Date: Wed, 04 Dec 1996 18:14:19 -0500

From: Alex Bogomolny

Dear Hans:

- 0 is a number with well defined properties. For example, a+0=a and a*0=0 for any number a.
- 0 can be used in arithmetic calculations regardless of its representation. For example, 7*(5*5-4*4-3*3)=0.
- 0 has a name - "zero", while an undefined term does not. Indeed,
a term may be undefined in a variety of ways. If you talk of
integers, for example, the 15/5 is defined while 12/5 is not.
If you talk of real numbers, sqrt(9) is defined while sqrt(-9)
is undefined. 1/0 is undefined unless you think of what's known as
the Nonstandard Analysis. Even then the meaning of 1/0 is not quite
defined.

Thus, when I say zero, you know what I mean; whereas when you say undefined - I do not :-)

Just in case, you may note that being unknown is not the same as being undefined. When something is unknown one still assumes that it is possible to associate a value (perhaps not unique) with this something. On the other hand, you can't associate a value with an undefined term without removing the reason for its being undefined. (I.e., to remove the blemish from 12/5, one has to define and switch to rational numbers.)

Hope this helps. Please let me know if you still have doubts.