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Examples of intensive properties include temperature, T; refractive index, n; density, ρ; and hardness, η. By contrast, an extensive property or extensive quantity is one whose magnitude is additive for subsystems. [4] Examples include mass, volume and entropy. [5] Not all properties of matter fall into these two categories.
Two meaningful declarative sentences express the same proposition, if and only if they mean the same thing. [citation needed] which defines proposition in terms of synonymity. For example, "Snow is white" (in English) and "Schnee ist weiß" (in German) are different sentences, but they say the same thing, so they express the same proposition.
However, in first-order logic, these two sentences may be framed as statements that a certain individual or non-logical object has a property. In this example, both sentences happen to have the common form () for some individual , in the first sentence the value of the variable x is "Socrates", and in the second sentence it is "Plato". Due to ...
For example, isotropic properties do not change with the direction of observation, and anisotropic properties do have spatial variance. It may be difficult to determine whether a given property is a material property or not.
An example of that is the presupposition trigger too. This word triggers the presupposition that, roughly, something parallel to what is stated has happened. For example, if pronounced with emphasis on John, the following sentence triggers the presupposition that somebody other than John had dinner in New York last night.
For example, if the domain is the set of all real numbers, one can assert in first-order logic the existence of an additive inverse of each real number by writing ∀x ∃y (x + y = 0) but one needs second-order logic to assert the least-upper-bound property for sets of real numbers, which states that every bounded, nonempty set of real numbers ...
A material property is an intensive property of a material, i.e., a physical property or chemical property that does not depend on the amount of the material. These quantitative properties may be used as a metric by which the benefits of one material versus another can be compared, thereby aiding in materials selection.
For example, the order does not matter in the multiplication of real numbers, that is, a × b = b × a, so we say that the multiplication of real numbers is a commutative operation. However, operations such as function composition and matrix multiplication are associative, but not (generally) commutative.