Why is something divided by zero undefined

With undefined, think back to the terrible pizza party. If you try to split 3 pizzas and everybody gets 0 slices, the pizza will not be split no matter how many people come. Since no number of people can split the pizza, undefined means no value. But indeterminate is slightly different: there is no meaning to 00 because we have competing approaches on how to solve this problem.

We know that 0 divided by any number is 0, but we also know that any number divided by 0 is undefined. Which piece of information do we use? This conflict is why we call this form indeterminate. Replace the 3 by some other positive integer , and the problem works out the same way. Here's a fantastic video by Numberphile explaining what goes on behind the scenes when you divide by 0, have 00, and have We know that division is the same as repeated subtraction.

Dividing by 0 would be repeatedly subtracting 0 from a number. This would go on forever and we would never reach an answer. Let's think about fractions for one second. If two fractions have the same denominator , the one with the bigger numerator is bigger. Suppose b and c are both non-zero. Then, in a sense that can be made precise. A similar statement applies to the numerator of a ratio except that it may be zero. There are many ways in which we can choose a and b and let them become smaller.

For example, we might pick. But we could just as well pick. Then the ratio is always 2! In math-speak, we would say that this is undefined. My understanding of division by zero goes back to the definition of rings. You can repeat this with other numbers as well, so the children can see that the result is arbitrary. This should make it pretty clear that if we allow division by zero, other laws cannot hold. So it's better undefined. I think you've pretty much got it and others have gone into more detail on the various bits of maths related to this.

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Learn more. A thorough explanation on why division by zero is undefined? Asked 2 years, 6 months ago. Active 1 year, 9 months ago. Viewed 4k times. It has so many examples in the answers, too. This problem really has been explained so many times, with so many good answers. Here are some thoughts I typed up, which may be helpful: ee.

The whole scenario ignores you, and assumes that you have none left over. If you take a fair share instead, then you are dividing it by a number one greater. To model division by zero in that case, even you yourself would disappear, and so would the remaining apples. So, let's label it as that. Make sure that when you are faced with something of this nature, where you are dividing by zero make sure you don't put an actual number down, or a variable down.

Just say that it equals "undefined. We can say that zero over zero equals "undefined. Learning Support. What is Learning Support? How do I know my Placement? What are the requirements? English Learning Support. Math Learning Support. Placement Test Practice. Study Resources.