## Comment Re:Open set it is! (Score 1, Insightful) 248

So you don't have the set of all primes after all... that's the point. The proof goes like this:

1) suppose you have a set of all primes, and the set is finite.

2) show that there's another prime not in your set - that contradicts (1).

3) therefore, there is no finite set that contains all primes.

All you've done is demonstrate one example of step 2. The original proof given by phantomfive gives a different example of a prime not in the set. Either works - the proof is valid.

1) suppose you have a set of all primes, and the set is finite.

2) show that there's another prime not in your set - that contradicts (1).

3) therefore, there is no finite set that contains all primes.

All you've done is demonstrate one example of step 2. The original proof given by phantomfive gives a different example of a prime not in the set. Either works - the proof is valid.