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An extensive property is a physical quantity whose value is proportional to the size of the system it describes, [8] or to the quantity of matter in the system. For example, the mass of a sample is an extensive quantity; it depends on the amount of substance. The related intensive quantity is the density which is independent of the amount.
[6] [7] It is possible to have multiple independent variables or multiple dependent variables. For instance, in multivariable calculus, one often encounters functions of the form z = f(x,y), where z is a dependent variable and x and y are independent variables. [8] Functions with multiple outputs are often referred to as vector-valued functions.
A quantity that has only both a ≠ 0 and b ≠ 0 is known as a kinematic quantity. A quantity that has only all of a ≠ 0, b ≠ 0, and c ≠ 0 is known as a dynamic quantity. [3] A quantity that has all exponents null is said to have dimension one. [2] The unit chosen to express a physical quantity and its dimension are related, but not ...
Base quantity Symbol Description SI base unit Dimension Comments Amount of substance: n: The quantity proportional to the number of particles in a sample, with the Avogadro constant as the proportionality constant: mole (mol) N: extensive, scalar Length: l: The one-dimensional extent of an object metre (m) L: extensive: Time: t: The duration of ...
A traditional Aristotelian realist philosophy of mathematics, stemming from Aristotle and remaining popular until the eighteenth century, held that mathematics is the "science of quantity". Quantity was considered to be divided into the discrete (studied by arithmetic) and the continuous (studied by geometry and later calculus ).
A quantifiable physical property is called physical quantity. Measurable physical quantities are often referred to as observables . Some physical properties are qualitative , such as shininess , brittleness , etc.; some general qualitative properties admit more specific related quantitative properties, such as in opacity , hardness , ductility ...
[6] In continuous-time dynamics, the variable time is treated as continuous, and the equation describing the evolution of some variable over time is a differential equation. [7] The instantaneous rate of change is a well-defined concept that takes the ratio of the change in the dependent variable to the independent variable at a specific instant.
[1] [2] In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. [3] The scope and application of measurement are dependent on the context and discipline.
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