Definition:Perfect Digit-to-Digit Invariant/Also defined as
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Definition
Some sources disallow the zero from use in the definition of a perfect digit-to-digit invariant.
This is because $0^0$ is more usually defined defined as $0^0 = 1$ rather than as $0^0 = 0$.
If we define $0^0 = 1$ then not only does $438 \, 579 \, 088$ no longer qualify as a perfect digit-to-digit invariant, then nor does $0$ itself.
Sources
- Weisstein, Eric W. "Münchhausen Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MuenchhausenNumber.html