In mathematics, a property is any characteristic that applies to a given set. 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. However, it may be objected that the rigorous definition defines merely the extension of a property, and says nothing about what causes the property to hold for exactly those values.
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| - Property (mathematics)
- Proprietà (matematica)
- 性质 (数学)
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| - In matematica, il concetto di proprietà corrisponde all'idea intuitiva di una caratteristica che un oggetto può avere o non avere. Formalmente, una proprietà è data da una formula con una sola variabile libera . Si dirà che verifica la proprietà (o equivalentemente che la proprietà vale su ) se vale (più spesso scritto semplicemente ). Per semplificare la notazione, solitamente la proprietà si identifica con la formula e si scriverà quindi invece che o .
- 在数学中，性质是指给定集合的任何特征。严格地，性质 p 定义集合 X 中的所有元素，通常表示为这样的函数p : X → {true, false}，如果性质存在，取值就是真；或者，也可以被视作是X的子集，其中p存在。也就是说，集合{x | p(x) = true}; p是其中的指示函数。但是，如果不表明什么导致性质的取值，严格定义只定义了性质的外延，这一点是可能会被拒绝的。 关于性质的例子包括实数和复数的交换性质、分配性质。
- In mathematics, a property is any characteristic that applies to a given set. 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. However, it may be objected that the rigorous definition defines merely the extension of a property, and says nothing about what causes the property to hold for exactly those values.
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| - In matematica, il concetto di proprietà corrisponde all'idea intuitiva di una caratteristica che un oggetto può avere o non avere. Formalmente, una proprietà è data da una formula con una sola variabile libera . Si dirà che verifica la proprietà (o equivalentemente che la proprietà vale su ) se vale (più spesso scritto semplicemente ). Per semplificare la notazione, solitamente la proprietà si identifica con la formula e si scriverà quindi invece che o .
- 在数学中，性质是指给定集合的任何特征。严格地，性质 p 定义集合 X 中的所有元素，通常表示为这样的函数p : X → {true, false}，如果性质存在，取值就是真；或者，也可以被视作是X的子集，其中p存在。也就是说，集合{x | p(x) = true}; p是其中的指示函数。但是，如果不表明什么导致性质的取值，严格定义只定义了性质的外延，这一点是可能会被拒绝的。 关于性质的例子包括实数和复数的交换性质、分配性质。
- In mathematics, a property is any characteristic that applies to a given set. 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. However, it may be objected that the rigorous definition defines merely the extension of a property, and says nothing about what causes the property to hold for exactly those values. Examples of properties include: Parity is the property of an integer of whether it is even or odd. There is the commutative property of real and complex numbers and the distributive property.
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