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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.
A property holds "generically" on a set if the set satisfies some (context-dependent) notion of density, or perhaps if its complement satisfies some (context-dependent) notion of smallness. For example, a property which holds on a dense G δ ( intersection of countably many open sets ) is said to hold generically.
Rarely used in modern mathematics without a horizontal bar delimiting the width of its argument (see the next item). For example, √2. √ (radical symbol) 1. Denotes square root and is read as the square root of. For example, +. 2. With an integer greater than 2 as a left superscript, denotes an n th root.
Personal property can be understood in comparison to real estate, immovable property or real property (such as land and buildings). Movable property on land (larger livestock, for example) was not automatically sold with the land, it was "personal" to the owner and moved with the owner.
In mathematics, Painlevé transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property (the only movable singularities are poles), but which are not generally solvable in terms of elementary functions.
FIP – finite intersection property. FOC – first order condition. FOL – first-order logic. fr – boundary. (Also written as bd or ∂.) Frob – Frobenius endomorphism. FT – Fourier transform. FTA – fundamental theorem of arithmetic or fundamental theorem of algebra.
Is a complex number that can be written as a real number multiplied by the imaginary unit i, [note 2] which is defined by its property i 2 = −1. [54] The square of an imaginary number bi is −b 2. For example, 5i is an imaginary number, and its square is −25. Zero is considered to be both real and imaginary. [55] implicit function
Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. For example, the physicist Albert Einstein 's formula E = m c 2 {\displaystyle E=mc^{2}} is the quantitative representation in mathematical notation of mass–energy ...