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### 1 to the power infinity

If you calculate with infinity you should always be careful, as

1

^{∞}= ?

So the result is not 1. *How is that possible?*

##### Explanation

You might not expect that. But the number 1 has special properties, and infinity is not a number. Therefore, you may not just conclude that

It depends on how the number 1 and how infinitely came into being in the course of a calculation.

##### Example 1

We start from the composite function

where *f* (*x*) = 1 and *g* (*x*) = *x*. For *x*→∞ the following occurs

Now we take the same function, but with and *g* (*x*) = *x* this gives

This is the base *e* of the natural logarithm. By choosing other functions you can get different results. Therefore 1^{∞} only has a meaning if its origin is known. So in general applies

1

^{∞}= ?