The Two Faces Of Zero
Abstract
Many of our assumptions about numbers are culturally-based and have a
long and varied history. Among these are our conceptions of zero. If our
model of zero was incorrect, could we tell?
Our assumptions could be maintained most of the time, but might fall
over in cases such as division by zero, at certain boundary conditions or
in our interpretations of physics.
Let us indulge in a little heresy as there is more to zero than we
think. Let us look at zero in physics - it's not the same arithmetic that
we learnt at school.
There are 2 different kinds of zero (as an ordinal or as a quantity)
and there are different types of infinities. In our culture we tend to
treat all infinities alike and both representations of zero as the same.
Key Points
- In mathematics, we conventionally treat both ordinal values of zero
and zero quantities as { 0 } : the set of an integer 0. A sort of
"real number" half-way between -1 and 1.
- The mathematics of Physics does not follow our conventions and
instead treats zero
quantities as null,
nothing or an empty set { }.
- We commonly treat 1/0 as infinity
( or 2/0, 3/0, etc ).
- Nature treats it as { }.
- In conventional mathematics 0 + 0 must add up to something other
than 0. This is because if 1 / 0 = infinity, then infinity * 0 = 1.
- Treating zero as the absence
of a number, i.e. { }, then 1 / 0 = 0 and 1 * 0 = 0. This
then gives 0 + 0 = 0.
- In conventional mathematics using { 0 }, Plancks
Constant is a variable.
- Using { } Plancks Constant is a constant.
- The conventional view of the Lorentz
Factor returns infinity at v=c.
- Using { } it returns nothing at v=c. This is because v=c is out
of scope.
- The interpretation of Null that is used here ( absence of value or
"nothing" ) is from the American
National Standards Institute for SQL NULLs.
- We apply these ANSI rules for null and we treat zero quantities and
null interchangeably.
- The following results can be duplicated in your head or on a pocket
calculator.
Continued
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AJ Corcoran
1 Bogan Street
Summer Hill NSW 2130
Australia
December 2008, Revised March 2009.
Reproduction
"The Two Faces Of Zero" is released in public domain.
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