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  2. Property (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Property_(mathematics)

    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.

  3. Associative property - Wikipedia

    en.wikipedia.org/wiki/Associative_property

    In mathematics, the associative property [1] is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result. In propositional logic , associativity is a valid rule of replacement for expressions in logical proofs .

  4. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Examples include e and π. Trigonometric number: Any number that is the sine or cosine of a rational multiple of π. Quadratic surd: A root of a quadratic equation with rational coefficients. Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number.

  5. Commutative property - Wikipedia

    en.wikipedia.org/wiki/Commutative_property

    Today the commutative property is a well-known and basic property used in most branches of mathematics. The first recorded use of the term commutative was in a memoir by François Servois in 1814, [ 1 ] [ 10 ] which used the word commutatives when describing functions that have what is now called the commutative property.

  6. Group (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Group_(mathematics)

    For example, the integers with the addition operation form an infinite group, which is generated by a single element called ⁠ ⁠ (these properties characterize the integers in a unique way). The concept of a group was elaborated for handling, in a unified way, many mathematical structures such as numbers, geometric shapes and polynomial roots .

  7. Glossary of mathematical jargon - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_mathematical...

    In many occasions, these can be and often are contradictory requirements, while in other occasions, the term is more deliberately used to refer to an object artificially constructed as a counterexample to these properties. A simple example is that from the definition of a triangle having angles which sum to π radians, a single straight line ...

  8. Infimum and supremum - Wikipedia

    en.wikipedia.org/wiki/Infimum_and_supremum

    The least-upper-bound property is an example of the aforementioned completeness properties which is typical for the set of real numbers. This property is sometimes called Dedekind completeness . If an ordered set S {\displaystyle S} has the property that every nonempty subset of S {\displaystyle S} having an upper bound also has a least upper ...

  9. Universal property - Wikipedia

    en.wikipedia.org/wiki/Universal_property

    The typical diagram of the definition of a universal morphism. In mathematics, more specifically in category theory, a universal property is a property that characterizes up to an isomorphism the result of some constructions. Thus, universal properties can be used for defining some objects independently from the method chosen for constructing them.

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