Does it have to do with how we arrived at [tex] k+1 [/tex]?
Won't work for n=2: Let G_1 and G_2 be blonde girls and le't assume the theorem is true for n=1. If, for example G_1 is blonde, we can't take G_2 to the collection with her (that would be n=2), so we can't prove that G_2 is also blonde.
Hence the induction stops at n=1 and you'll never reach the step 3->4.
If you were guaranteed that the theorem is true for all pairs of blonde girls and I told you that my sister is blonde and has blue eyes then, yes, all blonde girls would have blue eyes.
That is a non sequitur.
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