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

On 11/28/24 7:29 AM, WM wrote:

On 27.11.2024 22:24, Richard Damon wrote:

On 11/27/24 3:55 PM, WM wrote:

On 27.11.2024 15:19, Richard Damon wrote:
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Nope, EVERY unit fraction is expressible, by DEFINITION.
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But not in fact. In fact most are not expressible because there are infinitely many but only finitely many are expressible. Infinitely many minus finitely many are infinitely many.

 

EVERY unit fraction is the recpircal of a natural number.
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EVERY natural number is finitely expressable.

 No. There are infinitely many, but only finitely many can be expressed.

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There are an infinite number of finitly expressible numbers, since there is no fixed upper limit to the size of an expression to express it with.

 That is potential infinity. Actual or completed infinity is a fixed quantity larger than every natural number. The set of expressed numbers however remains finite in every instance.
 Regards, WM
 

Which means that the "set of expressed numbers" has nothing to do with either actual or potential infinity, and thus not suitable to talk about here.
Your problem is you think you can HAVE and UNDERSTAND an ACTUAL infinite set, when you mind is limited to finite concepts.
Your problem is you just hack of a finite chunk off of the actual infinity and claim that minuscule part of it is its whole, and doom your logic with that lie.
Your 'logic' is just a bunch of lies you have told yourself are true, because you can't face the truth tht reality is bigger than you can imagine.