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No

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Actually 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.

Learn more about this author, Joe Murray.
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