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Topic: § 524 Are finite cardinal numbers natural numbers?
Replies: 54   Last Post: Jul 22, 2014 10:45 AM

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 wolfgang.mueckenheim@hs-augsburg.de Posts: 3,394 Registered: 10/18/08
Re: ?? 524 Are finite cardinal numbers natural numbers?
Posted: Jul 21, 2014 4:25 AM

Am Montag, 21. Juli 2014 00:29:26 UTC+2 schrieb Zeit Geist:

> You have Shown that no Finite Number of Processes on Finite Sets can Produce an Infinite Set.

Wrong. There are infinitely many natural numbers and as many processes.

> Your Claimed Contradiction is that Every s_n is Infinite, yet N Exhausts Q to the Empty Set.

Show a proof of a bijection that does not use all finite n only.
>
> You say We must have a Contradiction because of the Discontinuity.
>

No. I say there is no discontinuity. The belief in a discontinuity would be a belief that after all natural numbers have failed to to exhaust Q some magic process does it. Simply nonsense.
>
> Just because you don't Realize that it is, does Not mean it isn't.

It is not real. Therefore it cannot be realized. It is simply matheological nonsense, a belief that is not supported by formalism, because this formalism simply proves the bijection for finite numbers only.

> The Remaining Rationals are Enumerated by the Remaining Naturals.

There are no naturals remaining after all naturals. My proof is for all naturals.

> Using the Infinite Set N as the Domain of a Function, that what accomplishes that.

> Why do I have to keep saying that?

That remains your secret. I use the infinite set N as the domain of a function from N to S with S being the set of all s_n.

Regards, WM