# Editing 622: Haiku Proof

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{{w|Euclid's theorem}} states that there are an infinite number of primes, prime numbers being numbers that are only divisible by themselves and 1. The most notable proof of this theorem, and the one presented in this comic, was first given by Euclid himself in his ''{{w|Euclid's Elements|Elements}}''. A more traditional form of this proof follows: | {{w|Euclid's theorem}} states that there are an infinite number of primes, prime numbers being numbers that are only divisible by themselves and 1. The most notable proof of this theorem, and the one presented in this comic, was first given by Euclid himself in his ''{{w|Euclid's Elements|Elements}}''. A more traditional form of this proof follows: | ||

β | :If we suppose that there are a finite number of primes, then they must have a product, i.e. ''p''<sub>1</sub>''p''<sub>2</sub>...''p''<sub>n</sub> = ''q''. Now consider ''q'' + 1. If this number | + | :If we suppose that there are a finite number of primes, then they must have a product, i.e. ''p''<sub>1</sub>''p''<sub>2</sub>...''p''<sub>n</sub> = ''q''. Now consider ''q'' + 1. If this number prime itself, then we have discovered a new prime number, contrary to the assumption that we listed them all. If it is not prime, it must have a prime divisor. Since all of the ''p''<sub>k</sub> are a factor of ''q'', they cannot be a factor of ''q'' + 1. So ''q'' + 1 is divisible by a prime not on the list, which again is a contradiction. Therefore, there must be infinitely many primes. |

At the last line of the haiku, [[Miss Lenhart]] says "Q.E.D., bitches!", Q.E.D. stands for "Quod Erat Demonstrandum", a latin phrase which is used to show a proof is over. Ironically, the proof is not complete. | At the last line of the haiku, [[Miss Lenhart]] says "Q.E.D., bitches!", Q.E.D. stands for "Quod Erat Demonstrandum", a latin phrase which is used to show a proof is over. Ironically, the proof is not complete. |