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1d
comment Formal definition of function: equality
It is a matter of convention whether you define a function to be a set of pairs $f\subset A\times B$ satisfying certain properties, or a triple $(f,A,B)$ where $f\subset A\times B$ is as before. Usually we follow the second convention, in which case your troubles should disappear. At any rate, this is not a research level question, hence off-topic here.
1d
comment Yitang Zhang's paper
@John Nicholson: The first 54 primes do not form an admissible tuple. To get a convenient choice of an admissible $k$-tuple, take the first $k$ primes beyond $k$.
2d
comment Integer solutions of $ z^3 y^2 = x(x-1)(x+1)$
Why are $u$ and $v$ integers? Can you give some reference or the proof?
2d
revised Why is the Gamma function shifted from the factorial by 1?
fixed spelling
Apr
14
comment Did Nash prove that every game or every symmetric game has a symmetric equilibrium?
@Michael: Actually I read the 1951 paper, but only the proof of Theorem 1. I never read the part about symmetries, so I was certainly wrong in my first comment.
Apr
14
comment Did Nash prove that every game or every symmetric game has a symmetric equilibrium?
Thanks. I did not read his Ph.D. thesis.
Apr
14
comment Did Nash prove that every game or every symmetric game has a symmetric equilibrium?
As far as I remember, Nash's paper only talks about equilibrium, there is no reference to any symmetry whatsoever. Sorry if I am wrong.
Apr
10
comment Yitang Zhang's paper
@Stijn: Actually there are weaker but effective versions of Pintz's result. So probably we know that there is a number between 252 and 70 million that occurs infinitely often as a difference of two primes. For that, all we need is an admissible 51-tuple whose pairwise distances fall between 252 and 70 million.
Apr
10
comment Yitang Zhang's paper
@John: To your second comment, it was proved by János Pintz that there is a positive integer $C$ such that among any $C$ consecutive positive integers there is a number that occurs infinitely often as a difference of two primes. This follows from the quoted result of Zhang. On the other hand, we only know the existence of such a $C$, and in fact the quoted results of Zhang/Maynard/Tao/PolyMath8 do not allow to specify this $C$.
Apr
10
comment Yitang Zhang's paper
@John: To your first comment, I am saying that if you take 51 integers that do not form a complete residue system modulo any integer greater than 1, then one of the pairwise distances among these integers occurs infinitely often as the difference of two distinct primes. In particular, there is a gap less than or equal to 252 that occurs infinitely often.
Apr
10
revised Yitang Zhang's paper
added 5 characters in body
Apr
10
answered Yitang Zhang's paper
Apr
9
awarded  Guru
Apr
9
awarded  Enlightened
Apr
9
awarded  Nice Answer
Apr
8
comment Why was John Nash's 1950 Game Theory paper such a big deal?
@R Hahn: I agree with you. In Nash's paper, the payoff function of each player is an arbitrary linear function on the convex polytope representing the mixed strategies.
Apr
8
answered Why was John Nash's 1950 Game Theory paper such a big deal?
Apr
8
awarded  Necromancer
Apr
7
comment Why are Goldbach laggards biased towards $2 \mod 6$?
@Joel: Thank you, but note that my comment with the link is more than 2 years old. Links come and go!
Apr
4
awarded  Enlightened