Prove that the empty set is a subset of every set.
36721
Is "The empty set is a subset of any set" a convention?
141806
Prove that a nest of sets has an empty intersection
123613
Double Complement of a set proof
9158
Proving that a propositional theory of any cardinality has an independent set of axioms
33064
Powerset of set with empty sets
93771
Prove that for any set $A$ there is some $x \notin A$
132778
All distances are rational prove the set is countable
1307
Infimum and supremum of the empty set
45508
Is the empty set a group?
80827
Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
82009
Prove that every totally ordered set has a well-ordered cofinal subset
92534
Prove that any finite subset of a linearly independent set is linearly independent
143105
Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$
123498
Is "empty set" an element of a set?
39293
Given a compact set $K$ and closed set $E,$ prove: $E\cap K\neq \emptyset $
35692
The set of all finite subsets of the natural numbers is countable
92249
Every finite set contains its supremum: proof improvement.