I have to multiply the left hand AND the right hand side by zero. Well, then by this assumption that I am never willing to give up, this left hand side right over here, must be equal to x. And by this assumption right over here, that I am not willing to give up, This right hand side right over here must be equal to 0. But I just hit a contradiction! And I am not willing to give up the idea, I am not willing to give up either of these ideas.
I am defining what it means to divide by zero. Or if I am defining what it means to divide by anything And I am not willing to give up the idea that anything times 0 is 0. So all of these things The only thing that I can give up is this right over here. And I'll say, well, I guess k will have to stay undefined.
Now that out of the way This was a situation when x does not equal zero. But what about when x DOES equal zero. So let's think about that a little bit.
And once again, I will try to define it. So I will assume Wolfram Alpha » Explore anything with the first computational knowledge engine. Wolfram Demonstrations Project » Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Step-by-step Solutions » Walk through homework problems step-by-step from beginning to end.
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Asked 6 years, 7 months ago. Active 4 years ago. Viewed 47k times. Q- Prove that the roots of the following equation are real. Community Bot 1. Sufyan Naeem Sufyan Naeem 2, 3 3 gold badges 16 16 silver badges 30 30 bronze badges. It doesn't mean that. Every answer below is telling you that is not what "undefined" means. Before you try to understand what "undefined" means, perhaps you should try to understand what "defined" means because "undefined" means nothing more or less than "not defined.
I have never heard that "a number divided by zero can be any real number" - on the opposite, it is no real number. I would have recommended linking to the other question while explaining the relationship rather than just cutting and pasting.
If there is some doubt or confusion that is not based on such an imprecise statement then it would be better to have an example that is not based on such an imprecise statement. In particular, changing "mathematics" to "maths" is not absolutely necessary! Show 4 more comments. Active Oldest Votes. Carsten S Carsten S 8, 1 1 gold badge 18 18 silver badges 39 39 bronze badges. It would be better if the question read something like this "Prove [ The result is not undefined, as there is no result.
You can't even get to a result other than to say, "I can't do what you want me to do, so I stopped. The operation is undefined, so there is no result.
In a computer, it generates an exception , since there is no defined algorithm or set of instructions for dividing by 0. Such an exception prevents the computer from trying to check the result, which has no representation. Show 5 more comments. This is even worse. Christian Blatter Christian Blatter k 13 13 gold badges silver badges bronze badges. Add a comment. Daniel W. Farlow Daniel W. Farlow Todd Wilcox Todd Wilcox 1, 1 1 gold badge 12 12 silver badges 17 17 bronze badges.
I just wanted to address this because it looked like none of the other very good answers have. Sufyan Naeem 2, 3 3 gold badges 16 16 silver badges 30 30 bronze badges. Isn't it? Sorry this was confusing. In math, for me, there isn't "right" and "wrong" definitions. There's "useful" and "less useful" definitions. You can choose to use that definition if you like, but you may find in your career that it is "less useful" than you may have initially thought.
I can't come up with a good reason to use such a definition. This has a nice equational theory, and has been studied by J. Bergstra and others.
Hagen von Eitzen Hagen von Eitzen k 28 28 gold badges silver badges bronze badges. What is an undefined expression? Category: science space and astronomy. What makes a rational expression? What makes a number undefined? What is an undefined equation?
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