/sci/ - Science & Math » Thread #12679740

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Anonymous Mon 08 Feb 00:39:20 2021 No.12679740 View Reply Original Report

Quoted By: >>12679767 >>12679782 >>12679794 >>12679799

Can someone explain Aleph-null to someone who no math experience past business calc?

Anonymous

Anonymous Mon 08 Feb 2021 00:52:08 No.12679767 Report

Quoted By: >>12679813 >>12679873

>>12679740
Aleph-null (or naught) is basically how many
natural numbers exist in a set of natural numbers.

Also, sets that have correspondence with sets
of natural numbers also have aleph-null quantity,
or cardinality.

Anonymous

Anonymous Mon 08 Feb 2021 00:59:28 No.12679782 Report

Quoted By:

>>12679740

$|\{a\}|=1,\quad |\{a,b\}|=2,\quad \\|\{a,b,c\}|=3,\quad |\{a_1,a_2,\cdots a_n\}|=n,\quad \\|\mathbb{N}|=\aleph_0,\quad |\wp (A)|=2^{|A|},\quad \\|\mathbb{R}|=|\wp (N)|=2^{\aleph_0}=\aleph_1$

Anonymous

Anonymous Mon 08 Feb 2021 01:02:04 No.12679794 Report

Quoted By: >>12679818

Anonymous

Anonymous Mon 08 Feb 2021 01:03:11 No.12679799 Report

Quoted By: >>12679823

>>12679740
In the spirit of impredicative infinitist schizo mathematics, here's your explanation bro:
Aleph-null is aleph-null.

Anonymous

Anonymous Mon 08 Feb 2021 01:09:13 No.12679813 Report

Quoted By: >>12679873 >>12680630

>>12679767
What operations are valid on aleph-null? Is it defined to add it to an element of R or C, or to itself...what is its natural log etc

Anonymous

Anonymous Mon 08 Feb 2021 01:10:19 No.12679818 Report

Quoted By:

>>12679794
not true, continuum still unsolved

Anonymous

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Anonymous Mon 08 Feb 2021 01:11:13 No.12679823 Report

Quoted By:

>>12679799
The proof is Trivial :
Left as exercise for the reader

Anonymous

Anonymous Mon 08 Feb 2021 01:30:34 No.12679873 Report

Quoted By:

>>12679767
>>12679813
Well, it doesn't do much like an element in R or C
would in terms of operations. It simply is a symbol
denoting the number of natural numbers in a set.

Anonymous

Anonymous Mon 08 Feb 2021 06:13:30 No.12680630 Report

Quoted By:

>>12679813
https://www.math.ksu.edu/~nagy/real-an/ap-b-card.pdf

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