Subject: Re: [HM] A question around zero
From: John Harper (John.Harper@MCS.VUW.AC.NZ)
Date: Fri Jan 21 2000 - 23:02:56 EST
On Fri, 21 Jan 2000, Samuel S. Kutler wrote:
> Jean-Luc asked
>
> > So, how do you define an even number?
>
> Euclid's answer from Book VII, definition 6:
>
> An even number is that which is divisible into two parts.
>
> The first even number then is two. Zero can't be an even number,
> for it isn't a number at all. One isn't a number either. For a
> number is a multitude. One is the polar opposite of a number,
> since the poles are one and many.
Terminology has changed since Euclid's time. I would answer the
question "What is the number of professors who retired from your School
in 1999?" by saying "One", not "That question is meaningless."
Can one trust all Euclid's definitions anyway? According to Todhunter's
translation, Book 1 Def. 15 says "a circle is a plane figure bounded by
one line, which is called the circumference ..." But that fails to make it
clear whether the boundary is part of the circle or not, and even worse,
it suggests the intersection of 2 circles is a ()-shaped figure. However
Proposition 1 assumes circles consist of their circumferences: "From the
point C, at which the circles cut one another, draw the straight lines
..." Heath's translation has the same problems: Def 15 "A circle is a
plane figure contained by one line such that...", Prop 1 "... and from the
point C, in which the circles cut one another, to the points A, B let the
straight lines..."
John Harper, School of Mathematical and Computing Sciences,
Victoria University, Wellington, New Zealand
e-mail john.harper@vuw.ac.nz phone (+64)(4)463 5341 fax (+64)(4)463 5045
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