Shirley Crawford

Intermath – Algebra

February 20, 2003



PROBLEM:  Dividing by Zero --  Don’t just say it is undefined.



Why do we say that a number divided by 0 is undefined?  Why do we say that number “has no meaning?” 


Using a graphing calculator to illustrate the expression y = 1/x, where x = zero, we find that as the number x goes toward zero on the graph, the value for y goes up or down  toward infinity, but never touches zero on the graph.  The value for y comes very to zero, but does not actually touch it. 


For the formula y = 1/x, the following graph appears:



As the number y approaches zero on the x axis, it goes up or down (apparently to infinity) and comes close to the number zero, but never touches the point zero on the graph:


By zooming out on the graph, we see where it continues to avoid coming to the point zero:


This is one visible demonstration of why dividing by zero has no meaning.  Another example of dividing by zero is in the use of zero as a denominator in any fraction.  Here we find that the expression is “not a legal fraction because the overall value is undefined.”  For example, in the expression 4/0, the values are undefined and therefore have no meaning in mathematics.  This will hold true for any fraction where the denominator yields a zero, and is not a “legal fraction,” as in the expression y = 12/3-3 or y = 12/0; thus creating a fraction with an undefined value.