subclass_of map 
In ___MASK69___ , a ___MASK78___ on a set is an additional ___MASK70___ that , in some manner , attaches ( or relates ) to that set to endow it with some additional meaning or significance . ___MASK98___ theory formalizes ___MASK53___ and its concepts in terms of a collection of " objects " and of " arrows " ( also called morphisms ). A category has two basic properties : the ability to compose the arrows associatively and the existence of an identity arrow for each object . The language of category theory has been used to formalize concepts of other high - level abstractions such as sets , rings , and groups . ___MASK10___ is a ___MASK41___ that can exist as a magnitude or multitude . Quantities can be compared in terms of " more ", " less ", or " equal ", or by assigning a numerical value in terms of a unit of measurement . ___MASK10___ is among the basic classes of things along with quality , substance , change , and relation . Some quantities are such by their inner nature ( as number ), while others are functioning as states ( properties , dimensions , attributes ) of things such as heavy and light , long and short , broad and narrow , small and great , or much and little . A small quantity is sometimes referred to as a quantulum . In ___MASK69___ , and more specifically in ___MASK88___ , a ___MASK57___ is a ___MASK78___ amounting to a set of objects in which some pairs of the objects are in some sense " related ". The objects correspond to mathematical abstractions called " vertices " ( also called " nodes " or " points ") and each of the related pairs of vertices is called an " edge " ( also called an " arc " or " line "). Typically , a ___MASK57___ is depicted in diagrammatic form as a set of dots for the vertices , joined by lines or curves for the edges . Graphs are one of the objects of ___MASK35___ in discrete ___MASK69___ . In ___MASK69___ , the ___MASK26___ mapping , usually shortened to map , refers to either A function , often with some sort of special ___MASK78___ , or A morphism in ___MASK98___ theory , which generalizes the idea of a function . There are also a few , less common uses in ___MASK54___ and graph theory . A ___MASK8___ is a ___MASK58___ of the meaning of a term ( a word , phrase , or other set of symbols ). Definitions can be classified into two large categories , intensional definitions ( which try to give the ___MASK100___ of a term ) and extensional definitions ( which proceed by listing the objects that a term describes ). Another important category of definitions is the class of ostensive definitions , which convey the meaning of a term by pointing out examples . A term may have many different senses and multiple meanings , and thus require multiple definitions . Discrete ___MASK69___ is the ___MASK35___ of mathematical structures that are fundamentally discrete rather than continuous . In contrast to real numbers that have the property of varying " smoothly ", the objects studied in discrete ___MASK69___  such as integers , graphs , and statements in logic  do not vary smoothly in this way , but have distinct , separated values . Discrete ___MASK69___ therefore excludes topics in " continuous ___MASK69___ " such as calculus and analysis . Discrete objects can often be enumerated by integers . More formally , discrete ___MASK69___ has been characterized as the branch of ___MASK69___ dealing with countable sets ( sets that have the same cardinality as subsets of the natural numbers , including rational numbers but not real numbers ). However , there is no exact definition of the term " discrete ___MASK69___ ." Indeed , discrete ___MASK69___ is described less by what is included than by what is excluded : continuously varying quantities and related notions . ___MASK71___ is the boundless three - dimensional extent in which objects and events have relative ___MASK18___ and direction . Physical space is often conceived in three linear dimensions , although modern physicists usually consider it , with ___MASK84___ , to be part of a boundless four - dimensional continuum known as spacetime . The concept of space is considered to be of fundamental importance to an understanding of the physical universe . However , disagreement continues between philosophers over whether it is itself an entity , a relationship between entities , or part of a conceptual framework . In ___MASK69___ ___MASK88___ is the ___MASK35___ of " graphs ", which are mathematical structures used to model pairwise relations between objects . A graph in this context is made up of " vertices ", " nodes ", or " points " which are connected by " edges ", " arcs ", or " lines ". A graph may be " undirected ", meaning that there is no distinction between the two vertices associated with each edge , or its edges may be " directed " from one vertex to another ; see Graph ( discrete ___MASK69___ ) for more detailed definitions and for other variations in the types of graph that are commonly considered . Graphs are one of the prime objects of ___MASK35___ in discrete ___MASK69___ . ___MASK69___ ( from ___MASK60___  " máthma ",  knowledge , ___MASK35___ , learning ) is the ___MASK35___ of topics such as quantity ( numbers ), structure , space , and change . There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics .