Why is division by 0 undefined

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.

So, in that case , what does it mean to divide by zero? And this first part, if you were to plug in, say, a 1, a 2, or any other number, then it wouldn't equal that so we can actually say that "c" is unique. So it satisfies that this is actually the only number that you can put there to actually equal zero.

We can say that zero divided by 1 equals zero and we can also say that this is "defined" as well. Our next example is going to be 1 divided by zero. And a lot of people like to guess that it would be zero. So, let's try that out. We take our "b" which is zero and multiply it by our "c" which is zero. We don't get what "a" is because of course, zero times zero does not equal 1.

Since it doesn't satisfy at least one part of that definition, then that means that it is considered "undefined. Well, I think all of us can agree that we can obviously put in a zero there and the second part will be defined. So, this part works. Well, we can also put in a 5 if we wanted to because zero times 5 equals zero, so it still works for that second part.

We can actually plug in anything into there. We can say, zero over zero equals x. We still have zero times x equals zero. But what I'm getting at is that it is the first part that is not being satisfied.

Show 4 more comments. Active Oldest Votes. Acccumulation Acccumulation Being able to explain why division by zero is undefined requires breaking the process down into terms they can understand.

If you give 10 people 50 apples, the apples still exist. Maybe think about baskets instead? Add a comment. Michael Rybkin Michael Rybkin 6, 2 2 gold badges 9 9 silver badges 26 26 bronze badges.

For a more thorough explanation, please consult the Wikipedia page that talks about raising zero to the zeroth power: en. Thanks for that! Wuestenfux Wuestenfux Thomas Weller Thomas Weller 2 2 silver badges 12 12 bronze badges. The simplest way to describe this for kids I can think of: Anything multiplied by zero is zero.

Multiplying anything with two non-zero values gives a non-zero value. Shouldn't be a problem. Division of the result by one of those values gives you the other. We did the opposite of 2. There is no such number because of statement 1 - hence divide by zero is undefined. As different algorithms give different answers that shows the point.

From a purely functional perspective where there are no algorithms this is the most sensible mapping for the inverse of the multiplication function. Upcoming Events. Featured on Meta. Now live: A fully responsive profile.

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