Maeckes logo

<    1    >


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 = ?

 


Deutsch   Español   Français   Nederlands   中文