Re: Two results of set geometry

WM wrote:
On 17 Sep., 21:47, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:

Do you disagree that, for any rational number, it can be distinguished
from pi, as being either greater or less than pi?
I diagree. The rational number which is made up from the first 10^100
digits of pi and a subsequent 5 cannot be distinguished from pi as
being greaer or less.
Based on what premise? If you already knew the first 10^100 digits of
pi, you couldn't calculate the next digit and tell if it were greater or
less than 5? To whatever accuracy you have attained, you can attain
greater, so that argument flops with me. Sorry.

It is impossible to know the first 10^100 digits of pi because the
universe including your and my brain has less memory space.

Then you could not have a rational number of that accuracy to begin with, and the question becomes moot, because you don't have the rational number to compare. It doesn't answer the question.

So, let me try again. Given that you could actually represent some rational number, do you disagree that you could determine whether it was greater than or less than pi?

All numbers are ideas, but there is a difference between the point on
the real line and the digital representation of it. No completed digital
representation, in any natural base, exists for pi. That doesn't mean
the point doesn't exist on the real line.
It does.
It is.

Try to show it.

Behold! Observe my circle of unit diameter, upon the circumference of which I have marked a point, right here. Allow me to place that point on the real line, at 0, thusly. Now, to the sound of hushed silence, I shall roll the circle along the line. Will that point touch the line again, or will the circle somehow hop off of the line, every time it reaches some irrational point on its circumference? Aha!! The point touched the line. Did you see it? Shall I show it again? Now, how many units is that point from 0, along that line? :)

It can be distinguished from
every rational number, in the general quantitative order of the line.
False. See above.
Seen it. Wasn't impressed.


Your fault.

See above.



I am not, of course, referring to physical atoms, but to "atom" in the
more general sense as an indivisible element, such as a point in space,
or a symbol in a string.

Mathematics needs physics for representation.

I am not sure Heisenberg needs to be applied to mathematics for it to be mathematics.


Regards, WM


Peace,

Tony
.

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