Sets
A set is an unordered collection of distinct objects, called its elements or members.
Engineering Mathematics · topic
Sets, relations and functions
Set identities and power sets; relation properties with matrix tests and counts; reflexive, symmetric and transitive closures; equivalence relations, classes and partitions with Bell and Stirling numbers; injective, surjective and bijective functions with counts, composition, inverses and countability.
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Relations
A relation records which elements of one set are associated with which elements of another: "a divides b", "x is a prerequisite of y", "page p links to page q". Formally, a (binary) relation from a set A to a set B is any subset R ⊆ A × B; we write a R b or (a, b) ∈ R.
Functions
A function assigns to every element of one set exactly one element of another. Hash functions, encodings, permutations of an array, the transition function of an automaton and the indexing of an array are all functions.
Sets, relations and functions cheat sheets
One-page visual sheets for this topic, in the sheet library on the store. Previews are free; the full sheets come with the subject pack.