Subject: Re: [HM] A question around zero
From: Dr. Frank Pecchioni (fpecchio@pop.jcc.uky.edu)
Date: Mon Jan 24 2000 - 15:35:34 EST
>
> Last week I sat in on a class of teachers and the topic of the
> evenness or oddness of zero came up.
>
Most modern mathematicians (at least those who write textbooks) apply
concepts such as "even" only to "natural numbers," in connection with
primes and factoring. By "natural numbers" they mean positive integers,
not including zero. (They call the positives with zero "whole numbers".
Those who work in foundations of mathematics, though, consider zero a
natural number, and for them the integers are whole numbers.) From that
point of view, the question whether zero is even just does not arise,
except by extension.
I would be interested in knowing how far back this view extends.
> I would prefer to do it this way: there was a time when zero was unknown
> (Dionysius Exiguus had never heard of it, so 1 BC was immediately
> followed by 1 AD in his system, which is why this year is the last year
> of the 20th century not the first of the 21st.)
This comment -- or rather others like it -- have been irritating me for the
past several months. Years are intervals; numbers are points. There is no
year zero and no year one. Zero was the origin for the calendar
(supposedly the date of the birth of Jesus, but we know that event occurred
a few years earlier, or not at all, depending on your religious
convictions). The so-called years 1, 2, 3, . . . were really the _first_,
_second_, _third_, . . . years after the origin; and the years -1, -2, -3,
. . . were the _last_, _next-to-last_ or_second_, _third_, . . . years
before the origin.
Yes, calendar arithmetic is difficult, but not because we are missing zero.
Consider the old arithmetic question: John was born in 1965 and Jane in
1966. How much older is John than Jane? The answer, of course, can be
anywhere from a few seconds to two years, depending on _when_ in those
intervals the two people were born. It is always a mistake to treat years
as points.
Road's in front o' me,
Nothin' to do but walk.
Langston Hughes
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