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In mathematics, a property is any characteristic that applies to a given set. [1] Rigorously, a property p defined for all elements of a set X is usually defined as a function p: X → {true, false}, that is true whenever the property holds; or, equivalently, as the subset of X for which p holds; i.e. the set {x | p(x) = true}; p is its indicator function.
In materials science, an intrinsic property is independent of how much of a material is present and is independent of the form of the material, e.g., one large piece or a collection of small particles. Intrinsic properties are dependent mainly on the fundamental chemical composition and structure of the material. [1]
Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction , that do not have it (for example, "3 − 5 ≠ 5 − 3" ); such operations are not commutative, and so are ...
Commutative property: Mentioned above, using the pattern a + b = b + a reduces the number of "addition facts" from 100 to 55. One or two more : Adding 1 or 2 is a basic task, and it can be accomplished through counting on or, ultimately, intuition .
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.
For example, in elementary arithmetic, one has (+) = + (). Therefore, one would say that multiplication distributes over addition . This basic property of numbers is part of the definition of most algebraic structures that have two operations called addition and multiplication, such as complex numbers , polynomials , matrices , rings , and fields .
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