Why is 0 0 indeterminate when any number divided by zero is undefined?

The reason, in short, is that whatever we may answer, we will then have to agree that that answer times 0 equals to 1, and that cannot be ​true, because anything times 0 is 0. Created by Sal Khan.

Is 0 0 DNE or undefined?

in substituiting, we get 0/0 so it has an indeterminate form which requires further work to ascertain if it is truly DNE or if it has a limit. That is correct.

What is indeterminate and undefined?

Broadly speaking, undefined means there is no possible value (or there are infinite possible values), while indeterminate means there is no value given the current information.

Is undefined same as DNE?

“Undefined” and “Does not exist” are pretty much just different ways of saying the same thing, unless we further clarify what we’re saying. For example, is undefined OVER THE REAL NUMBERS, but it DOES exist. It is defined if we allow complex numbers to be considered.

Is infinity a DNE?

If the function is continuous at the value x approaches, then substitute that value and the number you get will be the limit. If you get something that is not zero divided by zero, the limit does not exist (DNE) or equals infinity (see below).

Why is the value of 1/0 undefined?

To address the question why 1 / 0 is undefined, note that if 1 / 0 is some real number r then 1 = 0 ⋅ r = 0 by one of the properties shared by the usual number systems. So if you want to preserve that “nice” property then you cannot define 1 / 0; and if you want to define 1 / 0 then you abandon the property.

Is there a limit to 1/0?

Even when you are considering limits, it’s still undefined. The limit doesn’t exist because there is no limit. You will only see that 1/x gets larger and larger (in either direction) when x gets closer and closer to zero. That means 1/0 is undefined. Both are undefined. Division by zero doesn’t exist in the real number system. Why is 1/0 undefined?

What is the value of 0/0 =?

0/0 = 1 ==> 0 * 1 = 0. Oops, that also works. and so does 0/0 = 2 and 0/0 = 6 and 0/0 = any real number. This is where it breaks down.

Why is 0/0 and Infinity divided by Infinity indeterminate?

As we cannot guess the exact number, we consider it as a length of a number or infinity. In normal cases, the value of something divided by 0 has not been set yet, so it’s undefined. 0/0 and infinity divided by infinity is indeterminate. Why? In this case, the mathematical expressions are correct.