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#Therefore, our initial assumption ("there are finitely many primes") is invalid
 
#Therefore, our initial assumption ("there are finitely many primes") is invalid
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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.
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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 Mathematics]]. These are not necessarily held to be distinct concerns. Most mathematicians disregard any such controversy and accept proofs by contradiction.
    
[[Category:Mathematics]]
 
[[Category:Mathematics]]
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