Prove that $\alpha$ is a limit ordinal iff $\alpha = \sup(\alpha)$.
137768
Limit Ordinal Question
8414
Proof verification: Set of partial limits of a sequence is closed
38242
Explicit bijection between the successor of $\alpha$ and $\alpha$ (infinite ordinal).
43168
Prove that $\limsup\left(b_{n}a_{n}\right)=\limsup\left(a_{n}\right) $ when $\lim_{n\rightarrow\infty}\left(b_{n}\right)=1$
18907
Is this proof of $\liminf E_k \subset \limsup E_k $ correct?
43197
Showing that two definitions of $\limsup$ are equivalent
47820
How can I show a supremum of a set is also its limit point?
82405
For f continuous on $[0,1]$, show that there exist points $\alpha_k$ such that $\sum \limits_{k=1}^n \frac{1}{f'(\alpha_k)} = n $
143146
Help with completing the proof: Any unbounded sequence is either infinitely large or has a convergent subsequential limit
116811
Proofs with limit superior and limit inferior: $\liminf a_n \leq \limsup a_n$
111449
Prove there is an increasing sequence ($s_n$) of points in $S$ such that $\lim s_n = \sup S$.
68913
Proving that $1_{\limsup A_n}=\limsup1_{A_n}$.
63115
If $\alpha$ is an indecomposable ordinal, why $\Gamma(\alpha\times{\alpha})=\alpha$?
50142
If sup A $\lt$ sup B show that an element of $B$ is an upper bound of $A$
33976
Prove that $\lim_{n \to \infty} \sqrt[n]{a} = 1$ using only the basic properties of sequences
105107
How to explain the following definition of $\lim\sup s_n$ intuitively?
23076
Proof of limit of quotient sequence property