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Controverys noted: excluded middle etc
#Since ''N+1'' is composite, there must be a prime missing from our set of primes. But this set contains all primes
#Since ''N+1'' is composite, there must be a prime missing from our set of primes. But this set contains all primes
#Therefore, our initial assumption ("there are finitely many primes") is invalid
#Therefore, our initial assumption ("there are finitely many primes") is invalid
There is an academic controversy over whether proofs by contradiction (see also [[Excluded Middle]]) should be accepted qua proofs; either due to concerns regarding computability, or [[Intuitionist Mathmematics]]. These are not necessarily held to be distinct concerns. Most mathematicians disregard any such controversy and accept proofs by contradiction.
[[Category:Mathematics]]
[[Category:Mathematics]]