Re: Zero Points?

On Fri, 11 Sep 2009 13:56:01 -0700, Hatunen wrote:

On Fri, 11 Sep 2009 13:42:19 -0700, Evan Kirshenbaum
<kirshenbaum@xxxxxxxxxx> wrote:

Hatunen <hatunen@xxxxxxx> writes:

On Fri, 11 Sep 2009 10:00:45 -0700, Evan Kirshenbaum
<kirshenbaum@xxxxxxxxxx> wrote:

Hatunen <hatunen@xxxxxxx> writes:

On Fri, 11 Sep 2009 07:30:10 -0700, Evan Kirshenbaum
<kirshenbaum@xxxxxxxxxx> wrote:

nospam@xxxxxxxxxxxxxxxx (J. J. Lodder) writes:

Mathematics deals with real numbers.

Mathematics deals with all sorts of numbers. Computers can't
efficiently deal with real numbers, so they deal with floating-point
numbers as a useful approximation.

Welll.... The binary numbers it uses for the calculations are real
integers.

No, they're an approximation of a subset of the integers. In
particular, the wraparound behavior by which incrementing the most
positive fixed-point number results in the most negative fixed-point
number isn't typical behavior for what mathematicians would call
"integers". (Back when I was working on program evolution, I would
occasionally evolve solutions that depended on this overflow
behavior.)

Binary numbers are still integers, not an approciamation. Any
non-negative integer, such as 65535, is still an exact integer when
expressed in binary form.

Sure, but n-bit two's-complement fixed-point numbers ("the binary
numbers it uses for the calculations") are not the mathematical
integers.

The fact that they are base-2 rather than base-10 doesn't change
anything.

In particular, if n=16, then 65,535 + 1 = -65,636, which is not a
property that the integer 65,535 has.

I've put no limit on the number of binary digits to be used.

I seem to recal that early versions of PC-DOC had integer arithmetic.

But I may have misunderstood what you meant by "the binary numbers it
uses for the calculations". If you meant the ones I was talking about
as floating-point numbers, they aren't integers in any useful sense that
I can think of.

But they are made up of binary digits used in a manner approximating
another type of number. They are just as much digits whether they are
coding floating point numbers or they are coding ASCII characters or
they are coding the current temperature. All computer usages use the
integers 0 and 1 and only 0 and 1.

As I said way up at the top, "The binary numbers it uses for the
calculations are real integers."

Of course all civilized high-level languages offer arbitrary-precision
(so-called infinite precision) integers as a data type. Maybe even as
the default data type for representing integers.

--
Roland Hutchinson

He calls himself "the Garden State's leading violist da gamba,"
.... comparable to being ruler of an exceptionally small duchy.
--Newark (NJ) Star Ledger ( http://tinyurl.com/RolandIsNJ )
.

Relevant Pages

  • Re: Zero Points?
    ... Mathematics deals with all sorts of numbers. ... Computers can't ... floating-point numbers as a useful approximation. ... The binary numbers it uses for the calculations are real ...
    (alt.usage.english)
  • Re: Zero Points?
    ... Mathematics deals with all sorts of numbers. ... floating-point numbers as a useful approximation. ... I've put no limit on the number of binary digits to be used. ... and are computers that use other bases in the hardware. ...
    (alt.usage.english)
  • Re: Zero Points?
    ... Mathematics deals with all sorts of numbers. ... floating-point numbers as a useful approximation. ... positive fixed-point number results in the most negative fixed-point ... and are computers that use other bases in the hardware. ...
    (alt.usage.english)
  • Re: Zero Points?
    ... Mathematics deals with all sorts of numbers. ... floating-point numbers as a useful approximation. ... positive fixed-point number results in the most negative fixed-point ... and are computers that use other bases in the hardware. ...
    (alt.usage.english)
  • Re: Zero Points?
    ... Mathematics deals with all sorts of numbers. ... floating-point numbers as a useful approximation. ... The binary numbers it uses for the calculations are real ... positive fixed-point number results in the most negative fixed-point ...
    (alt.usage.english)