Proof that primes are finite

Consider the set of all natural numbers and the set of all primes.
Since the set of all natural numbers less the set of primes is equal to the products or the elements of the subsets in the power set of the primes, then it is clear that mapping is injective, as all combinations are unique. This is by definition, as composite numbers are exactly those numbers that can the product of primes.
The cardinality of the set of natural numbers is infinite, but it is a much smaller infinity that that of real numbers, obviously, as there are an infinity of infinities (an infinite amount of irrational numbers between each rational, which are themselves infinite) in that set, but only a single infinity in that of the natural numbers.

Now consider: as the number progress to infinity, the likelihood of each number to be a product of some combination of each before it decreases to zero faster than the number line progresses. For example:
in {1,2}, there is a 50% chance of each being prime
in {1,2,...,10}, there is a 40% chance of each being prime
in {1,2,...,100}, there is a 25% chance of each being prime
in {1,2,...,1000}, there is a 16.8% chance of each being prime
in {1,2,...,10[sup]10[/sup]}, there is a 0.04% chance of each being prime
Thus, as infinity is approached, the number of primes approaches a finite number. This leads us to a contradiction, since any finite number of elements arranged in a any number of combinations will still only lead to a finite number of results.

Thus, since there cannot possibly be an infinite number of primes, there cannot be an infinite number of numbers.

The mere existence of infinity disproves infinity.

install gentoo

>>1
What's the last number, then?

>>3
^{9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999}+1

>>1

Non sequitur. The chance of finding a prime number in 1..n approaching 0 as n approaches infinity does not lead to the logical conclusion that there are a finite number of primes, or even that there are a finite number of twin primes, only that the average distance between primes is increasing.

>>4

What you just posted, +2, is higher than what you just posted. Therefore it is not the last number.

A number approaching zero isn't not the same as the number zero.

http://en.wikipedia.org/wiki/Prime_gap#Upper_bounds
fuck off retard, you're not even funny

>>9
>le /pedokike/ admin
go back to your pedo board

>>6
>le pedophile student

>>7
>le pedophile sage

>>8
>le pedophile sage

why is the font fucked up on wikipedia?

Ayo...I got more *WORDPLAY* than youve had ~HOT-DINNERS~. The *THIRD*DAY* on my ride i ~GOT-SPINNERS~. I 'HeArD' your *BIRD*SAY* that i ~SHOT-SINNERS~. We always ~SPOT-WINNERS~ cuz my *CREWS*GOT*TALENT* but ya *BRUISE*ENT*GALLANT* like a 'ShE hOrSe' thats on the ~LOSING-SIDE~. But i dont get any 'ReMoRsE' when im in my ~CRUSING-RIDE~ /// You went to a shop called ~RENT-A-DON~. It was a fake and you got ~SENT-A-CON~. It was a geek and you got ~LENT-A-JOHN~ (lmfao) /// Hoes were all *SEDUCING*ME* at the ~SAME-TIME~. In my basketball game you were *REDUCING*ME* and got a ~GAME-FINE~ /// Homie me and you used to be as ~COOL-AS-ICE~. But you were jealous of me cuz my rhymes were as hot as a ~POOL-OF-SPICE~ (daym) ///
<<<h-NiGgA>>>     ..::BORN THREAT::..

Somehow i read horse shoe in there

>>6
In that case 0.999...!=1 because
1-0.9-0.09-0.009 is a number approaching zero(0.0...01)

If there were only n primes in 10^n, there would still be infinite primes?

infinity isnt real

stop playing word games and deluding yourselves