Giorgio
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 Sep24 awarded Autobiographer Aug3 awarded Critic Jan24 comment Are half of all numbers odd? Thanks, I did not know the prime number theorem. Jan24 comment Are half of all numbers odd? What can be said about the asymptotic density of prime numbers? Oct27 comment a circle graph is not a function? Ah, ok, you mean $\pm y = (+y, -y)$, so you would have a function $f:\mathbb{R}\rightarrow \mathbb{R}\times\mathbb{R}$. Oct27 revised a circle graph is not a function? added 436 characters in body Oct27 comment a circle graph is not a function? Yes, but $y = \pm \sqrt{1 - x^2}$ is not a function. Oct27 revised a circle graph is not a function? added 18 characters in body Oct27 comment a circle graph is not a function? I would not say that an equation is function: an equation can define a function. Both an equation and a function can define a curve on the plane, but some equations do not have an associated function. Oct27 answered a circle graph is not a function? Sep17 comment What's wrong with my proof of infinitely many primes of the form $am+b$, $\gcd(a, b) = 1$ For all integers $a$, $b$, $m$ and $GCD(a, b) = 1$, there are infinitely many primes of the form $am + b$. Is this written correctly? Shouldn't it read: There are infinitely many primes $p$ such that there exist $a$, $b$, $m$ for which $GCD(a, b) = 1$ and $p = am + b$. Sep8 comment What is your favorite application of the Pigeonhole Principle? @Brandon Carter and Ilmari Karonen: yes, Ilmari 's formulation is correct. My mistake. Thanks. Sep8 comment What is your favorite application of the Pigeonhole Principle? +1 Thanks for the feedback and the link. Sep8 comment What is your favorite application of the Pigeonhole Principle? Did you mean: "it's not very hard to construct formal languages which are not pumpable, but which can be easily shown to be non-regular using the pigeonhole principle."? Sep8 awarded Editor Sep8 revised What is your favorite application of the Pigeonhole Principle? added 3 characters in body Sep8 awarded Teacher Sep7 awarded Supporter Sep7 answered What is your favorite application of the Pigeonhole Principle?