Zero Destroys the Number Line

Nearly everyone with a high school diploma has been forced to learn at least the basic laws of Algebra that are the foundations for all other mathematics. However, very few people ever really question the underlying theory from which we form our logic. We no longer carry the Renaissance approach to learning in which an individual would study a wide range of liberal arts to acquire a well rounded education. However, most of our early mathematicians were also philosophers and influential figures that shaped politics and religion. As a result, zero brought with it a threat to our understanding of logic. If we imagine the real number line as an elastic rubber band that can stretch and shrink, we are able to visually see how zero can create problems. Multiplication can be thought of as stretching the rubber band by a scalar. But when any integer is multiplied by zero, the entire number line collapses into an infinitely small point. So if multiplication crushes the number line, then division in theory should undue to destruction. This wishful thinking is anything but true. Dividing by zero, even one time, destroys the entire framework of mathematics. It is difficult to show without a simple proof, but by multiplying and then dividing any number by zero one can show that the ratio of zero to zero [0:0] is equal to anything and everything. One can imagine the problem this would have created among philosophers and mathematicians. Eventually, mathematicians came up with a clever solution to the problem by saying that the answer is “undefined”. This in itself is an oxymoron for in the very act of defining the unanswerable as “undefined”, we have in fact given it a definition.