/sci/ - Science & Math » Thread #12076678

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Anonymous Wed 02 Sep 13:16:53 2020 No.12076678 View Reply Original Report

Quoted By: >>12076952 >>12079426

Is the set of all numbers between 1 and 2 equal in size to Aleph-0 or Aleph-1?
Picture unrelated.

Anonymous

Anonymous Wed 02 Sep 2020 13:22:30 No.12076693 Report

Quoted By: >>12076801

what do you mean by "all numbers"? if you are thinking about the reals, then yes, any interval of non-zero length has cardinality $\aleph_1$

Anonymous

Anonymous Wed 02 Sep 2020 13:24:30 No.12076698 Report

Quoted By: >>12076801

This is the continuum hypothesis. Its an infinity whose cardinality is greater than $\aleph_0$ , but we have no way of knowing which infinity it is unless we introduce new axioms independent of ZFC.

Interestingly, though, $|(0,1)| = 2^{\aleph_0} = | \{ f \; | \; f : \aleph_0 \to 2 \}|$ .

Anonymous

Anonymous Wed 02 Sep 2020 13:50:21 No.12076759 Report

Quoted By: >>12076801

It's $\aleph_{1}$ . Any interval of real numbers has that cardinality. Use the diagonal argument if you are new to this stuff. The main thing is there is a bijection $f:\mathbb{R} \longmapsto (1,2)$ .

Anonymous

Anonymous Wed 02 Sep 2020 14:08:23 No.12076801 Report

Quoted By: >>12076821 >>12076879

>>12076693
>>12076759
You fags are wrong, its not aleph 1. See >>12076698

Anonymous

Anonymous Wed 02 Sep 2020 14:14:35 No.12076821 Report

Quoted By: >>12077275 >>12077956

>>12076801
Well, it can be, for example, in the constructive universe. (If I can trust Wikipedia on this.)

Anonymous

Anonymous Wed 02 Sep 2020 14:43:06 No.12076879 Report

Quoted By:

>>12076801
>You fags are wrong, its not aleph 1
Oh? Go ahead and disprove the continuum hypothesis for everyone then.

Anonymous

Anonymous Wed 02 Sep 2020 15:22:20 No.12076952 Report

Quoted By:

>>12076678
Aleph-1
https://youtu.be/i7c2qz7sO0I?t=4m

Anonymous

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Anonymous Wed 02 Sep 2020 17:07:39 No.12077275 Report

Quoted By: >>12077289 >>12077829 >>12077887

>>12076821
>constructive universe
The constructible universe isn't constructive

Anonymous

Anonymous Wed 02 Sep 2020 17:10:38 No.12077289 Report

Quoted By: >>12077437 >>12077447

>>12077275
What is compound interest?

Anonymous

Anonymous Wed 02 Sep 2020 17:51:20 No.12077437 Report

Quoted By:

>>12077289
>implying that exists 2000000 years ago

Anonymous

Anonymous Wed 02 Sep 2020 17:53:57 No.12077447 Report

Quoted By:

>>12077289
What is deflation?

Anonymous

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Anonymous Wed 02 Sep 2020 19:18:22 No.12077829 Report

Quoted By: >>12081935

>>12077275
>stock is the same as cash

Anonymous

Anonymous Wed 02 Sep 2020 19:32:18 No.12077887 Report

Quoted By:

>>12077275
Oops. I'm much more used to typing constructive than constructible, since I'm not actually a set theorist.

Anonymous

Anonymous Wed 02 Sep 2020 19:50:12 No.12077956 Report

Quoted By: >>12077964

>>12076821
It is consistent that $\aleph_1$ , this is what the constructible universe $L$ shows. It is also consistent that the continuum has size any cardinal (with uncountable cofinality). This is what Cohen showed using forcing.

Anonymous

Anonymous Wed 02 Sep 2020 19:51:49 No.12077964 Report

Quoted By:

>>12077956
*It is consistent that the continuum has size $\aleph_1$ .

Anonymous

Anonymous Thu 03 Sep 2020 03:03:25 No.12079375 Report

Quoted By:

bump

Anonymous

Anonymous Thu 03 Sep 2020 03:30:48 No.12079421 Report

Quoted By:

All natural, rational, real or surreal numbers?

Anonymous

Anonymous Thu 03 Sep 2020 03:32:51 No.12079426 Report

Quoted By: >>12079429 >>12080286

>>12076678
2^(Aleph_0) is the right answer.

Bastards that say Aleph_0 need to see continuum hypothesis.

Anonymous

Anonymous Thu 03 Sep 2020 03:36:11 No.12079429 Report

Quoted By:

>>12079426
Aleph_1* i dont know how to keyboard

Anonymous

Anonymous Thu 03 Sep 2020 12:27:51 No.12080286 Report

Quoted By: >>12080403

>>12079426
>continuum hypothesis.
Fake news

Anonymous

Anonymous Thu 03 Sep 2020 12:59:58 No.12080403 Report

Quoted By:

>>12080286
go back

Anonymous

Anonymous Thu 03 Sep 2020 20:31:08 No.12081935 Report

Quoted By:

>>12077829
this. I bet Jeff would kill to have 130 billion liquid

Anonymous

Anonymous Fri 04 Sep 2020 14:36:25 No.12084384 Report

Quoted By:

It is empty set.

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