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# Find the error in a “proof” by induction

Find the error in the “proof” that Apostol gives that all blonde girls have blue eyes. See I.4.4, Exercise #12, in Volume 1 for a statement of the false proof.

This proof assumes that the statement is true for $n=3$, i.e., it assumes that if there are three blonde girls one of which has blue eyes, then they all have blue eyes. Clearly, this is a false assumption.