Zero to the Power of Zero/Cardinality of Mappings
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Example of Zero to the Power of Zero
By Cardinality of Set of All Mappings, the number of mappings from the empty set to the empty set should be given by:
| \(\ds \card {\O^\O}\) | \(=\) | \(\ds \card \O^{\card \O}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 0^0\) | Cardinality of Empty Set |
By Empty Mapping is Unique, there is exactly $1$ such mapping, demanding that $0^0 = 1$.