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Show that if a Banach space is generated by a countable set with finite dimension then it has finite dimension

I don't know what to do with the following question:Show that if a Banach space is generated by a countable set with finite dimension then it has finite dimensionSupposedly it's...

Mathematics Asked on 2 years ago

Can $a bmod 3$ be represented arithmetically without the mod or other integer-related functions?

I've noticed that $a bmod b$ (with 'mod' in the operational sense) can also be represented using various tricks of formulation. For instance, that $$a bmod b =...

Mathematics Asked on 2 years ago

When is $sum_{i=1}^{m}i^n =0 bmod dfrac{m(m+1)}{2}$?

I have tried to creat such formula related to divisibility using triangulair numbers and series , I have got the following problem such that I ask when is ...

Mathematics Asked on 2 years ago

My proof of $A^{mathrm{c}}$ is closed iff $A$ is open

$newcommand{c}{mathrm{c}}$ I have already attempted the proof but I feel like there are some holes in my argument. if someone could look at it and point it out even...

Mathematics Asked by mathematicaxyz on 2 years ago

Define $X_n=sum_{k=1}^n kx_k$ and $Y_n=sum_{k=1}^n ky_k$. Prove that there exists an $n$ such that $X_n<Y_n$.

Question: Let $x_k, y_kgeq 0$. Suppose that $sum_{k=1}^infty x_k<infty$ and $sum_{k=1}^infty y_k=infty$. Define $X_n=sum_{k=1}^n kx_k$ and $Y_n=sum_{k=1}^n ky_k$. Prove that there exists...

Mathematics Asked on 2 years ago

Find the values of $k$ that satisfy $gcd(a,b)=5$

Let $a$,$b$ and $k$ be integers such that$$a=6k+4$$$$b=11k+4$$Find $k$ values that satisfy $gcd(a,b)=5$ Note: $(a,b)$ are solutions to the...

Mathematics Asked by ricin on 2 years ago

How find the solution to $ sum_{i=1}^{infty} left( frac{1}{2} right)^i left( frac{1}{i}right)$?

I am having trouble trying to figure out the solution to the infinite series $ sum_{i=1}^{infty} left( frac{1}{2} right)^i left( frac{1}{i}right)$. What kind of infinite series is this, and...

Mathematics Asked on 2 years ago

Closed form for the maximum of the two-variable function $(a x + (1 - a) y) (b (1 - x) + (1 - b) (1 - y))$

I'm trying to characterize the maximum of this function within the unit interval ($x,yin [0,1]$): $$f(x,y)=(a x + (1 - a) y) (b (1 - x) + (1...

Mathematics Asked on 2 years ago

Interesting connection between a word problem and a physics formula

I came across a math word problem about the time it takes workers to finish a job when they're together vs. separately and I found its connection to a formula...

Mathematics Asked on 2 years ago

Possible Rule of thumb for sums of variances?

For questions dealing with insurance problems, I will often run into questions that involve finding aggregate variance. In a certain problem, I'm told that there are 50 policies, and various...

Mathematics Asked by PortMadeleineCrumpet on 2 years ago

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