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2. Absolute value (algebra) - Wikipedia

   en.wikipedia.org/wiki/Absolute_value_(algebra)

   In algebra, an absolute value (also called a valuation, magnitude, or norm, [1] although "norm" usually refers to a specific kind of absolute value on a field) is a function which measures the "size" of elements in a field or integral domain. More precisely, if D is an integral domain, then an absolute value is any mapping |x| from D to the ...

3. Valuation (algebra) - Wikipedia

   en.wikipedia.org/wiki/Valuation_(algebra)

   Valuation (algebra) In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of the size or multiplicity of elements of the field. It generalizes to commutative algebra the notion of size inherent in consideration of the degree of a pole or multiplicity of a zero ...

4. Archimedean property - Wikipedia

   en.wikipedia.org/wiki/Archimedean_property

   By Ostrowski's theorem, every non-trivial absolute value on the rational numbers is equivalent to either the usual absolute value or some -adic absolute value. The rational field is not complete with respect to non-trivial absolute values; with respect to the trivial absolute value, the rational field is a discrete topological space, so complete.

5. Triviality (mathematics) - Wikipedia

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

   Triviality (mathematics) In mathematics, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or an object which possesses a simple structure (e.g., groups, topological spaces). [1][2] The noun triviality usually refers to a simple technical aspect of some proof or definition.

6. Absolute value - Wikipedia

   en.wikipedia.org/wiki/Absolute_value

   The absolute value of a number may be thought of as its distance from zero. In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and . For example, the absolute value of 3 is ...

7. Regularization (mathematics) - Wikipedia

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

   In mathematics, statistics, finance, [ 1 ] and computer science, particularly in machine learning and inverse problems, regularization is a process that converts the answer of a problem to a simpler one. It is often used in solving ill-posed problems or to prevent overfitting. [ 2 ]

8. Mean - Wikipedia

   en.wikipedia.org/wiki/Mean

   Main article: Arithmetic mean. The arithmetic mean (or simply mean or average) of a list of numbers, is the sum of all of the numbers divided by their count. Similarly, the mean of a sample , usually denoted by , is the sum of the sampled values divided by the number of items in the sample. For example, the arithmetic mean of five values: 4, 36 ...

9. Norm (mathematics) - Wikipedia

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

   In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a ...