Re: WM and end segments...

On 7/23/2024 4:17 PM, Moebius wrote:

Am 23.07.2024 um 21:57 schrieb Chris M. Thomasson:

On 7/23/2024 9:49 AM, WM wrote:

"LLLLLLLL....." is a finite expression,

>
WM is right here.
>

"LLLLLLLL....." is an infinite expression, indeed....

>
Nope.
Hint: print(len("LLLLLLLL....."))
But by convention
(we think -except WM that is- that)
"LLLLLLLL....." DENOTES (refers to) an infinite sequence of "L"s.
:-P

I agree.
It is a very powerful distinction between
the length of an expression  and
the length of what the expression refers to.
Because the expression with all our expressions
is finite,
we can know that they are all true
when they are all not.first.false,
which we can know by looking at the expressions,
without looking at what they refer to.
(AKA logic)
Because what our expressions refer to
can be infinite, and, even though infinite,
we can know what they say is true,
we can learn about infinitely.many
without we ourselves being infinite.
It takes us both parts to explore the infinite.
Finite expressions and infinite domain.
(That seems to be what WM objects to.)

"LLLLLLLL....." DENOTES (refers to) an infinite sequence of "L"s.

There are many ways to describe an infinite sequence of "L"s.
Pick a description and say that
"LLLLLLLL....." abbreviates that description.
My most.recent favorite.description is
'well.ordered with step.up and non.min.step.down'.
⎛ Each non.{} subset B of "LLLLLLLL....." holds a first.in.B "L"
⎜ Each "L" in "LLLLLLLL....." has a first.after "L"
⎝ Each non.first "L" in "LLLLLLLL....." has a last.before "L"
That doesn't use the word 'infinite'.
It says what the word 'infinite' means (in this case).
That is actually a much more powerful and useful
thing to say.