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1无穷大

如果你用无穷大来计算,你一定要小心,因为

1 = ?

所以结果不是 1。这怎么可能呢?

 


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 = ?

 


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