Re: Two results of set geometry

On Sep 11, 3:19 pm, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 11 Sep., 20:50, William Hughes <wpihug...@xxxxxxxxxxx> wrote:



On Sep 11, 1:47 pm, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:

On 11 Sep., 14:00, William Hughes <wpihug...@xxxxxxxxxxx> wrote:

On Sep 11, 7:46 am, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:

On 11 Sep., 13:33, William Hughes <wpihug...@xxxxxxxxxxx> wrote:

You have the full column. It is the union of the finite segments.

And this union is infinite.

Correct. You now see that it is possible to have an infiniteset
made up of finite things.

I never denied that. But it is impossible to have an infinitesetmade
up by different finite things which differ by a fixed amount like 1.

Please don't mistake the one for the other.

Note that each finite segment differs by the fixed amount 1.

So it is. And what can we say about the (completed) infinite set?
It contains an infinite segment! At no other point infinity is completed.

The two statements

The set A is complete.
There is no point at which the set A is completed.

are not contradictory.

No? There is no contradiction if we say:
The set A is complete and the set A is not complete?
(What else would
it mean to say there is no point at which the set A is completed.

Certainly not "the set A is not complete"

Saying that there is no point at which the set A is completed
means just that. There is no point at which an element of a certain
type is added
to the set B and the set B turns into a complete set A.

To say that A is complete means that it contains every element of
a certain type (e.g. natural numbers, primes, finite segments, two
digit numbers, etc. )

So it not contradictory to say

The set A is complete.
There is no point at which the set A is completed.

The fact that you don't like something does not make
it a contradiction


Change of subject.

Please answer: An infinite set of equidistant positive steps implies
an infinite height?

Yes. However, the fact that an *infinite set* of steps
has infinite height, does not imply that any single step
has an infinite height. There is no last step.

Back to the subject.

It is not contradictory to say

The set A is complete.
There is no point at which the set A is completed.

The fact that you don't like something does not make
it a contradiction

- William Hughes

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