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### Zero to the power infinitely small

As you perhaps might expect applies

0

^{Δx}= 1

##### Explanation

For every power *n* ≠ 0 applies 0^{n} = 0. The exponent may become very small or large, the result remains 0. So we say

as Δ*x* is very small, but infinitely small is not zero.

*Is this correct?*

It shows, that there is obviously a difference between infinitely small and zero. And because of this, it is determined *by definition* that 0^{0} ≝ 1, as you cannot calculate it.