Re: Forth PARANOIA

Andrew Haley wrote:
Ed <nospam@xxxxxxxxxxx> wrote:
...
I'm not a mathematician so I leave it to the experts to prove or
disprove. If mathematics determines a computation to be illegal
then it is an error and 'discontinuous' no matter what.

In that case, I'd prefer a 0 result which can signal 'error' and is
testable, rather than a 1 which could result from a valid computation.

As regards zero and its powers, here's a reference:
http://mathforum.org/library/drmath/view/55764.html

There's a much better discussion at

http://mathforum.org/dr.math/faq/faq.0.to.0.power.html

which concludes that "consensus has recently been built around setting
the value of 0^0 = 1."

I see nothing in the article that suggests mathematics is about to cave in
and adopt 0^0 = 1. Can one ignore the other statements therein? :

"According to some Calculus textbooks, 0^0 is an "indeterminate form."
What mathematicians mean by "indeterminate form" is that in some cases
we think about it as having one value, and in other cases we think about it
as having another."

"This means that depending on the context where 0^0 occurs, you might
wish to substitute it with 1, indeterminate or undefined/nonexistent.

"Some people feel that giving a value to a function with an essential
discontinuity at a point, such as x^y at (0,0), is an inelegant patch and
should not be done."

Did you not also quote the C spec for POW as asserting that x=0 was
illegal/ambiguous:

"C99 says: "The pow functions compute x raised to the power
y. A domain error occurs if x is finite and negative and y is finite
and not an integer value. A domain error may occur if x is zero and y
is less than or equal to zero. A range error may occur." This seems
sensible."

Clearly not everyone is rushing for a resolution, or even thinks that
one is necessary.

This isn't a matter of God-given truth but of
usefulness.

Useful to who? There will always lobbyists pushing for what they
want because it happens to suit their area of interest. Mathematics
isn't a Forth Standard. Maths has principles and won't compromise.

I think it is the application that can and should determine what will
happen when x=0. That is the most useful.



.

Relevant Pages

  • Re: Forth PARANOIA
    ... A domain error occurs if x is finite and negative and y is finite ... A domain error may occur if x is zero and y ... IEEE operates in a field which is fraught with limitations, ... But IEEE isn't mathematics. ...
    (comp.lang.forth)
  • Re: Cantor Confusion
    ... That's called an essential discontinuity. ... then the derivatives do not exist. ... this is mathematics. ... Discovery and definition are not mutually exclusive. ...
    (sci.math)
  • Re: Bobby Fischers Conquest of Everest..
    ... attended Robin Wilson?s talk a few months ago about zero in mathematics ... more important and pivotal in all sorts of ways of thinking about the ... the void and the vacuum that we?re familiar with. ...
    (rec.games.chess.misc)
  • Re: Bobby Fischers Conquest of Everest..
    ... attended Robin Wilson?s talk a few months ago about zero in mathematics ... more important and pivotal in all sorts of ways of thinking about the ... the void and the vacuum that we?re familiar with. ...
    (rec.games.chess.misc)
  • Re: The annotated annotated annotated C standard
    ... outside the Standard in order to achieve a platform-specific goal. ... mathematics found itself ... it is true that there are some cases where division by zero ...
    (comp.programming)
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