by David Roberson

Created on: September 19, 2008

Is it possible to divide a number by zero? Conventional thinking in mathematics declares this to be impossible, but this answer is contingent on a point of view. The problem here lies in the normal interpretation of the value of the number zero; a representation of "nothing" zero is seen as more of a place holder, a number that has no value. By contrast, infinity is a value that has no number. In multiplication, the value of any number times zero is zero. It is like declaring a number in theory. It is like saying "no number" and when it comes to division by zero, one might as well be saying "no division" because use of the number zero declares no number of parts into which a value could be separated, including one, producing a value in no parts. The common assumption is that division by zero would equal infinity.

The question to ask here is, is there any other representation of zero that could allow for a different point of view, one from which a number can be divided by zero? The answer to this question is, surprisingly, yes. It can be done on any number line that includes positive and negative numbers. For simplicity's sake, ten divided by zero is equal to five plus minus five; it is a line segment with an absolute value of ten and an effective value of zero - or zero to the power of one (indicating one bisection). It could also equal two-point-five-sub-x minus two-point-five-sub-x plus or minus two-point-five-sub-y minus two-point-five-sub-y; it is an intersection of vertical and horizontal line segments with an absolute value of ten and an effective value of zero - or zero to the power of two (indicating two bisections).

To be a bit more explicit, any number divided by zero is equal to a symmetrical, neutral "excluded" equation. As stated above, division by zero declares no number of parts into which a value can be separated, but it does not matter. Any rational number of parts that, in absolute value, cancels out the apparent value will suffice. A valid solution of ten divided by zero might be a circle with the circumference of ten at a radius perfectly perpendicular to the number line at zero. In application, a number divided by zero is effectively "displaced" from the working continuum; the segment of the number line bridging zero is effectively compressed into the singularity of the zero point. This could be represented by placing that segment across the zero point perpendicular to the base number line. It represents a number or value that still exists but is now external to or in a different dimension from the original system.

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