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Zero to the power infinitely small

As you perhaps might expect applies

0Δx = 1



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.


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