731 Report

Quoted By: >>14183732

>>14183409
lol what?

Screencap doesnt exist

Screencap doesnt exist Thu 03 Feb 2022 22:53:20 No.14183732 Report

Quoted By: >>14183741

>>14183731
He is confused

Anonymous

Anonymous Thu 03 Feb 2022 22:53:50 No.14183734 Report

Quoted By: >>14183761

>>14183336
The cardinality definition is the same, the number of elements in the set i.e.the size of the set. There are more numbers in Q than in Z, and more numbers in R than in Q.

Anonymous

Anonymous Thu 03 Feb 2022 22:57:34 No.14183741 Report

Quoted By: >>14183842

>>14183732
All of the material is original content. Get bent.

Anonymous

Anonymous Thu 03 Feb 2022 22:59:35 No.14183750 Report

Quoted By:

>>14183291
I can easily give you a model of ZFC when CH is indeed false. Why would I care about your blatantly incorrect proof?

Anonymous

Anonymous Thu 03 Feb 2022 23:01:47 No.14183756 Report

Quoted By: >>14183776

>>14183413
When you write 1, do you actually mean 0.99999...?

Anonymous

Anonymous Thu 03 Feb 2022 23:03:35 No.14183761 Report

Quoted By: >>14183769

>>14183734
"Just because the integers are a proper subset of the rationals doesn't mean that the rationals have a higher cardinality than the integers. Actually, there is a theorem that says that a set is infinite if and only if it has the same cardinality to a proper subset of itself (so your logic would only apply to a finite set).

A set is countable, or has the same cardinality as the integers, if you can count the elements. "

Anonymous

Anonymous Thu 03 Feb 2022 23:04:41 No.14183765 Report

Quoted By:

>>14183291
>8.) The infinite sets in statement (6) have different cardinal numbers
>Proof: trivial
lmao.

Anonymous

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Anonymous Thu 03 Feb 2022 23:05:48 No.14183769 Report

Quoted By: >>14183777

>>14183761
Not all of the fractions found in Q are found in Z. They are very much different measures.

Anonymous

Anonymous Thu 03 Feb 2022 23:07:30 No.14183776 Report

Quoted By:

>>14183756
No, my 1 doesn't crossdress, tranny.

Anonymous

Anonymous Thu 03 Feb 2022 23:07:30 No.14183777 Report

Quoted By: >>14183794

>>14183769
Its countable so it has the same cardinality? Or not?

Anonymous

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Anonymous Thu 03 Feb 2022 23:07:47 No.14183779 Report

Quoted By: >>14183784 >>14183814

Here's a newer version. I changed the wording slightly.

Anonymous

Anonymous Thu 03 Feb 2022 23:09:44 No.14183784 Report

Quoted By:

>>14183779
>10.) Therefore the rational numbers Q have the smallest cardinal number after the integers.
This part isn't true, for example the union of Z and {1/2} is smaller than Q.

Anonymous

Anonymous Thu 03 Feb 2022 23:12:29 No.14183794 Report

Quoted By: >>14183807

>>14183777
0.5, 1.5, 1.89, etc.
the numbers in between are totally not there

Anonymous

Anonymous Thu 03 Feb 2022 23:13:13 No.14183798 Report

Quoted By: >>14183865

>>14183326
All rationals can be represented as points on a grid where the x axis is the numerator and the y axis denominator. Let the origin be the 0th rational. Draw a spiraling path from the origin to the points adjacent to it on the grid. This path can go through every point one by one, forming a bijection between the rationals and the natural numbers. Their they have the same cardinality.

Its countable

Its countable Thu 03 Feb 2022 23:14:52 No.14183807 Report

Quoted By:

>>14183794
It has the same cardinality

Anonymous

Anonymous Thu 03 Feb 2022 23:16:11 No.14183814 Report

Quoted By: >>14183865

>>14183779
8 and 9 are wrong.

Anonymous

Anonymous Thu 03 Feb 2022 23:17:57 No.14183826 Report

Quoted By: >>14183865

You guys don't have a rebuttal.

Its countable

Its countable Thu 03 Feb 2022 23:22:27 No.14183842 Report

Quoted By:

>>14183741
What is original content? Ive seen this thread many times already

Anonymous

Anonymous Thu 03 Feb 2022 23:26:58 No.14183865 Report

Quoted By: >>14183873

>>14183826
See >>14183798 and >>14183814

Anonymous

Anonymous Thu 03 Feb 2022 23:28:27 No.14183873 Report

Quoted By: >>14183931 >>14183934

>>14183865
Prove that that the numbers 1/2, 3/8, and 12/7 are in Z.

Anonymous

Anonymous Thu 03 Feb 2022 23:42:45 No.14183931 Report

Quoted By:

>>14183873
Why would I have to prove something I never claimed? Prove 2 is in {1} since {1} and {2} have the same cardinality.

Anonymous

Anonymous Thu 03 Feb 2022 23:43:59 No.14183934 Report

Quoted By: >>14183941

>>14183873
So you don't have a rebuttal.

Its countable

Its countable Thu 03 Feb 2022 23:46:33 No.14183941 Report

Quoted By: >>14183953

>>14183934
Its countable

Anonymous

Anonymous Thu 03 Feb 2022 23:51:25 No.14183953 Report

Quoted By: >>14183961

>>14183941
What is?

Its countable

Its countable Thu 03 Feb 2022 23:55:15 No.14183961 Report

Quoted By: >>14184026

>>14183953
The set of rationals.

Anonymous

Anonymous Fri 04 Feb 2022 00:12:16 No.14184026 Report

Quoted By: >>14184033

>>14183961
Yes, so it has the same cardinality as the naturals. What is your point?

Anonymous

Anonymous Fri 04 Feb 2022 00:15:24 No.14184033 Report

Quoted By: >>14184118

>>14184026
I thought the person was claiming that it has a different cardinality.

Anonymous

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Anonymous Fri 04 Feb 2022 00:27:20 No.14184059 Report

Quoted By:

Can I have Tooker back? This schizo can’t even use TeX.

Anonymous

Anonymous Fri 04 Feb 2022 00:57:40 No.14184118 Report

Quoted By:

>>14184033
He was, I wasn't.

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