Re: Two results of set geometry

William Hughes wrote:
On Sep 15, 10:38 pm, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
William Hughes wrote:
On Sep 15, 9:54 pm, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
William Hughes wrote:
On Sep 13, 2:01 pm, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
(what did I write?)
Consider the set of points 1/2, 2/3, 3/4, ...
Note that there is a point, 1, *by* which all the numbers in the set
have
been listed. However, there is no point, *at* which all the numbers
in the set
have been listed.
Some sequences do not have a last point.
- William Hughes
And, so, what?
You claimed if there were some point *by* which all the numbers in the
set
were listed, there must be some point *at* which all the numbers in
the set
were listed. It is nice to see
you have changed your mind.
What makes you think any such thing?

You made the claim in a previous thread that
you ran away from.

I said *if* there is a point at
which count reaches any infinite value, then count has, too, and vice
versa. They are equal.

Watch out. My theory is almost ripe. :)



If you have counted x many times, that is how far you are
from the origin, in some finite unit. There is an equivalence between
element count and value in the naturals, and so, you cannot have
infinite count without infinite value.
Your error is thinking that the number of elements in a sequence
without
an end must be a count. A count is only appropriate if there is a
last
element. As you see from the example above, even having a bound does
not guarantee a last element.
A count is valid as long as it does not end and start somewhere else
entirely.

A count is not appropriate if it does not end.

We can say the number of elements in a sequence
with a last element is the value
of the count when we count the last element. If the sequence
does not have a last element this will not work. If we want
to know the number of elements in a sequence without an end
this will not work.

Note that in a sequence without an end there are more elements
than any finite natural number. Therefore there are an infinite
number of elements.

- William Hughes



Yes, you would have an infinite count. There is nothing preventing one from defining such a count, despite your insistence to the contrary.

Peace,

Tony
.

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