From: D. F. Siemens, Jr. (email@example.com)
Date: Thu Sep 04 2003 - 00:29:50 EDT
On Wed, 03 Sep 2003 13:58:59 -0500 (CDT) firstname.lastname@example.org
> Given your logic of different kinds of numbers, zero may or may not
> Then I wonder (as a sidebar), does zero really exist or just the
> concept of
> zero? If I have zero, do I have anything? Western civilization,
> including the
> Greeks, did not acknowledge or have the need for zero until "recent"
> yet nothing is a very real concept that cannot be ignored forever.
> Does the
> acceptance of zero or the acceptance of irrational numbers change
> existence/reality? Sometimes the simplest answer is the best
Does zero exist? There are at least two answers springing from math that
I think of. If the null or empty class exists, then, within the use of
set theory, it does. On the other hand, it may be an undefined primitive,
as in Peano's postulates. Then the existence of any number, not just
zero, is problematic. There is no question that zero as a numeral exists.
We write or type it often. But numbers are abstract entities, to which
the ascription of being is at best problematic. I have the feeling that
the question, "Does zero exist?" involves a category mistake, like asking
"How much space does a spirit occupy?"
One can do quite well adding, subtracting and multiplying with Roman
numerals or with Greek numerals, which require calling on archaic
letters. Archimedes did very well with his myriads of myriads. But
division gets to be a problem without a place system. The Egyptians had a
technique for division which links to binary, though it was not yet
recognized. But I wouldn't want to extract roots with anything but a
place system. I can remember the square root of C, but not of XCIX. There
are algorithms which inexpensive calculators can implement for all kinds
of roots and powers. Even with the zero concept, one does not necessarily
have a place system. The Maya's vigesimal system at level 1 changed to 18
as multiplier at level 2.
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