Re: Infinite precision floating-point

josephoswaldgg@xxxxxxxxxxx schrieb: 

André Thieme wrote:

As I said, there is (at least in my belief) no analog world. "Analog" is
something we invented to describe "something that gets very small or
exact". We will find things whose first 20 decimal places are exactly
the ones of an irrational number. We would need better measuring methods
to see that it is *not* an irrational number. Anyway, it doesn't matter
because for any irrational number you tell me, there is a rational
number with which we can represent in our real world this irrational one.

You have never seen Pi, i.e. circles.



This is a meaningless statement. Have you ever "seen" a rational
number? A negative number? Have you ever "seen" a cons cell? (to bring
things back into comp.lang.lisp territory). Have you ever "seen" an
algorithm?

We can "see" *material things* (when the lights are on) but also
*depictions* of immaterial ones. Some things cannot be seen directly,
but can be thought about (and rigourously calculated with) nonetheless.


The world might be digital, but we can still do calculus, so apparently
we can make an analog world even if one isn't provided for our
convenience. Giving up calculus because it isn't "real" is almost the
opposite of what should be done: better to give up reality, instead.
:-)

If you need a good irrational number, start up Maxima and use %e or
%pi.



Oohoo! Stop! I don't want to get rid of calculus! It is fine that we
have it. Although everything in our practical world can (and gets) be
done with rational numbers it is nice to have calculus. Having
irrational numbers makes things much easier, in calculus.
I have no problem with mathematical constructs that only exist in math
and have nothing to do with our real world. Just doing it for doing the
science can be stimulating for several people.

And my "you have never seen Pi" was meant in a practicle way. While
coming back to the mathematical view we can represent Pi. Anyway, even
when talking in the mathematical world there are irrational numbers that
we can't represent (concretely). We can only say "let x be an irrational
number". This then stands for any irrational number, but unlike Pi or e
we can't express them with an algorithm, as this algorithm would have to
be as long as the row of decimal places - but in that fact the best
algorithm would be just enumbering all digits of the number.


André
--
.

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