J.Sun's definitions
Which Was What We Wanted. The abbreviation WWWWW may be placed at the end of a mathematical proof to serve a similar purpose as QED.
We will prove by reductio ad absurdum that there are infinitely many primes.
Assume the opposite, that there are exactly n primes. Let set S contain all n primes in increasing order, such that S={X1, X2, X3... Xn}.
Consider Y such that Y=1+(X1*X2*X3*...*Xn)
Y gives a remainder of 1 when divided by any element of S. Hence Y is not divisible by any prime and must be a prime itself. Yet this contradicts the assumption that there are only n primes, as the existence of Y means there must be at least n+1 primes.
The assumption must then be false and there must be infinitely many primes.
WWWWW.
Assume the opposite, that there are exactly n primes. Let set S contain all n primes in increasing order, such that S={X1, X2, X3... Xn}.
Consider Y such that Y=1+(X1*X2*X3*...*Xn)
Y gives a remainder of 1 when divided by any element of S. Hence Y is not divisible by any prime and must be a prime itself. Yet this contradicts the assumption that there are only n primes, as the existence of Y means there must be at least n+1 primes.
The assumption must then be false and there must be infinitely many primes.
WWWWW.
by J.Sun March 22, 2009
Get the WWWWWmug.