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### Zero to the power of negative infinity

We want to know if 0^{–∞} has a meaning.

##### Investigation

Infinity is a strange notion, negative infinity is even more obscure. We don't understand what it means. But we can use it in calculations. Combinations of 0 and ∞ give surprises, as

It can be anything, and also just zero. Well, infinity is not a number. Let's calculate

Division by zero is not allowed. The answer is therefore undefined.