# Tagged Questions

For questions concerning the definition and properties of limit superior and limit inferior.

94 views

### Prove or disprove: $\sup\left \{ x\in\mathbb{R}\mid x^2-5x+6\leq0 \right \}=3$

No homework:http://www2.mathematik.hu-berlin.de/~gaggle/S15/MATHINFO/UEBUNG/nachholklausur.pdf Prove or disprove: $\sup\left \{ x\in\mathbb{R}\mid x^2-5x+6\leq0 \right\} =3$ I would say the ...
31 views

28 views

27 views

### Proofs involving limsup and liminf

I've been working with proofs involving $\limsup$ and $\liminf$, and I'm a bit confused regarding their general methodology. More specifically, I'm unsure about whether my approach to the following ...
22 views

### Radius of convergence of integral series; problem with limsup

Let $\sum c_k x^k$ be a power series with radius of convergence $R$. Then the integral series $$\sum_{k=0}^\infty \frac{c_k}{k + 1}x^{k+1}$$ also has radius of convergence $R$. I'm reading Real ...
37 views

### On a superior limit involving the multiplication formula for the Gamma function and the divisors $d\mid n$ of a positive integer

I did the specialization for the $m's$ in the multiplication formula for the Gamma function, see the identity (4) in page 250 of Apostol, Introduction to Analytic Number Theory Springer (1976) as the ...
76 views

26 views

### Subsequential limit of $S_n=\left(-\frac{\sqrt{2}}{4}\right)^n$

I'm having trouble identifying the subsequences, or patterns of the sequence. I recognize the problem can be rewritten: $S_n=\left(-\frac{\sqrt{2}}{4}\right)^n=-\frac{\sqrt{2}^n}{4^n}$ And if I ...
24 views

### Show that $f$ defined on the interval $(a,b)$ is not differentiable for every point in $E$ with $m(E)=0$

Let $E$ have measure zero contained in the open interval $(a,b)$. In a previous problem I showed that there is a countable collection of open intervals, $\{(c_k,d_k)\}_k$, contained in $(a,b)$ for ...
31 views

41 views

24 views

25 views

### Let $A\subset \mathbb{R}$ such that $l=\text{inf }(A)$ exists. Prove that $\forall \epsilon >0$ there is $a\in A$ in the interval $[l,l+\epsilon)$

I need to prove the following: Let $A\subset \mathbb{R}$ such that $l=\text{inf}(A)$ exists. Prove that $\forall \epsilon >0$ there is $a\in A$ in the interval $[l,l+\epsilon)$ That's what I did:...