Much Ado about Nothing

  Both the Greeks and the Romans lacked something in their mathematics that we now take for granted, ‘nothing’, a concept we don’t even think about anymore.  The number Zero, while common isn’t well understood, and as many school boards adopted the ‘new math’ the confusion only grew, a move that has typically been rescinded.  This writing is going to try to sort things for both the author and the audience.

  Starting with some of the basics, zero (0) is a whole number which represents an absence of value or quantity.  Zero is not a natural number, a natural number is the whole number greater than zero; probably a throwback to the Greeks and the Romans.  Also, zero is an even number as it fits the requirements: flanked on each side by an odd number, divisible by two (2), and it ends in the digit zero.

  Many people get confused about zero in that they don’t understand what zero actually does; and while zero represents ‘nothing’: the question must be asked – nothing of what?  As an example, we can take the number one thousand (1,000) and examine it from right to left: there are zero ones, zero tens, no hundreds, and a single thousand; showing once again that zero represents a lacking of value or representation. 

  Now we get to the catalyst for this paper, as here there are potentially three conflicting rules.  Zero also gets a pass on some of the other rules within mathematics.  This is the area where things get confusing: as A) any number divided by itself equals 1 (5÷5=1), though B) with zero it equals itself (0÷0=0), and C) zero divided by a number also equals zero (0÷5=0).  So, did mathematicians break the logic inherent in mathematics or perhaps it was slightly broken all along?

  Seemingly, when zero is used in the numerator slot the result is always zero, however when in the denominator position things turn tricky if you let them.  Before starting this writing, my position was that any number divided by an absence of value or representation remains the same and yet this is where Google and I disagree as Google reports it as ‘undefined’, also MS Excel throws a ‘division by zero error’ and so I carried on looking into it.

  Here is how it works, when one goes just to math, please play this out with the equations shown in A, B, and C above; take the denominator and move it to the other side of the equal sign and multiply;  via this method, all of the equations work as intended.  So now we can try the equation 1÷0=1.  This breaks, for once you move the zero to the right side of the equal sign and multiply, one ends up with 1=1×0, which results in 1=0 which is impossible; and so there you have it; I was wrong.

  In a recent conversation, my confidence superseded my competence and this writing was an attempt to re-balance that problem.