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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 $1$.