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8h
comment What is value of k in next hermonic serie?
Almost all positive integer values of $k$ will work. Please be more specific about what you want.
8h
comment Computing conditional expectation $\mathbb E(U^V \mid U)$
What definition of conditional expectation are you using?
8h
reviewed Close Computing conditional expectation $\mathbb E(U^V \mid U)$
8h
reviewed Leave Open Arranging Couples
8h
reviewed Close An equation to describe a bowl shape in 3D
8h
reviewed Close Is Fermat's Last theorem equivalent to $1 + 1 = 2$?
9h
comment Pythagorean theorem expressed without roots in an old Tamilian (Indian) statement
@TonyK I wish I'd seen those comments :).
9h
comment Distribution of the sum reciprocal of primes $\le 1$
@MarcusM What a curious title OEIS has for the sequence! Since the number of digits roughly doubles every term, I think there are much slower-growing sequence with this reciprocal sum (even oeis.org/A225669 sort of qualifies since it takes more terms to reach 10-20 digits). It's certainly the lexicographically first sequence, though.
11h
comment Pythagorean theorem expressed without roots in an old Tamilian (Indian) statement
There is a genuine question hidden in here, which is "what linear combination of (ordered) side lengths gives the smallest relative error?". The one in the OP can be as bad as 12.5%, which I suspect can be improved substantially.
11h
comment Pythagorean theorem expressed without roots in an old Tamilian (Indian) statement
@rtindru A 5% discrepancy is not very astonishing. As John points out this approximation is smaller than the other side of the triangle for the case 1980, 9801, 9999 that you describe, which is remarkably poor. There is some evidence that ancient Babylonians had knowledge of Pythagoras's theorem several centuries earlier.
12h
answered Let $A \subset \mathbb Z^3$ / $|A| < \infty$. Prove that: $|A| \le \sqrt{|A_x| |A_y| |A_z|}$
14h
comment “less than $+\infty$” is not bounded above?
Bounded above means there is a real number $M$ such that $f(x) < M$ for all $x \in E$. Just because $f$ always takes values $< +\infty$ doesn't mean that the maximum value of $f$ is finite.
1d
comment Proving that $\forall x>0$, $\lim\limits_{n\to\infty}x^{1/n}=1$
In your statement of Lemma 6.5.2 don't you mean $x^n$ rather than $x^{1/n}$?
1d
reviewed Looks OK The set of all interior points. Set equality
1d
comment Find the smallest prime number that doesn't divide any 5-digit number whose digits are in strictly increasing order.
Nice little question! An alternative way to rule out $2,3,5$ is to use the fact that $12345–12349$ are five consecutive numbers satisfying the constraint. This isn't decidedly easier but it takes less computation to confirm. Similarly, one could rule out $7$ by using the block $123(4–5)(6–9)$. It's not hard to see that this generalized arithmetic progression covers all possible residues mod $7$.
2d
reviewed Reopen A good equation system
2d
reviewed Looks OK Determining the formula for a linear map
Jul
2
reviewed Close How do you show that $\displaystyle\lim_{x\to 0}\frac{\sin(x)}{\sqrt{x\sin(4x)}} $does not exist?
Jul
2
reviewed Close This n can not be odd
Jul
2
reviewed Close Prove $u=\ln\ln\left(1+\frac{1}{|x|}\right)\in W^{1,n}(\Omega)$