Is $1$ and $-1$ the Supremum and Infimum of the set $A=\left\{\sin(n), n \in \mathbb{N}\right\}$
94425
What is $\sup(\sin(n))$?
116966
Prove $\limsup_{n \rightarrow \infty} a_n\geq1$ if $\lim_{n \rightarrow \infty} a_na_{n+1}=1$
43168
Prove that $\limsup\left(b_{n}a_{n}\right)=\limsup\left(a_{n}\right) $ when $\lim_{n\rightarrow\infty}\left(b_{n}\right)=1$
117257
Proving the supremum of the set {$\cos (1/x)$} is 1
50142
If sup A $\lt$ sup B show that an element of $B$ is an upper bound of $A$
1409
Proving that the given set has at most $2^{n-1}$ elements
137257
The Supremum and Infimum of a sequence of measurable functions is measurable
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
54791
Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
100565
Property of sup of a set of numbers
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
49054
Show that $\left | \sin a - \sin b \right | \leq \left | a-b \right |$
16749
Let $A_i= \left \{...,-2,-1,0,1,...,i \right\}$. Find $\bigcup_{i=1}^{n} A_i$ and $\bigcap_{i=1}^{n} A_i$
16253
Proof that $|\sin(nx)| \le n|\sin(x)|$
31295
$x+y\sqrt{2}$ infimum ($x,y\in \mathbb{Z}$)
136789
How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?