Definition 2.3.11 (Exponentiation for natural numbers). Let \(m\) be a natural number. To raise \(m\) to the power \(0\), we define \(m^0:=1\); in particular, we define \(0^0:=1\). Now suppose recursively that \(m^n\) has been defined for some natural number \(n\), then we define \(m^{n\pp}:=m^n\times m\).
Definition 2.3.11.
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Exercise 2.3.4
\(=\) { Definition of exponentiation: \(m^0:=1\); \(m^{n\pp}:=m^n\times m\);
\(\hspace{1cm} a^2=a^{1\pp}=a^1a=a^0aa=1aa=aa\) }\(=\) { Definition of exponentiation: \(m^0:=1\); \(m^{n\pp}:=m^n\times m\);
\(\hspace{1cm} m^2=m^{1\pp}=m^1\times m=m^0\times m\times m=1\times m\times m=m\times m\) }