35 terms

automation

a construct that possesses all the indispensable features of a digital computer

formal language

an abstraction of the characteristics of programming languages

set

a collection of elements without any structure other than membership

set union

the set of all elements in the collection; one of the fundamental operations through which sets can be combined and related to each other

set intersection

the set that contains all elements of a set that also belong to another set

set difference

a generalization of the idea of the complement of a set and as such is sometimes called the relative complement of T with respect to S

set complementation

the items which are not in a set

empty set

a set that contains nothing

singleton set

a set containing only one item

De Morgans law

the compliment of the union of two sets is the intersection of their compliments and the complement of the intersection of two sets is the union of their complements

subset

a set which is contained in a larger set ⊆ (note: two sets can be exactly the same and be subsets of each other)

proper subset

a subset which is not equal to its superset ⊂

disjoint set

two sets that do not have any common elements

finite set

a set that contains a finite number of elements

infinite set

a set that contains an infinite number of elements

power set

the set of all subsets of a set including the empty set and the set itself

Cartesian product

a mathematical operation that returns ordered sequences of elements from other sets

set partition

a grouping of a set's elements into non-empty subsets in such a way that every element is included in one and only one of the subsets

function

a rule that assigns to elements of one set a unique element of another set

domain

the complete set of possible values of the independent variable

range

the set of all output values of a function

total function

a function which is defined for all possible input values

partial function

a function which is not defined for all possible input values

order at most

the maximum number of operations that could be carried out for a function's best case

order at least

the minimum number of operations that could be carried out for a function's best case

same order of magnitude

two functions' orders who are this magnitude which is identical

relation

a relationship between sets of information when the qualifications of being a function are not satisfied

equivalence

relations that satisfy the reflexivity rule, the symmetry rule, and the transitivity rule

equivalent classes

the class of all members of a set that are in a given equivalence relation

vertex or node

the fundamental unit of which graphs are formed

edge

the connection between nodes in graph theory

path

a walk in which no edge is repeated

walk

in graph theory, the traversal among edges and vertices in a graph

simple path

a path in which no vertices are repeated

cycle

a walk from one vertex to another