Re: Is continuum completely filled up?


"Dave Seaman" <dseaman@xxxxxxxxxxxx> wrote in message
news:epflfs$7cg$3@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Mathematicians define a line as reals as you said, then can't we define
a
line as computable number?

Sure, but you shouldn't call that the "real line", because that term
already has a different meaning.

Some candadates are true line, measure line, proper line. It is not build
with computable number only, because it has non zero measure. Where might be
uncomputable number, is simply unperceptible place.

Who is precluding the construction of computable numbers?

I want to interpret traditional theory in this concept and write comments or
opinions. I think an uncomputable number being for convenience. Functional
mathematics might not be constructed without such a thing, but want to build
usefull, fruitfull, consistent foundation of matematics with only conputable
number. Matematics of countable objects are already such a things, so that
its foundation should be solid too.

I want to loosen the restriction of constructive theory, by admitting the
use of
LEM. Though it comes to permit ambiguity in mathematics, the constructive
theory
may function as examination.
As for plane filling curve, does it pass trough un computable number too?


Regards
Ozaki Toshiaki


.

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