Re: Incompleteness of Cantor's enumeration of the rational numbers

WM used his keyboard to write :

On 18.11.2024 22:53, FromTheRafters wrote:

on 11/18/2024, WM supposed :

On 18.11.2024 18:11, FromTheRafters wrote:

WM pretended :

On 17.11.2024 21:59, FromTheRafters wrote:
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It is sometimes better to think of cardinality as a number indicating a notion of 'set size' rather than a notion of 'number many'. For finite sets these two notions merge.

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In the infinite they differ:
ℵo is not the same as |ℕ| although |ℕ| is in the set of numbers described by ℵo.

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aleph_zero is the same object as the cardinality of N.

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Yes, but |ℕ| is the number of elements of ℕ.

 Or, more generally, it is the "SIZE" of the set. Size equals the number of elements in a *FINITE* set.
 You said aleph_zero minus aleph_zero was different to the cardinality of N

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|ℕ| is the number of elements, not the cardinality!

That is why you have such difficulty in understanding infinite sets.
N is the set, and |N| is the size of the set.

aleph_zero *IS* the cardinality of N.

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Of course, but it is also the cardinality of all other countable sets which have more or fewer elements.

No, only countably infinite sets. You have that all finite sets are countable too and have fewer elements.