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Worth noting here is that there is an additional level of certainty in the validity of a statement when you have multiple proofs of said statement. By having multiple ways to solve the same problem, all yielding the same answer, our surity of the statement increases dramatically. In a classroom setting you could perhaps bring up examples of "proofs" which were thought to be groundbreaking but were later proved wrong by subsequent results; on the other hand, you might also consider giving examples of when a theorem was questioned by the mathematical community but was confirmed by independent proofs, causing the theorem to be more widely accepted.