In the handout it mentioned “for some 0 < a < 1”, i am wondering why is it not “0 <= a <= 1” because since we are adding an arbitrarily small positive delta to a, limiting the choice of a to be a fraction does not seem necessary.
Please specify an a such that 0 < a < 1. It will make the answer clearer.
As this can’t be explained without revealing the answers,
I suggest you work on the problem with the given description, specify a,
and if you still have an issue, ask by e-mail, not in the bb.