Why is the supremum of the empty set $-\infty$ and the infimum $\infty$?
1307
Infimum and supremum of the empty set
58456
Why is $ 1^{\infty} \not= \lim_{t \to \infty} 1^t = 1$?
41298
Understanding proof of completeness of $L^{\infty}$
31124
The closure of $c_{00}$ is $c_{0}$ in $\ell^\infty$
102202
The smallest infinity and the axiom of choice
13018
Why is $1^{\infty}$ considered to be an indeterminate form
136755
Direct proof of empty set being subset of every set
7112
Product of sets and supremum
65768
What is the cardinality of the set of the empty set?
22804
Interpretation of limsup-liminf of sets
19962
Why is $\infty \cdot 0$ not clearly equal to $0$?
89712
For every set $A$, the empty set is a subset of $A$. The empty set is a set. Therefore, the empty set has a cardinality $\geq 1\ldots$
96931
Supremum and infimum of $\{\frac{1}{n}-\frac{1}{m}:m, n \in \mathbb{N}\}$
88823
How can the empty set be open in the definition of the cofinite topology?
78463
Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
105107
How to explain the following definition of $\lim\sup s_n$ intuitively?
42108
Prove that $c_0$ is closed in $\ell^\infty$