So 6.4 was difficult to understand. It seemed very similar to the principle of mathematical induction except there is another step added in where you define where a variable i lives. It made sense until they made an assumption by the recurrence relation. In the end, it think it just means showing an added case.
This obviously applies to live because recursion is used a lot by computers and calculators to calculated things numerically. The shorter the recursive formula, the more efficient the calculator, and the quicker that things are processed. I think that this is the relationship.
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