The Summer Hill Journal Of New Physics

Arithmetic With Null and Zero

There is little difference between the { } and { 0 } views for addition, subtraction and multiplication except the difference in views as either the presence or absence of a value. There is a considerable difference however, for division.

If, when dividing or multiplying quantities, zero really represents "nothing at all" then there is literally nothing to operate on and the result is "null" or nothing, rather than any value. (The examples below work equally well with 2+0, 3-0, 4/0, etc, I use "1" for simplicity and consistency).

Using the conventional view of zero { 0 }:

1  +  0 =  1
1  -  0 =  1
1  *  0 =  0
1  /  0 =  Infinity

Viewing zero as null { } these may be thought of as:

1  +    =  1
1  -    =  1
1  *    = 
1  /    = 

Which is equivalent to:

1  +    =  1
1  -    =  1
1  *    =  0
1  /    =  0 (Note)

Taking the null view, if we interpret zero as null then we also interpret the null results of multiplication and division as zero, i.e. 1 * 0 = 0 and 1 / 0 = 0. We use null and zero interchangeably.

Division By Zero

Note the variation in the results between the views above: division by zero.

Interestingly, the old axiom that you "should not divide by zero" still holds true, not because it arbitrarily avoids infinities but because there is nothing to divide by and it is the right thing to do.

The null view then gives two differences:

(a) results may be null or "incomplete" reflecting the absence of a value, and

(b) the result of division by zero is zero or "nothing".

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