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The rooted Fibonacci trees Tn are defined recursively in the following way. T1 and T2 are both the rooted tree consisting of a single vertex, and for n=3,4, …, the rooted tree Tn is constructed from a root with Tn-1 as its left subtree and Tn-2 as its right subtree. What is wrong with the following "proof" using mathematical induction of the statement that every tree with n vertices has a path of length n-1 . Basis step: Every tree with one vertex clearly has a path of length 0 . Inductive step:
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