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Feedback: You can't divide by zero!
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Feedback: You can't divide by zero!
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thedoc
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Feedback: You can't divide by zero!
«
on:
01/08/2012 17:30:01 »
Calvin Lee asked the Naked Scientists:
Dear Dr. Chris,
I'm
a devoted listener
to your
Naked Scientists podcasts
and have marveled at your expertise in all matters scientific and otherwise. However, I must inform you that you erred in your reply about "When will you be able to divide by zero?"
The correct answer should have been "Never!".
Your answer was (I'm paraphrasing): "You can! It's infinity. We regard division by zero as having an infinite number of solutions."
This is not true.
First of all, there is no such number as infinity. In mathematics, infinity is not a number. It's just a useful representation of something that goes on forever (like an infinite sum in calculus), a measure of the size of a set (set theory), and many other uses. It is not a number. Also, your last statement that division by zero can have an infinite number of solutions is exactly why mathematicians say that division by zero is undefined. When something cannot be defined unambiguously it is deemed undefined.
I'm a university math instructor and the way I explain why you can't divide by zero is to remind my students of what is meant by division. When you divide x by y and let’s assume that x is some positive number. When you ask for the value of x/y you are asking how many times can y fit into x. Obviously, if y is zero this is a meaningless question since no matter how many zeros you have they cannot add up to x. To hammer this point into my students I'd say the question "What is x/0?" is not so much a math question as it is a philosophical question, namely "How many angels can fit onto the head of a pin?" No one knows. My final point is this: It can be demonstrated that division by zero (if allowed) will introduce contradictions galore into mathematics. In fact you can prove that any number is equal to any other number, which is nonsense!
I remain a big fan of your show and your explanations are generally spot-on, but not on this particular question.
Calvin Lee, Ph.D.
San Francisco, California
U.S.A.
What do you think?
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Last Edit: 01/08/2012 17:30:01 by _system
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