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A place is an area that is defined by everything in it. It differs from location in that a place is conditions and features, and location is a position in space. [4] Places have physical characteristics, such as landforms and plant and animal life, as well as human characteristics, such as economic activities and languages. [1]
Just as in chemistry, the characteristic property of a material will serve to identify a sample, or in the study of materials, structures and properties will determine characterization, in mathematics there is a continual effort to express properties that will distinguish a desired feature in a theory or system. Characterization is not unique ...
For example, if p is prime and q(X) is an irreducible polynomial with coefficients in the field with p elements, then the quotient ring [] / (()) is a field of characteristic p. Another example: The field C {\displaystyle \mathbb {C} } of complex numbers contains Z {\displaystyle \mathbb {Z} } , so the characteristic of C {\displaystyle \mathbb ...
Attributes, characteristics of a feature other than location, often expressed as text or numbers; for example, the population of a city. [19] In geography, the levels of measurement developed by Stanley Smith Stevens (and further extended by others) is a common system for understanding and using attribute data.
In classical mathematics, characteristic functions of sets only take values 1 (members) or 0 (non-members). In fuzzy set theory, characteristic functions are generalized to take value in the real unit interval [0, 1], or more generally, in some algebra or structure (usually required to be at least a poset or lattice).
Central place theory is an urban geographical theory that seeks to explain the number, size and range of market services in a commercial system or human settlements in a residential system. [1] It was introduced in 1933 to explain the spatial distribution of cities across the landscape. [ 2 ]
Examples of unexpected applications of mathematical theories can be found in many areas of mathematics. A notable example is the prime factorization of natural numbers that was discovered more than 2,000 years before its common use for secure internet communications through the RSA cryptosystem. [127]
For example, Plücker coordinates are used to determine the position of a line in space. [11] When there is a need, the type of figure being described is used to distinguish the type of coordinate system, for example the term line coordinates is used for any coordinate system that specifies the position of a line.