Re: Interesting math

In article <f72e1j$ft6$1@xxxxxxxxxxxxxxxxxxxx>,
K. Edgcombe <ke10@xxxxxxxxxxxxx> wrote:
In article <5fj0efF3cbci5U2@xxxxxxxxxxxxxxxxxx>,
blmblm@xxxxxxxxxxxxx <blmblm@xxxxxxxxxxxxx> wrote:

And I wouldn't be too sure about "it" knowing that "zero is
neither even nor odd" is nonsense: I teach computer science
to undergraduates, and a surprising number of the students are
confused on this very point.

Come back, Charles Riggs, all is forgiven. We did this one to death some years
ago.

In fact I participated in a thread that could be described that way.

Of course, it *is* actually a matter of convention and definition.
It just turns out that if you define "even" in such a way as to exclude
zero (which is perfectly possible), you have to keep making exceptions to
practically every subsequent statement you might want to make about even
and odd numbers. So it's unproductive and inelegant, rather than untrue.

The same sort of issue arises across all sorts of mathematics. Once you've
settled on a definition of "x", it will (if yu're lucky) become clear whether
some known object has the property "x" or not. There are plenty of properties
(evenness is not one of them) where there are two perfectly sensible and very
slightly different definitions in circulation, and the difficulty I have with
my computer science and maths students is persuading them that the difference
between two textbooks may not be a matter of one being right and the other
wrong.


A possibly interesting example from discussion in another
newsgroup recently: Is 1 a prime number? An answer of "yes"
makes the definition of "prime" a bit simpler, but an answer
of "no" makes other things a bit simpler. Someone claimed that
there had been a shift over the past few decades, and that
the "yes" answer used to be more widely accepted than it is now.

Anyway, your point is exactly the one I was trying to make in
a previous post -- or at least I think so: Definitions are not
in themselves true or untrue, but there are other standards by
which they can be evaluated (usefulness, elegance, consistency
with other definitions).

But you said it better.

--
Decline To State
(But the e-mail address in the header should work.)
.

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