Zero to the Power of Zero/Historical Note
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Historical Note on Zero to the Power of Zero
Whether $0^0 = 0$ or $0^0 = 1$ has been in question since the concept of zero was first raised as a concept.
From one point of view:
- $\forall a \in \R: a^0 = 1$
and so $0^0 = 1$.
From the other point of view:
- $\forall a \in \Z_{\ge 0}: 0^a = 0$
and so $0^0 = 0$.
Sources
- 1934: Karl Menninger: Zahlwort und Ziffer
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $0$ Zero
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $0$ Zero