Editing 622: Haiku Proof
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 12: | Line 12: | ||
{{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 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. Since each ''p''<sub>k</sub> is a factor of ''q'', they cannot be a factor of ''q'' + 1. So ''q'' + 1 has no prime factors, which means it must be prime itself; however, we assumed we had listed every prime number, which means a contradiction has occurred. Then our supposition is false, so there must be an infinite number of primes. |
At the last line of the haiku, [[Miss Lenhart]] says "Q.E.D., bitches!", Q.E.D. stands for "Quod Erat Demonstrandum", which means "Thus, it has been demonstrated." This is 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", which means "Thus, it has been demonstrated." This is a Latin phrase which is used to show a proof is over. Ironically, the proof is not complete. |