By inductive assumption, v . distance after " i " " 1 iterations is at most the length of this path.
2.
The inductive step is similar to the above, but instead of applying proportionality to the volumes of the-balls, the inductive assumption is applied instead.
3.
If a deductive justification for induction cannot be provided, then it appears that induction is based on an inductive assumption about the connection, which would be begging the question.
4.
The inductive assumption can be applied here since each event is conditioned on lesser number of other events, i . e . on a subset of cardinality less than | S |.
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