Re: Cantor Confusion


Franziska Neugebauer wrote:
William Hughes wrote:

Franziska Neugebauer wrote:
William Hughes wrote:

The length of the set of natural numbers is the supremum of the
lengths of the initial segments.

Since when do sets have a length?

Substitute size or cardinality if you do not like the term
length in this context.

It is clear to *me*. Please do me a favor and ask *WM* whether
substituting "length" by "cardinality" changes - in his eyes - the
subject of your current discussion.

I am quite willing to go to a much more formal set
of terms and definitions, but I try to use the language
preferred by whomoever I am discussing something with
so if WM insists on using informal language that is what
I will use..

Yes, my switch from "length of a line or a diagonal"
to "length of the natural numbers" was an attempt to
move back to slightly more formal language. Whether
this will work I do not know.

Note. It has become clear that at the base
we have two statements.

a: Any infinite set of numbers must contain
an infinite number

b: It is possible to have an infinite set of numbers
that does not contain an infinite number.

that cannot both be true. WM claims that a is true and that
furthermore b leads to a contradiction. However, all of the
contradictions he has been showing depend on assuming that
a is true. I would like to discuss statements a and b directly,
however, I do not think that WM will cooperate. Note that
WM has the standard crank habit or not replying to a message
unless he thinks he has a counterargument.

- William Hughes

.

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