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| No | 46% | 564 votes | Total: 1214 votes | |
| Yes | 54% | 650 votes |
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Add to FavoritesWe are sometimes bothered by the question: 'what happens when you divide by zero?' What really stumps us, though, is not what the result is, it is how one goes about performing the action. How can one slice an apple in zero pieces, for example. Our minds can't get past that conundrum, so often the question is abandoned as absurd.
However, an answer may yet be found.
Mathematics are often used to form a model that describes reality. For example, much of theoretical physics exists in a math-only form. Math is used to develop complex theories long before they can be tested experimentally, and even to make such experiments possible.
Yet, sometimes, the process needs to work the opposite way.
Great advances in mathematics have been made by incorporating the principles of science into the discipline. Cartesian curves, Geometry, and Algebra all arose out of translating elements of reality into mathematical concepts. The entire field of calculus was developed so that existing theories of motion could be described in mathematical terms.
Division by zero is one of the last strongholds of the much-despised term "undefined". Yet, for this too, we might find a reality-based model that can help us apply a definition.
Consider a massive star. When that star reaches the end of its lifespan, it undergoes a gravitational collapse, in keeping with the dictates of Einstein's Relativity and the theories derived from it. If it possesses a mass within certain limits, it collapses beyond all measurable boundaries, beyond even the electromagnetic limits of its sub-atomic particles. It becomes a Black Hole.
By definition, a Black Hole is a massive body of infinite density. Now, bearing in mind that the collapsing star does not automatically become more massive just because it has collapsed in this certain way, how can it be that it has an infinite density?
Well, density is basically mass divided by volume. As the star becomes a Black Hole, it shrinks into a singularity, a point of zero volume. Thus, at that point, there is an infinite density, even though there is only a finite quantity of mass.
Ergo, take any mass, divide it into zero volume, produce a Black Hole. Or, in mathematical terms, M/V=D where V is 0 yields M/0=Infinity. Even if Black Holes don't actually exist, the math is still valid.
Division by zero is possible, if only in extreme circumstances, and it yields a definite, predictable, defined result: infinity.
Not only do we now know that division by zero is possible, but we have an answer too.
Learn more about this author, Bryan Belrad.
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Yes
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,logicall y, 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 quickly dispelled! Thus division by zero is NOT allowed! Otherwise 2=1!
Have you followed me so far? Foundational systems are set up with rules, whether they are postulational, axiomatic, or via theorems as in plane geometry. For division by zero to be possible, an implementation of new rules needs to introduced to allow this to happen. Unfortunately, for the supporters of division by zero, you have no foundational backup for your claims. At this point may I ask my readers for any feedback before I present a resounding question to you relative to our topic.
Please indulge yourselves with the information I have just presented you, because the final question will be presented to you at this point. You have one hour to give me an answer. (I speculate that it will take you a lot longer to complete your answer. This is your final exam! Here's our situation. Division is really an allocation of items to specific targets. For example, I have 8 boxes of clothes. I wish to divide these among 2 people. How many times will I perform the allocation of these boxes to these 2 people? Let's see. On my first division, I have given 2 boxes to the 2 people. That leaves 6 boxes. On my second attempt, I have 4 boxes left. On my third attempt I have 2 boxes left. On my fourth attempt, I have 0 boxes left. Thus my division of 8 boxes divided by 2 resulted in 4. I allocated 2 boxes at a time to 2 people. I got rid of them in 4 tries!
Now, here is your final exam. I have 20 boxes of a liquid that contains the fountain of youth. Each box contains a bottle of 64 ounces of the liquid. It is guaranteed to be the foutain of youth. Now you're going to divide or allocate these boxes among 0 people. On your first attempt you gave 0 boxes because there are 0 people. There are 20 boxes left. On your second attempt, you gave 0 boxes, thus we have 20 boxes left. On the third attempt, you gave 0 boxes, thus we have 20 boxes left. Here is the problem. How many times will you distribute 0 boxes to 0 people until you exhaust the 20 boxes? You've got the rules of division behind you. Any conceptions of justification to exhaust the 20 boxes must be met by known mathematical rules. What is your answer? How many times will you give 0 boxes to 0 people until the 20 boxes are gone? Contact me with your answer. Remember 8/4=2 because 4*2=8. Thus 20/0=? because ?*0=20 (HINT)
Learn more about this author, Ron Pena.
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