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visits member for 2 years, 10 months
seen Jul 18 at 7:47

Mar
27
comment When does the next bus come?
This is awesome and exactly what I was looking for. Just working through it now. Thanks!
Mar
27
accepted When does the next bus come?
Mar
27
asked Prove a function has $k$ continuous derivatives from its Fourier series
Mar
23
asked When does the next bus come?
Mar
13
comment Property of an algebra of continuous functions on a compact set which separates points
@BaronVT Thanks that already helps immensely! I'm still stuck on one part though. So we have either $\mathscr{A}$ vanishes or it does not. If it does not then Stone-Weierstrass gives us $\mathscr{A}=C(K)$. Otherwise, here I'm still stuck. I can show that if $\mathscr{A}$ vanishes at $p$ then a sequence $f_n$ in $\mathscr{A}$ which converges to $f$ vanishes at $p$ and is continuous, but I can't show the inclusion in the other direction.
Mar
13
comment Whats better: 1 million dollars in a month or a penny(USD) doubled (and added) every day for 30 days?
You're really choosing to do this the longest way with the recurrence relation.
Mar
13
asked Property of an algebra of continuous functions on a compact set which separates points
Mar
6
comment Prove for all sequences $\{a_n\}$ and $\{b_n\}$, if $\lim a_n = a$ and $\lim b_n = b$, then $\lim a_n + b_n = a+b$ entirely in first-order logic
"The first thing I would like to see is a formal line by line first-order logic proof of the above with each step justified" Why on Earth do you want this? Even just the triangle inequality will become the silliest most tedious exercise possibly in history.
Mar
6
comment Find a nonzero $3\times 3$ matrix with all 0 eigenvalues. Is there a systematic way?
@AndréNicolas thank you for telling me what I was looking for! That+Wikipedia was a great help.
Mar
6
accepted Find a nonzero $3\times 3$ matrix with all 0 eigenvalues. Is there a systematic way?
Mar
6
comment How to derive formula for $\sin(A-B)$ from formula for $\sin(A+B)$?
Let $C=-B$. Then $\sin(A-B)=\sin(A+C)$. See if you can take it from there.
Mar
5
asked Find a nonzero $3\times 3$ matrix with all 0 eigenvalues. Is there a systematic way?
Mar
5
accepted Prove that there is a subsequence of functions which converges uniformly
Mar
4
asked Prove that there is a subsequence of functions which converges uniformly
Mar
4
accepted Prove $I:C([0,1])\rightarrow C([0,1])$ defined by $I(f)(x)=\int_0^x f(t)dt$ is uniformly continuous
Mar
1
comment Does this problem make sense? “Give an example of a set $F\subset C([0,1])$ which is pointwise bounded but not bounded”
So as far as I understand, we need one function $\phi\in C([0,1])$ such that for every $f\in F$, $|f(x)|<\phi(x)$ for all $x\in[0,1]$. But if $\phi\in C([0,1])$ then $\phi$ is bounded, say by $M$, so doesn't this imply that each $f\in F$ is bounded by $M$, and so $F$ is uniformly bounded? Or does $\phi$ not need to be in $C([0,1[)$?
Mar
1
asked Does this problem make sense? “Give an example of a set $F\subset C([0,1])$ which is pointwise bounded but not bounded”
Mar
1
accepted Prove that if $f$ is Riemann-Integrable on $ [0,1]$ then $\lim_{c\rightarrow 0} \int_c^1 f(x)dx$ exists and is equal to $\int_0^1 f(x)dx$
Mar
1
revised Don't understand casting out nines
added 475 characters in body
Mar
1
accepted Generalizing $\sum_{n=1}^{N}f(n)=\int_{a}^{b}f(x)dx+\int_{a}^{b}f'(x)\langle x\rangle dx+f(a)\langle a\rangle-f(b)\langle b\rangle$