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1/0 = 1/0. Who Says It's Not Defined?

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Posted by Aurino Souza on November 28, 2003 17:08:07 UTC

Hi Tim, nice to see you posting again. I'm tired of reading Mike's posts.

[division by zero] is undefined. who came up with that? what was the reasoning behind it?

You know, I always took it that for granted that you can't define x/0 without opening the door for mathematical nonsense, but in the end the only real problem I could find was how to define 0/0. Defining 1/0 = (any arbitrary symbol) works just fine for any value of x other than zero.

I guess mathematicians are not really interested in the problem, as it has no practical meaning. As I said in my previous post, there is no real problem (as opposed to abstract mathematical problems) in which you must know the result of x/0.

Notice that mathematicians were faced with a similar dilemma when confronted with the question "what is the square root of -1", and I suspect the reason they came up with a solution was because there are real world problems in which you must know the square root of a negative number.

its ok to divide by really, really infinitesimaly small numbers but not by zero. just wondering if any one knows

It's ironic that people like Paul argue that math is completely abstract, and yet still think of "a very small number" as being entirely different from "zero". In truth the only thing that differentiates "zero" from "a very small number" is that things of very small magnitude are supposed to exist while things of zero magnitude do not. But the same mathematician who tells you that will completely evade the question of what is the mathematical meaning of "exists".

Abstract thought is the shortest route to confusion.

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