# Jorge Fernández

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bio website location Mexico City age member for 2 years, 6 months seen 17 secs ago profile views 1,975

Hello, I am a freshman at The National Autonomous University of Mexico (UNAM).

My interests are contest problems,elementary number theory, combinatorics, graph theory, linear algebra, group theory, abstract algebra and I have been meaning to learn category theory and matroids.

# 2,898 Actions

 Dec17 comment $S$ be the collection of groups $G$ in which every element in $G$ commutes only with the identity element and itself well, the only element in $\{e\}$ is $e$, and it only commutes with $e$ and itself, so it works. Dec17 accepted Is this calculus proof I came up with sound? Dec17 accepted cardinality of $\mathbb R$ is the same as the cardinality of $\mathbb R^2$ Dec17 answered cardinality of $\mathbb R$ is the same as the cardinality of $\mathbb R^2$ Dec17 revised Automorphism that is an Involution of a finite group added 15 characters in body Dec17 comment Factorial inequality $2!\,4!\,6!\cdots (2n)!\geq\left((n+1)!\right)^n$ using induction Oh wait, I proved the inequality. But if you want the equality you would have to have $2n(2n-1)\dots(n+2)=(n+1)^{n-1}$, and to have that you would need $2n=n+1$ which is clearly not true. Dec17 revised Factorial inequality $2!\,4!\,6!\cdots (2n)!\geq\left((n+1)!\right)^n$ using induction added 135 characters in body Dec17 answered Factorial inequality $2!\,4!\,6!\cdots (2n)!\geq\left((n+1)!\right)^n$ using induction Dec17 answered Is it a Permutation or Combinatorics? Dec17 comment How do I prove that for any set $A$, $|A| < |\mathbb{N}|$ implies that $A$ is finite? Oh yeah, thank you that's sweet. Dec17 comment Existence of continuous functions $f,g:(0,1) \to (0,1)$ such that $f\big((0,1)\big)=(0,1)$ ; and what if $(0,1)$ replaced by $[0,1)$ ? $f(x)=\frac{x}{2},g(x)=\frac{1}{2}+\frac{x}{2}$ Dec17 answered Existence of continuous functions $f,g:(0,1) \to (0,1)$ such that $f\big((0,1)\big)=(0,1)$ ; and what if $(0,1)$ replaced by $[0,1)$ ? Dec17 revised How many “good” graphs of size $n$ are there? added 1 character in body Dec17 answered How many “good” graphs of size $n$ are there? Dec17 comment How do I prove that there doesn't exist a set whose power set is countable? I think he is struggling with the second part. Nice to see you btw Brian. :). Or read your text,more than see you. Dec17 comment How do I prove that for any set $A$, $|A| < |\mathbb{N}|$ implies that $A$ is finite? I would love to see your answer on this, I have no background on set theory, all that I knew in my mind was Cantor Schroeder Bernestein and that $\mathbb N$ is well ordered. And I thought this was a neat idea. But I would really like to see an answer written by a pro. Dec17 revised How do I prove that for any set $A$, $|A| < |\mathbb{N}|$ implies that $A$ is finite? edited body Dec17 comment How do I prove that for any set $A$, $|A| < |\mathbb{N}|$ implies that $A$ is finite? I also think I should add that the sets I am using are never empty, for if there would come a time where one of those sets was empty we could conclude the set was finite. Dec17 comment How do I prove that for any set $A$, $|A| < |\mathbb{N}|$ implies that $A$ is finite? @copper.hat yeah, that what was I was thinking. Dec17 comment How do I prove that for any set $A$, $|A| < |\mathbb{N}|$ implies that $A$ is finite? I was just using the order on $\mathbb N$