instance_of space 
In ___MASK90___ , a ___MASK57___ is a set ( sometimes called a universe ) with some added ___MASK42___ . Mathematical spaces often form a hierarchy , i . e . , one ___MASK57___ ___MASK24___ inherit all the characteristics of a parent ___MASK57___ . For instance , all inner product spaces are also normed vector spaces , because the inner product induces a norm on the inner product ___MASK57___ such that : \ left \ x \ right \ = \ sqrt ( \ langle x , x \ rangle ) , where the norm is indicated by enclosing in double vertical lines , and the inner product is indicated enclosing in by angle brackets . Modern ___MASK90___ treats `` ___MASK57___ '' quite differently compared to classical ___MASK90___ . ___MASK90___ ( from Greek  " máthma ",  knowledge , ___MASK39___ , learning ) is the ___MASK39___ 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 . ___MASK53___ is a ___MASK83___ 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 . ___MASK53___ 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 . ___MASK57___ is the boundless three - dimensional extent in which objects and events have relative ___MASK58___ and direction . Physical space is often conceived in three linear dimensions , although modern physicists usually consider it , with ___MASK23___ , 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 ___MASK2___ . A ___MASK46___ is a ___MASK38___ of the meaning of a ___MASK44___ ( a word , phrase , or other set of symbols ). Definitions can be classified into two large categories , intensional definitions ( which try to give the essence of a ___MASK44___ ) and extensional definitions ( which proceed by listing the objects that a ___MASK44___ describes ). Another important category of definitions is the class of ostensive definitions , which convey the meaning of a ___MASK44___ by pointing out examples . A ___MASK44___ may have many different senses and multiple meanings , and thus require multiple definitions .