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Zero to the power infinitely small
As you perhaps might expect applies
0Δx = 1
Explanation
For every power n ≠ 0 applies 0n = 0. The exponent may become very small or large, the result remains 0. So we say
as Δx 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 00 ≝ 1, as you cannot calculate it.