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RSS FeedDivision by zero: Is it really impossible?
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| No | 45% | 316 votes | Total: 696 votes | |
| Yes | 55% | 380 votes |
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Add to FavoritesActually the answer is Yes and No, and Both, and Neither.
My belief in the infallibility of my teachers destroyed any facet of my comprehension of 1st year calculus. I had to drop the course and realign my philosophical understanding of mathematics. Sometimes pedantry is far worse than explaining an incorrect method.
Consider the arc of a baseball. Introductory physics describes it as the shape of a parabola. True? No. It's the top part, or apogee, of an elliptical orbit - with the center of the Earth occupying the ellipse's second point of focus - it's just that the surface of the Earth gets in the way of the baseball completing its orbit. (Mathematically, the "second" focus of a parabola is "at" infinity, which is why, when you drag that focus around to the opposite quadrant of the graph, the parabola "becomes" a hyperbola.) So why don't they teach this? The answer is that the math for an elliptical trajectory is 10 times more difficult. Better to let the student grasp the simple idea first.
That's why, as a former math teacher, I wouldn't encourage cramming into a student's head that division by zero is not possible. If the student is smart enough to think that 1 divided by zero is infinity, they should be praised, then told that the correct answer to "1/0" is D.N.E. - Does Not Exist. Then, if they've reached an appropriate level of algebra, they should be shown how "the limit" gets them there much more legally.
Otherwise, when they get to calculus, they're going to hate you...because...
A derivative in calculus IS division by a type of zero into ANOTHER type of zero. This is accomplished by a method that I first suspected to be a dodge.
The dodge is, again, "the limit."
The greater a denominator becomes in a fraction, the closer the fraction approaches zero. (It is a frequent method of engineers to imagine the denominator at infinity, so they can eliminate a term from often intricate and laborious calculations.)
Conversely, the smaller a denominator becomes, the greater the number the fraction equals. Just try this on your calculators.
So division by zero (which is not very good grammar) is accomplished by simply using better
grammar:
"The limit, as x tends to zero, of 1/x equals infinity."
One divided by zero will never equal infinity because infinity is a concept, not a number.
But anyone who's ever survived 1st year calculus, realizes that the limit function moves the denominator of the derivative dangerously close to zero. The trick is to simply eliminate all the "zeros" before the derivative is resolved.
Not only is a derivative a type of zero divided by another type of zero. But an integral consists of slices of "zero" width times a quantity of slices that can approach infinity - that's zero times infinity - the outcome of which gets a tangible (and useful) solution.
This is why I admire Newton, Leibniz, and the other "discoverers" of calculus. Their leap of logic required great insight, as well as philosophical courage.
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Yes
I don't know which is scarier:
1. That 32 people here not only think that division by zero is possible, but that they believe it strongly enough to explain why, or
2. The um, creative "logic" they use to make their case, or
3. That we're even having this "debate" in the first place! What's next - "The Earth: Is it really round?" Or maybe "Dynamite: Does it really explode?"
Either way, I find this all vastly depressing, a stunning indictment of our educational system in this country and its abject failure to convey even the most elementary concepts in a memorable fashion.
Anyway, short answer: no, it's not possible to divide by zero. No way, no how. Quit trying. It's also not possible to fly to the moon by flapping your arms, no matter how strongly you believe. And if you hook up a motor to a generator, they won't make free electricity. Honest.
Well, that's actually all I had to say on this topic, so you can really stop reading right here but Helium won't let me post it unless it reaches the impressive length of 2400 characters and all I could manage was a paltry 849. Of course it should be more by now, but I have a funny feeling that I still have a lot more to go. Words to go before I sleep. Zzzz. What? Are you still here? Oh well... Hmmm, uh, la de da, nice weather we're having, don't you think? They say it might rain tomorrow, unless the sun comes out. So did you hear what the necktie said to the hat? "You go on ahead, I'll just hang around". ("Ahead", "a head", get it?) When is a door not a door? When it's ajar! Nyuk nyuk. Are we there yet? Dang - still almost 1000 characters to go. Hey, do you like Steve Wright? I love this one: "I cried because I had no shoes. Then I met a man who had no feet. So I took his shoes. Heck, I figured he wouldn't be needing them." Let's see, what else? "Never criticize someone until you've walked a mile in his shoes. That way, if he gets mad, you're a mile away - and you've got his shoes." (Courtesy, Steven Wright). Hoh kay - that's 1882 characters. I wonder if they include the spaces as characters or just the alphanumerics? Hey, now there's a great debate topic: "The space: character or just nothing?" Oh wait, how about "Lightning: can it really kill?" Hah - I'd get a charge out of reading that debate! Sigh - are we there yet? Don't make me stop this word processor! Wait til your dad gets home. Hey, I got one: "The world: Does it really exist or is it just a fig newton of your imagination?" (I know, with some people it's hard to tell.) If you locked 1000 monkeys in a room in front of 1000 typewriters, how long would it take them to recreate this divide by zero thing? Dang, now I'm hungry for a banana. Oh wait, gotta sneeze Excuse me! Hey, how about "Smallpox: is it really caused by a virus?" Or "Water: is it really wet?" Or "The dollar: is it really worth four quarters?" Gaaad, this just *has* to be 2400 characters by now! I'm going bonkers here. Arrrrgh! Make it STOPPPP!
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