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2. Set theory - Wikipedia

   en.wikipedia.org/wiki/Set_theory

   Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was ...

3. Infinite monkey theorem - Wikipedia

   en.wikipedia.org/wiki/Infinite_monkey_theorem

   A chimpanzee (an ape, not a monkey) probably not writing Hamlet. The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, including the complete works of William Shakespeare. In fact, the monkey would almost surely type every possible ...

4. Set-builder notation - Wikipedia

   en.wikipedia.org/wiki/Set-builder_notation

   Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to true for an element of the set, and false otherwise. [2] In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate. Thus there is a variable on the left of the ...

5. Algebra of sets - Wikipedia

   en.wikipedia.org/wiki/Algebra_of_sets

   Fundamentals. The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".

6. Intersection (set theory) - Wikipedia

   en.wikipedia.org/wiki/Intersection_(set_theory)

   Set theory. Statement. The intersection of A and B is the set A ∩ B of elements that lie in both set A and set B . Symbolic statement. A ∩ B = {x: x ∈ A and x ∈ B} In set theory, the intersection of two sets and denoted by 1 is the set containing all elements of that also belong to or equivalently, all elements of that also belong to 2.

7. Glossary of set theory - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_set_theory

   The inclusive or operation in a Boolean algebra. (In ring theory it is used for the exclusive or operation) ~. 1. The difference of two sets: x ~ y is the set of elements of x not in y. 2. An equivalence relation. \. The difference of two sets: x \ y is the set of elements of x not in y.