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21h
comment If $F$ is finite then is $\sigma(F)$ also finite?
Think about it. If you have $n$ sets in a family, there are at most $2^n$ intersections of these sets. Now the sigma algebra generated by this family contains alll possible unions from these subsets. There are at most $2^{2^n}$ of these.
1d
answered If $F$ is finite then is $\sigma(F)$ also finite?
1d
comment Infinite closed subset of $[0, 1]$ that does not have any subset of the form $[a, b]$ for $a< b$?
Its a "perfect" answer.
1d
answered Forming a sequence from a Cauchy Sequence
1d
reviewed Close Difficuly in proving inequality
1d
reviewed Close Is the sequence $s_n= \frac{\sin\frac\pi2}{1\cdot 2}+\frac{\sin\frac\pi{2^2}}{2\cdot 3} + \dots + \frac{\sin\frac\pi{2^n}}{n\cdot(n+1)}$ convergent?
1d
reviewed Close Probability mass function for the number of defective light bulbs among selected
1d
reviewed Close On summation of series
1d
comment Prove that $\frac{(a+1)^k}{a^k+1} \leq 2^{k-1}$
For what $a$? All real $a$?
1d
comment $\iiint_V \ x^{2n} + y^{2n} + z^{2n} \,dx\,dy\,dz$
This is nasty because the integrand is not radial.
1d
answered Compact sets in the product of topological spaces.
1d
comment Expanding logarithm of function
What do you mean by "solve"? Find an inverse function to?
2d
comment Find the inverse $\dfrac{x}{\|x\|}$ in $\mathbb{R^2}$
That is the inverse image. There is no inverse function.
2d
comment Find the inverse $\dfrac{x}{\|x\|}$ in $\mathbb{R^2}$
This function is not 1-1, so you are sunk. It maps all points to the unit circle, so it is no onto either.
Feb
6
answered Solve the following sequence problem
Jan
29
awarded  general-topology
Jan
27
comment Find $f'(z)$ of the following $f(z)$
The chain rule works too.
Jan
27
comment Find $f'(z)$ of the following $f(z)$
All polynomials, the circular functoions and the exponential all differentiate exactly as you would expect.
Jan
27
comment Find $f'(z)$ of the following $f(z)$
Thiings differentiate pretty much as expected. But beware of the log function. Its a sticky affair.
Jan
22
answered Proof about uniform continuity