Assuming the negation of the conclusion but never deriving a contradiction—instead, you derive the original premise and call it a day (which is actually a direct proof). Extra Quality Fix: Explicitly write "We assume ( \lnot B )" at the start and "This contradicts ( A ) because..." at the end. If you cannot name the contradiction, you haven't finished.

Interpreting ( \forall \epsilon > 0 \exists \delta > 0 ) as "There is a delta that works for all epsilon." Extra Quality Fix: Use the game metaphor . You (the prover) choose ( \delta ) after the opponent (the adversary) chooses ( \epsilon ). Your ( \delta ) can depend on ( \epsilon ). Practice with epsilon-delta proofs from calculus.