Get a Widget for this title
RSS FeedDivision by zero: Is it really impossible?
Results so far:
| No | 46% | 564 votes | Total: 1216 votes | |
| Yes | 54% | 652 votes |
No
Write now
Print
Invite a writer™
Add to FavoritesMany people have argued over the question, "Can you divide by zero?." Some people believe you can divide by zero, and others firmly believe it is impossible to divide by zero. Division by zero is in fact possible. The reason division by zero is possible is because it allows important results to come to light. There are instances when division by zero is not possible and other circumstances where it is possible and necessary.
During your math education, you were probably told it was not possible. The reason for that was because most of the math that you dealt with during high school and even early college centered around the real number system. The real numbers contain the rational and irrational numbers. Rational numbers are numbers that can be expressed as a fraction and terminate after a decimal point. Irrational numbers are numbers that cannot be expressed as a fraction and never terminate after a decimal point. The real numbers are basically every number about which you were told.
Division is the inverse of multiplication. For instance, if the following is an equation: 5y = 20, one can easily solve for y by dividing both sides by 5 to yield an answer that y=4. This can be checked by multiplying 5 and 4 to get 20. Let's look at a more complicated example: 0y = 0. What is the value of y? Well, y can be any number. It can be any of these numbers: -231, 5, 2/3, . The answers are endless. Because of this fact, y can never be recovered by inverting the process of multiplication. No other number has this property, and it is because of this that division by zero is undefined for the real numbers.
You might be thinking that I am not supporting my side that division by zerp is possible. Well, here comes the supporting evidence. Division by zero is in fact possible. The real numbers are a subset of the complex number systems. In the complex number system, division by zero is defined. If z is any element of the complex number, and z is divided by 0, the result is known as complex infinity. This only holds true if z does not equal 0. This shows this important property: for z not equal to 0, the limit as w goes to 0 of w/z = . This does not mean that z = w. Zero still does not have a multiplicative inverse.
There you have it. Division by zero is not possible in the real number system, but it is possible in the complex number system. The next time someone asks you, "Can you divide by zero?" you will know the answer. It is possible to divide by zero.
Learn more about this author, Jeremy Ross.
Click here to send this author comments or questions.
Yes
I'll let you know up front that I'm not a mathematician. When I was in school I probably generated a half ton or more of eraser shavings from redoing botched math problems and there was more than one occasion where I stared in blank incomprehension at a page of algebraic equations, wondering about the sanity of mathematicians in general. I sweated and cursed through advanced mathematics and statistics when I went to college and metaphorically fell on my knees in thankfulness on the day I'd finished all the required math courses. That being said, there are a few things I know with certainty about math.. I know them with certainty if only because they were drilled into my head over and over and over again by several different teachers. One of these things is that it is friggin' impossible to divide by zero.
Zero is a number that represents nothing. A blank. A void. We humans have a hard time visualizing what nothing looks like. Imagine a space....er... no, not a space...maybe a patch or a blob. And in this blob there is...wait a minute...is this a three-dimensional space or just a flat surface? What about texture? There can't be any of those things because this is nothing, right? So how can we divide anything by something which is itself undefinable? There are those who argue that nothing is still something. This could be true but until we can set some parameters for what constitutes nothing then this theory is just theoretical thinking with no practical value. Smarter minds than mine can try to define the Undefinable. Theoretical physics is beyond me.
But just to have a little fun, I'm going to pretend for a moment that I am a freakin' fantastic theoretical physicist. Let's say that I have found a way to divide something by nothing. And the answer I get is...everything! Since the universe is full of nothing, then dividing something by nothing will give you everything that exists, has existed, or ever will exist in the universe. it's like adding a spoonful of salt to the ocean. The salt and water will mix until they become inseparable, at least not unless you happen to come across a really big strainer.
My logic is crazy logic, with Douglas Adams, Terry Pratchett, and a little Buddhism on the side. But I stand by what I said earlier, that it is impossible to divide anything by zero, unless your goal is to merge with the universe. I may become a theoretical physicist yet.
Learn more about this author, Anitra Marie.
Click here to send this author comments or questions.
