Re: 3DLDF

[Frank Heckenbach]

Hans Aberg wrote:

> At 01:50 +0100 2004/08/14, Frank Heckenbach wrote:
> >> >> It clearly so that in some computer language paradigms, the word
> >>"real" is
> >> >> used instead of the mathematically correct term "float". C/C++,
> >>however, do
> >> >> it correctly.
> ...
> >> >Well, I'm a mathematician and I haven't heard the term "float" (or a
> >> >German equivalent) used anywhere in mathematics except in computer
> >> >programs in C etc.
> >>
> >> Floating point numbers are quite common in applied math, for example
> >> physics.
> >
> >That's not the question. Your claim was that the *term "float"* was
> >mathematically correct. I don't see any evidence of that.
> 
> Are you stuck on the fact that I used "float" as a short hand for "floating
> point number"? Or are you claiming that floating point numbers cannot be
> given a mathematical description? Or what?

You started the rant about terminology, didn't you? You get upset
about using "real" for a type to represent some real values and
claim that using "float" for a type to represent some real values in
a floating point representation was "mathematically correct". While
at the same time using "int" for a type to represent some integer
values or integral values (which means the same AFAIK).

> > You can represent a different subset that
> >floating point numbers (say, expressions involving pi, e and certain
> >integrals), but it's still a small subset, and calling such a type
> >"real" is/isn't just as justified than calling a floating-point type
> >"real".
> 
> So this your statement probably declares null and void all the pure math
> about real numbers, that presumably is formally expressible via a
> metamathematical theory.

Are you trolling now? I suppose you know that mathematical
statements about real numbers (and most anything) are not made by
performing computations on examples (whether by hand or by
computers), but by using quantors.

> (If one wants to implement properly implement the
> set of real numbers in a computer, one does that exactly the same way as in
> pure math, via a finite, but potentially infinite via substitutions,
> axiomatic system.)

Yes. If that's your point, then all of "real", "float", "int" etc.
as used in most programming languages are incorrect, and should be
reserved for the sets of all real, floating point or integer
numbers. Then usual computer languages could only talk about
limited-integers-represented-in-twos-complement,
limited-reals-with-limited-precision-represented-in-floating-point
etc. I just don't think that many programmers would appreciate such
type names.

> >AFAIK, "integral" is just the adjective to "integer".
> 
> Yes, but this difference is exploited to technically distinguish integral
> type from integer number. :-)
> 
> > Since "real"
> >is both a noun and an adjective, it seems just as well suited.
> 
> To denote real numbers or floating point numbers?

In your terminology, I guess I should say a real (adjective) type,
as distinguished from the set of real numbers!?

Frank

-- 
Frank Heckenbach, address@hidden
http://fjf.gnu.de/
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