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Infinitely small to the power zero

The calculation of infinitely small to the power zero gives as outcome

∆x⁰ = 1

That we find to be strange.

 

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Explanation

For every number a ≠ 0 you can calculate that a⁰ = 1. Infinitely small does not exist (it has no fixed value) , and so applies

∆x⁰ = 1

because Δx is very small, but infinitely small is not zero. This is one of the many explanations why 0⁰ ≝ 1 is determined by definition.

 

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History The American computer scientist Donald Knuth (1938) contends strongly: 00 has to be 1.

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