Re: Two results of set geometry

On Sep 11, 4:12 pm, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 11 Sep., 21:42, William Hughes <wpihug...@xxxxxxxxxxx> wrote:

Change of subject.

Sorry, but you are in error.



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.

What is it then that causes infinite height?

If a step is not the last step, the set of steps has a height greater
than that step.

No step is the last step, so the set of steps has greater
height than any step.

For any natural number there is a step of that
height.

The set of steps has height greater than any natural number.

The set of steps has infinite height.



There is no last step.

But all steps which are there, are finite. Therefore they do not cause
infinite height.



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.

It is a contradiction. In order to say that A is complete, you must
know all elements of A.


No. To say that A is a complete set of things of type X, you
have to know that given a thing of type X you can show that it
is an element of A. You don't have to know all things of type X,
it is enough to know something that must be true of any thing of type
X.
Knowing all the elements of A is neither necessary nor sufficient.

It is not contradictory to say

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

- William Hughes


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