Use generalized induction as was done in Example 13 to
Chapter 5, Problem 45E(choose chapter or problem)
Use generalized induction as was done in Example 13 to show that if \(a_{m, n}\) is defined recursively by \(a_{0,0}=0\) and
\(a_{m, n}= \begin{cases}a_{m-1, n}+1 & \text { if } n=0 \text { and } m>0 \\ a_{m, n-1}+1 & \text { if } n>0\end{cases}\)
then \(a_{m, n}=m+n\) for all \((m, n) \in \mathbf{N} \times \mathbf{N}\).
Equation Transcription:
Text Transcription:
a_{m, n}
a_{0,0}=0
a_{m, n}= a_{m-1, n}+1 & { if } n=0 { and } m>0 \\ a_{m, n-1}+1 & { if } n>0
a_{m, n}=m+nl
(m, n) \in N X N
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