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2. Set (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Set_(mathematics)

   A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...

3. List of set identities and relations - Wikipedia

   en.wikipedia.org/wiki/List_of_set_identities_and...

   In constructive mathematics, "not empty" and "inhabited" are not equivalent: every inhabited set is not empty but the converse is not always guaranteed; that is, in constructive mathematics, a set that is not empty (where by definition, "is empty" means that the statement () is true) might not have an inhabitant (which is an such that ).

4. Well-defined expression - Wikipedia

   en.wikipedia.org/wiki/Well-defined_expression

   In mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Otherwise, the expression is said to be not well defined , ill defined or ambiguous . [ 1 ]

5. Category of sets - Wikipedia

   en.wikipedia.org/wiki/Category_of_sets

   Set is the prototype of a concrete category; other categories are concrete if they are "built on" Set in some well-defined way. Every two-element set serves as a subobject classifier in Set. The power object of a set A is given by its power set, and the exponential object of the sets A and B is given by the set of all functions from A to B. Set ...

6. Well-founded relation - Wikipedia

   en.wikipedia.org/wiki/Well-founded_relation

   If the order is a total order then it is called a well-order. In set theory, a set x is called a well-founded set if the set membership relation is well-founded on the transitive closure of x. The axiom of regularity, which is one of the axioms of Zermelo–Fraenkel set theory, asserts that all sets are well-founded.

7. Universally measurable set - Wikipedia

   en.wikipedia.org/wiki/Universally_measurable_set

   From such a set , form a new set ′ by performing the following operation on each sequence in : Intersperse a 0 at every even position in the sequence, moving the other bits to make room. Although A ′ {\displaystyle A'} is not intuitively any "simpler" or "better-behaved" than A {\displaystyle A} , the probability that the sequence of flips ...