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aleph0 < aleph1 < aleph2

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https://www.novabbs.com/tech/article-flat.php?id=65332&group=sci.math#65332

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: aleph0 < aleph1 < aleph2
Date: Sun, 4 Jul 2021 22:11:26 -0500
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by: Sergio - Mon, 5 Jul 2021 03:11 UTC

Time to move on;

By intention, aleph0 is not a size of a number but the size of a set. It
is unrelated to the concept of infinity in calculus.

aleph2 * aleph0 = aleph2 ,

aleph2 * aleph2 = aleph2,

aleph0 < aleph1 < aleph2

==> aleph2 * aleph1 = aleph2

aleph0 = 2*aleph0 - 1

Aleph zero can be represented by the infinite number of natural and
rational numbers,

Aleph one by the number of mathematical points on any line segment,

Real numbers are already aleph one

and Aleph two by the number of possible geometrical curves.

Disks travel in packs.

tech / sci.math / aleph0 < aleph1 < aleph2