Re: How many different unit fractions are lessorequal than all unit fractions?

Am Fri, 04 Oct 2024 11:33:02 +0200 schrieb WM:

On 04.10.2024 10:11, joes wrote:

Am Thu, 03 Oct 2024 20:31:41 +0200 schrieb WM:

On 02.10.2024 23:06, Jim Burns wrote:

On 10/2/2024 7:10 AM, WM wrote:

>

You (WM) believe in quantifier shifts,
the opposite of that.

I believe that if every n that can be chosen has ℵ₀ successors, then
all n that can be chosen have ℵ₀ successors. Proof by your inability
to contradict this.

That is not the same thing, but an invalid deduction.

It is fact. What you believe valid or invalid is not of interest to me.
I know that all numbers which you can choose have ℵ₀ successors.
Therefore the collection containing all numbers which you can choose has
ℵ₀ successors.

I don’t believe anything. The rules of logic which you are so fond of
simply do not admit that deduction in general (i.e. it is wrong).
What do you mean with the successor of a collection anyway?

1, 2, 3, ..., ω-2, ω-1, ω

...is a _finite_ sequence.
As you have written it,
ω and each non.0 α < ω has a predecessor,
which makes ω finite.

The predecessors in the dark realm cannot be known. You can subtract
every natural number from ω without traversing the dark realm. You can
add every natural number to every natural number without traversing
the dark realm. That is the essence of infinity!

No, the infinity is at the end, not in the middle.

A common misbelief about actual infinity based on potential infinity.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.