Re: The middle of the string

In article <gclhha$r28$1@xxxxxxxx>, John Jones <jonescardiff@xxxxxxx>
wrote:

Mitch wrote:
On Oct 8, 6:59 pm, John Jones <jonescard...@xxxxxxx> wrote:
Mitch wrote:
On Oct 3, 7:45 pm, John Jones <jonescard...@xxxxxxx> wrote:
There's no left or right in a string of beads.
OK. But there is one end and the other distinct end.
And the middle of a
string of beads is only dependent on our being able to ascertain left
and right.
Let's say the middle depends on having two ends then...
Yes, ok. We have defined our string as having two ends. That's our
definition of a string, we must define it in that way.

What? 'must'? Not necessarily.

And two ends MUST have a middle.

same response as above.

I'm referring to the plain observation that a finite string has length
with two ends. It would seem obvious.

Furthermore, any string, finite or infinite, with two ends, one end or
no ends, has the property that between any two of its members there are
at most only finitely many others.

This is quite different from a line, ray or line segment.

A lot of the progress on your problem would be made much easier if you
were a bit more precise, and by that I mean mathematical. Lack of
precision allows you to conjecture wildly in multiple directions
simultaneously, your choice of direction influenced by metaphorical
whim.

It isn't accuracy we are striving for. I don't want to know the exact
length of the string. We are looking to the everyday principles that
inform mathematical reasoning.

All I can offer against that objection is that I do not need to specify
a middle to have two ends. There is another object that has two ends - a
pair of points. But if we define 'ends' as being a property of length,
then that would get rid of that counter-example.

but... but then you're talking about something different?

Yes. But I need to say why it is different. It is different because a
pair of points has no length even though its range (like a finite line)
is covered completely by two points.

So it comes down to this: Does a finite line have a middle? Yes it does.

OK I guess.

So does a string have a middle? Only if it is a line.

My strings have middles whenever they consist of an odd number of items.

What? Why would that possibly be relevant?

A string can have a middle if it is a finite line.

Strings, unlike lines, have no more than finitely many members between
any two of their members.

But I say that a string is not a line.

Right!


Sure you can say that by fiat...define string, define point, then the
rest of us can decide.

We cannot tell left from right in a string because
a string is not a line. And if a string is not a line then it has no
middle.

The string "abc" has a middle.
.

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