Dan Shved
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 Apr7 comment Let $H$ and $K$ be normal subgroups of $G$ such that $H \cap K = \langle e \rangle$ and $HK = G$. Prove that $G$ is isomorphic to $H \times K$. @grayQuant no, it's not necessary here. When it's established that $\varphi$ is bijective and a homomorphism, then $\varphi$ is an isomorphism simply by definition. Mar17 revised Prove complements of independent events are independent. added 566 characters in body Mar16 answered Prove complements of independent events are independent. Mar15 awarded Organizer Mar15 revised Complete labeled Graph $K_6$ and Spanning Tree edited body Mar15 comment Complete labeled Graph $K_6$ and Spanning Tree I've already given a link to the Wikipedia article. I can't tell you anything on top of what you'll see there and/or find elsewhere on the Internet. Mar15 answered Complete labeled Graph $K_6$ and Spanning Tree Mar4 comment Finding two smallest composite numbers Not that it's very important, since we don't want primes, but $2$ and $3$ also satisfy the congruences simultaneously. Mar4 comment Changing order of integration in a double integral Does it really say $\sqrt{9-y}$ and not $\sqrt{9-y^2}$? It doesn't change anything important, but it looks a bit evil. Just saying. Mar4 answered Given a collection of functions $f_i$ with the same domain, how to replace with values (w/o axiom replacement) Mar4 revised discrete family of sets latexify Mar4 comment discrete family of sets What is your proof for the case when $F$ is finite? Do you really use the finiteness at all? Mar4 comment Hard Olympiad Proof Problem Doesn't look like a complete proof. You've only proved that your particular family cannot be made larger by adding new intervals. Feb26 comment The ideals of $A \times B$ for fields $A,B$.are principal First of all, you cannot show that $I \times J \subseteq \langle(a,b)\rangle$, as shown in quid's answer. Even more importantly, your plan has another flaw: you only consider ideals in $A\times B$ that can be decomposed into a direct product $I \times J$, where $I \subseteq A$ and $J \subseteq B$, but you actually need to consider arbitrary ideals in $A \times B$. Feb12 awarded Nice Answer Jan14 comment Symmetric Group acting on $X \times X$ Not really sure what the question is... Why don't you look at $n=3$, find the orbits by hand, and then generalize? Dec21 comment Finding median of union of two sorted (ordered) lists Your final comment seems a bit weird. I'd say that one can find the median of a sorted list in $O(1)$ (if the list is an array and we have instant random access). Dec20 awarded Caucus Oct30 awarded Yearling Oct27 comment Given $z_1, z_2$ prove that $4z^2_1+9z^2_2 = 0$ Also, even with De Moivre, there's no need to use approximate values written as decimal fractions. Write precise expressions, there's less of a chance to make a mistake that way.