Limits of inf and sup in a set
34677
Sequence Converging to Supremum
76863
How to show $ \sup \inf g(x,y) \leq \inf \sup g(x,y)$?
64081
Sequence converging to different limits
68781
proving if $a \le b$ then $\sup(A) \le \inf(B)$
11834
Prove that $\liminf x_n = -\limsup (-x_n)$
18907
Is this proof of $\liminf E_k \subset \limsup E_k $ correct?
6793
A linearly independent set about approximate units
45988
limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$
21070
Lim inf with norm and weak convergence
116811
Proofs with limit superior and limit inferior: $\liminf a_n \leq \limsup a_n$
155999
How to prove the following properties of infimum and supremum involving the union and intersection of the sets $A_k$
38624
Finding a tricky limit
7974
lim sup inequality $\limsup ( a_n b_n ) \leq \limsup a_n \limsup b_n $
8414
Proof verification: Set of partial limits of a sequence is closed
1409
Proving that the given set has at most $2^{n-1}$ elements
125821
Evaluating limits at positive and negative infinity
33030
Proof that $\inf A = -\sup(-A)$