Context: Quantity is a property 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. Quantity 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., A definition is a statement 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 essence 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., Mathematics (from Greek  "máthma", knowledge, study, learning) is the study 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., Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.
Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see Logic in computer science for those., Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, 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., Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects., In set theory and related branches of mathematics , a collection F of subsets of a given set S is called a family of subsets of S , or a family of sets over S. More generally , a collection of any sets whatsoever is called a family of sets . The term `` collection '' is used here because , in some contexts , a family of sets may be allowed to contain repeated copies of any given member , and in other contexts it may form a proper class rather than a set ., A mathematical object is an abstract object arising in mathematics. The concept is studied in philosophy of mathematics., Subject: family of sets, Relation: subclass_of, Options: (A) branch (B) class (C) classification (D) computer (E) definition (F) direction (G) essence (H) greek (I) language (J) learning (K) magnitude (L) mathematical logic (M) mathematical object (N) mathematics (O) number (P) order (Q) philosophy (R) phrase (S) position (T) property (U) quantity (V) range (W) relation (X) science (Y) set theory (Z) space ([) statement (\) structure (]) study (^) term (_) time (`) unit of measurement (a) value
Output: mathematical object