What if the limit is infinity?

We say that as x approaches 0, the limit of f(x) is infinity. Now a limit is a number—a boundary. So when we say that the limit is infinity, we mean that there is no number that we can name.

Is DNE and infinite the same?

The best way to approach why we use infinity instead of does not exist (DNE for short), even though they are technically the same thing, is to first define what infinity means. Infinity is not a real number. It’s a mathematical concept meant to represent a really large value that can’t actually be reached.

Is DNE and undefined the same?

In general “does not exists” and “is undefined” are very different things at a practical level. The former says that there is a definition for something which does not lead to a mathematical object in a specific case. The latter says that there is just no definition for a specific case.

Is infinity times 0 still 0?

Any number times 0 equals 0 and any number times infinity equals infinity.

Does infinity equal zero?

The concept of zero and that of infinity are linked, but, obviously, zero is not infinity. Rather, if we have N / Z, with any positive N, the quotient grows without limit as Z approaches 0. Hence we readily say that N / 0 is infinite.

Is negative infinity the same as DNE?

The best way to approach why we use infinity instead of does not exist (DNE for short), even though they are technically the same thing, is to first define what infinity means. Infinity is not a real number.

Are limits undefined or DNE?

There is a technical definition of a limit of a function which is usually worded using the Greek letters delta and epsilon. The answer to your question is that the limit is undefined if the limit does not exist as described by this technical definition.

Is undefined equal to infinity?

No, infinity and undefined are two different things.