ARE ALL NUMBERS EQUAL?

The title of this charmer is clearly preposterous! But as you will see from the demonstration below, such may not be the case. Present this demonstration line by line and let you draw your own conclusions.

We shall begin with the easily accepted equation:

Each succeeding row can be easily justified with elementary algebra. There is nothing wrong with the algebra. See if you can find the flaw.

When x = 1, the numbers 1,2,3,4,....,n are each equal to 0/0, which would make them all equal to each other. Of course, this cannot be true. For this reason, we define 0/0 to be meaningless. To define something to make things meaningful or consistent is what we do in mathematics to avoid ridiculous statements, as was the case here. Be sure to stress this point before leaving this unit.