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 15h comment Every subset of a finite set is finite.. confused why this proof is wrong.. You are assuming what you want to prove, it seems. You have $[n]$, which I'm taking to be $\{1,2,\ldots,n\}$ (a finite set), and you have a subset of that finite set. How do you know the subset is finite? 2d comment Is it possible to solve $\int_{0}^{1} t^4 \sqrt{1+t^2}\,dt$ @Ricardo: Doesn't that just change the way the integrand looks? You'll still have a square root term from the $du$ part, I believe 2d comment Is it possible to solve $\int_{0}^{1} t^4 \sqrt{1+t^2}\,dt$ Integration by parts and possibly trigonometric substitution. 2d comment Prove using the given condition… Hint: multiply the LHS by $\sin^2x/a$ to form Eq. $1$. Repeat the process with $\cos^2x/b$ to form Eq. $2$. Now add Eq. $1$ and Eq. $2$ and simplify. 2d comment One of the Heire-Borel lemmas states the following: The correct extension is closed and totally bounded, if I recall properly. It means that given any $\varepsilon>0$, there is a finite cover of $\varepsilon$-balls. I might have forgotten something, but I think this is correct. 2d comment What is the value of $x$ when $a^\frac{1}{x}=1$? $x\neq0$... :) ${}$ Apr 27 comment Proving that a field is not a splitting field of any polynomial @Joanpemo: You're correct! Haha, I knew what I had in mind, but I didn't express it very clearly. Thanks for the correction. There are, of course, a lot of polynomials that don't split in the field :-P Apr 27 comment Evaluation of $\int_0^\infty\frac{x^{1/3}\log x}{x^2+1}\ dx$ Just for clarification, what do you mean by "without symmetries, how could one..." ? I think I understand, but I would rather ask to be clear. Apr 27 comment Proving that a field is not a splitting field of any polynomial Actually, a lot of polynomials split in $\Bbb Q[x]$ (e.g., $p(x)=x^2-4$ splits in $\Bbb Q$, ergo in $\Bbb Q[2^{1/3}])$. What you need to show is that some polynomial doesn't split in $\Bbb Q[2^{1/3}]$. Apr 19 comment Connecting boundary definitions Show $\overline{A}\setminus A^\circ\subseteq\overline{A}\cap\overline{X\setminus A}$ and vice versa. Apr 13 comment Complex Integration of $\int_0^\infty e^{-ax}\cos(bx)\,dx$ @Craig: Not quite. The upper bound of the integral would be $0$, the lower bound is $R$, and we get a negative factor from the fact that $du=-dt$. This allows you to switch the bounds of the integral without problem. Apr 9 comment Complex Integration of $\int_0^\infty e^{-ax}\cos(bx)\,dx$ @Craig: Just use substitution with $u=R-t$. Apr 8 answered Supremum/Maximum and Infimum/minimum of a given set Apr 8 revised Supremum/Maximum and Infimum/minimum of a given set Fixed formatting and title Apr 7 awarded Popular Question Apr 5 revised Show that $2^{15}-2^3$ divides $a^{15}-a^3$ for all $a$ edited body Mar 25 comment Application of the Artin-Schreier Theorem @user114539: Characteristic $p$. Mar 22 comment Proof by contradiction to this inequality He is using the fact that $\sum\frac{1}{2^n}=1$. +$1$ Mar 22 revised Open cover, finite subcover added 115 characters in body Mar 22 comment Open cover, finite subcover @Faraad: I suppose it depends what part of the course they are in. At any rate, I'll add an edit to include up to $1$.