Division by ZeroDate: Wed, 2 Nov 94 14:20:49 EST From: "Terry Strohecker" Subject: Question! I am in need of a detailed answer to the following question: Why can't you divide a number by 0? Thanks for your time. Terry stroheck@student.msu.edu Date: Wed, 2 Nov 1994 14:50:44 -0500 From: Melissa D. Binde Subject: Re: Question!: division by zero I don't know of the "real" answer to this one, but this is how I always thought of division. When you divide a number by another number, you can think of splitting it up into groups. For example, 10/5 (ten divided by five): take the ten and divide it up between five groups so there is nothing left of the ten. You get two in each group, so 10/5 = 2. This works for numbers that don't divide evenly also: 5/2: take the five and divide it up between two groups so there is nothing left. You can put two in one group and two in the second group, but that leaves a remainder of one. So you can split the one between the two groups and get 2.5 (2 and 1/2) in each group. So 5/2 = 2.5. However, if you try to do this with zero, it doesn't work. Take any number -- we'll use 10 to make it simple. What happens when you try to split ten up into zero groups with no remainder?? You can't do it! If there aren't any groups, then you can't put the ten anywhere. To make this idea clear, mathematicians call division by zero "undefined" -- meaning that it doesn't really make any *sense* to try to split a number into zero groups. If I'm wrong on this, I'm sure one of the other "doctors" will correct me! Melissa From: Dr. Ken Subject: Re: Question! Date: Wed, 2 Nov 1994 16:53:27 -0500 (EST) Hello Terry! We here at Math Headquarters have been thinking about your question some more, and I think we've come up with something about why you can't divide by zero. There are sort of two reasons. For one thing, when you divide one number by another, you expect the result to be another number. So in particular, look at the sequence of numbers 1/(1/2), 1/(1/3), 1/(1/4), ... . Notice that the bottoms of the fractions are 1/2, 1/3, 1/4, ..., and that they're going to zero. So if there's a limit to this sequence, we would take that number and call it 1/0. So let's see if there is. Well, the sequence turns out to be 2, 3, 4, ..., and that goes to infinity. Since infinity isn't a real number, we don't assign any value to 1/0. We just say it's undefined. But let's say we did. Let's say that infinity is a real number, and 1/0 is infinity. Then look at the sequence 1/(-1/2), 1/(-1/3), 1/(-1/4), ..., and notice again that the denominators -1/2, -1/3, -1/4, ..., are going to zero. So again, we would want the limit of this sequence to be 1/0. But looking at the sequence, it simplifies to -2, -3, -4, ..., and it goes to negative infinity. So which would we assign to 1/0? Negative infinity or positive infinity? Instead of just assigning one willy nilly, we say that infinity isn't a number, and that 1/0 is undefined. I hope this helps. -Ken "Dr." Math |
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