Zero to the Power of Zero/Historical Note

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