Show 10 more comments. Add a comment. Fred Fred 1 1 silver badge 2 2 bronze badges. That's a very important point, many beginners confuse that, probably due to the ubiquitous abuse of notation.
After reading few post on this we came to know that it depends on the context of its use. Indeed, there are already a couple answers showing that is is well-defined in certain contexts. That is really what I meant by that comment The only ring where zero is invertible is the zero ring.
But what you wrote was a much more general assertion not restricted to rings, viz. That is false. Show 3 more comments. Michael Hardy Michael Hardy 1. Albert Albert 8, 1 1 gold badge 17 17 silver badges 47 47 bronze badges. Will Jagy Will Jagy k 7 7 gold badges silver badges bronze badges. Gives them character. Not what I would have done if I had been giving the first answer, rather than the fifth or so.
Mark Ribau Mark Ribau 4 4 bronze badges. If you force floating-point numbers you get the same result you attribute only to Javascript. Zev Chonoles Zev Chonoles k 18 18 gold badges silver badges bronze badges. Mikhail Katz Mikhail Katz But there is no precise definition of number in general use.
In fact some structures where such expressions are valid are called "number systems" by some authors. Back then you accept what a "number" is intuitively.
Technically I should say that infinity and minus infinity do not belong to the same "number system" that the OP is working in but that is just being pedantic for no reason. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. Linked 2. See more linked questions. Related 2. To begin with, how do we define division? The ratio r of two numbers a and b :.
That's a common way of putting things, but what's infinity? It is not a number! Why not? Because if we treated it like a number we'd run into contradictions. Ask for example what we obtain when adding a number to infinity. The common perception is that infinity plus any number is still infinity. If that's so, then. That in turn would imply that all integers are equal, for example, and our whole number system would collapse.
As we divide one by smaller and smaller and smaller positive numbers, we get a larger and larger and larger value. Based on just this you might say, well, hey, I've got somewhat of a definition for 1 divided by 0. Maybe we can say that 1 divided by 0 is positive infinity. As we get smaller and smaller positive numbers here, we get super super large numbers right over here. But then, your friend might say, well, that worked when we divided by positive numbers close to zero but what happens when we divide by negative numbers close to zero?
So lets try those out. Well, 1 divided by negative 0. And, if we go all the way to 1 divided by negative 0. So you when we keep dividing 1 by negative numbers that are closer and closer and closer and closer to zero, we get a very different answer. We actually start approaching negative infinity. So over here we said maybe it would be positive infinity, but you can make an equally strong argument that it could be a very different number.
Negative infinity is going the exact opposite direction. So you could make an equally strong argument that it should be negative infinity.
And this is why mathematicians say there's just no good answer here. Especially one that's consistent with the rest of mathematics. They could have just said it's equal to 42 or something like that.
But that would make no sense.
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