Why do some authors define the ordered pair as the set: $(a,b)=\{\{a\},\{a,b\}\}$?
124625
Why do we accept Kuratowski's definition of ordered pairs?
52451
Ordered Triples and Set Theory
76823
Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$?
82009
Prove that every totally ordered set has a well-ordered cofinal subset
151521
Set Theory: Tree Property
16112
Why is the order in dictionaries and sets arbitrary?
128544
What are the subcategories of ordered sets / groups?
21176
Closure of the set in dictionary order topology.
14711
set theoretic function, products of sets (product versus Cartesian product)
77957
How is $\mathbb N$ actually defined?
135250
Ordered Pair Formal Definition
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 $\geq 1\ldots$
13289
Order of Double Coset
109070
Question about the proof of the distributive property for sets
96025
Showing there is only one isomorphism between well ordered sets using transfinite induction
37921
Please Explain Kuratowski Definition of Ordered Pairs
56234
Isomorphism $f$ preserves the order of an element?