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375131
bio website sos440.tistory.com
location Los Angeles, CA
age 27
visits member for 3 years, 7 months
seen 6 hours ago

I am currently a UCLA student, particularly interested in probability theory.

I love mathematics, especially calculating some sort of integrals and summations with inner aesthetic appealing.

Language fluency: (G:green, A:amber, R:red)

  • Korean: Native
  • English: (Reading: G, Listening : A, Speaking : R, Writing : A)
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1d
awarded  Good Answer
2d
comment Hausdorff dimension of $\lim_{n\to\infty}\sin(2^nx)$
Does it help if we write $$ S = \bigcap_{k=1}^{\infty}\bigcup_{n=1}^{\infty}\bigcap_{m=n}^{\infty}\bigcup_{l\in \Bbb{Z}} \left( \frac{\pi l - \delta_{k}}{2^{m}}, \frac{\pi l + \delta_{k}}{2^{m}} \right), $$ if $\delta_k$ is any sequence of positive real numbers converging to zero?
Nov
25
awarded  Sportsmanship
Nov
25
comment How to evaluate $\int_0^1 (\arctan x)^2 \ln(\frac{1+x^2}{2x^2}) dx$
+1 for your calculation power!
Nov
24
revised Does any one-to-one function exist that satisfies this inequality for all real numbers?
added 897 characters in body
Nov
23
answered Formal proof that X and X squared random variables are dependent.
Nov
23
comment How to evaluate $\int_0^1 (\arctan x)^2 \ln(\frac{1+x^2}{2x^2}) dx$
@Gahawar, Oh, certainly that is not a happy formula to me.
Nov
23
comment How to evaluate $\int_0^1 (\arctan x)^2 \ln(\frac{1+x^2}{2x^2}) dx$
@Gahawar, have you ever met this uncomfortable guy $\Im \mathrm{Li}_{3}(\sqrt{i/2})$ somewhere before?
Nov
23
answered How to evaluate $\int_0^1 (\arctan x)^2 \ln(\frac{1+x^2}{2x^2}) dx$
Nov
21
awarded  Enlightened
Nov
21
awarded  Nice Answer
Nov
21
answered Does any one-to-one function exist that satisfies this inequality for all real numbers?
Nov
20
comment Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques
Nice work! (+1) This solution is elementary yet loses no intuition.
Nov
20
awarded  Nice Answer
Nov
20
comment Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques
Correction: the integrand in my first solution does converge uniformly as $n \to \infty$. What I meant was that $1/(n(x^{1/n} - 1))$ does not converge uniformly as $n \to \infty$, but thanks to the factor $x^{k} - 1$ we indeed obtain the uniform convergence of $(x^{k} - 1)/(n(x^{1/n} - 1))$.
Nov
20
comment Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques
@Idris That is exactly what I pointed out in my PS. In this case even uniform convergence fails, so we need the dominated convergence theorem. Thankfully, there is a way to circumvent this problem by using solely calculus techniques as I demonstrated in the edited version, but I do not think these solutions reveal the nature of our integral.
Nov
20
revised Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques
added 1689 characters in body
Nov
20
answered Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques
Nov
20
comment Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques
@columbus8myhw, That is exactly what Idris refuses to accept.
Nov
15
awarded  Good Answer