by Ron Pena

Created on: July 13, 2008

Well well, are we racking our brains over this issue? Ladies and gentlemen, please allow me to put this issue to rest! I am a professor of mathematics with lifelong studies in foundational systems of analysis. The answer to this debated question is unequivably,logically, and undoubtably, YES! Division by zero is impossible! Let me preface my argument by stating that there are many paradoxes out there that may present an illusionary concept of reality. For example, let me hold a pen twelve inches from the floor. I will release the pen. My contention is that the pen will never reach the floor. Now, you're saying that I'm wrong. Well, I say to you that the pen must first travel halfway towards the floor. Now it's six inches from the floor. Next it must travel halfway towards its destination. The fact is that it will always have to travel halfway towards the floor, forever. Thus it will never touch the floor because there is always a halfway journey to the floor. Now you may say, hey, I heard the pen hit the floor with a thud. NO! That is only an illusion! It is still traveling halfway down forever! Is your mind convinced? Well, this is the problem with paradoxes. However we are realists, and we don't accept that argument as fact.

Let me introduce a simple equation. Let a=b Any questions? Now multiply both sides by a. This yields a new equation a(squared)=ab Now let us subtract b(squared) This produces a(squared)-b(squared=ab-b(squared). Are you with me? At this point, please take a piece of paper and translate what I've written into a mathematical problem. Relax. Inhale! Exhale! Now factor both sides. Now we have (a-b)(a+b)=b(a-b). Remember, what we do to one side, we do to the other side without disturbing the value of the equation. Now, let us divide both sides by (a-b). This produces a+b=b. So far so good? Now let a=b This gives us b+b=b. Let's proceed. Now we have 2b=b. Divide both sides by b. WHOA! Our conclusion is 2=1! What happened! Let us proceed with our analysis of the problem. Let us assume that division by zero is allowed. This will be our premise. Now the keen observer will say that since we divided both sides by (a-b) which is really 0, since a=b, the result is invalid since division by zero is not allowed. This brings us to a conclusion of reductio ad absurdium, since we have a and not a. We have division by zero is allowed and division by zero is not allowed. This is a contradiction and therefore the premise that division by zero is allowed is

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