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In many cases, such as order theory, the inverse of the indicator function may be defined. This is commonly called the generalized Möbius function, as a generalization of the inverse of the indicator function in elementary number theory, the Möbius function. (See paragraph below about the use of the inverse in classical recursion theory.)
Such indicators have some special properties. For example, the following statements are all true for an indicator function that is trigonometrically convex at least on an interval (,): [1]: 55–57 [2]: 54–61
Indicator function – Mathematical function characterizing set membership; Linear discriminant function – Method used in statistics, pattern recognition, and other fields; Multicollinearity – Linear dependency situation in a regression model; One-hot – Bit-vector representation where only one bit can be set at a time
If S is the set of natural numbers, and T is some subset of the natural numbers, then the indicator vector is naturally a single point in the Cantor space: that is, an infinite sequence of 1's and 0's, indicating membership, or lack thereof, in T. Such vectors commonly occur in the study of arithmetical hierarchy.
Reference notes. A reference card or reference sheet (or quick reference card) or crib sheet is a concise bundling of condensed notes about a specific topic, such as mathematical formulas [1] to calculate area/volume, or common syntactic rules and idioms of a particular computer platform, application program, or formal language.
In mathematics, the ± sign generally indicates a choice of exactly two possible values, one of which is obtained through addition and the other through subtraction. In statistics and experimental sciences , the ± sign commonly indicates the confidence interval or uncertainty bounding a range of possible errors in a measurement, often the ...
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In potential theory (a branch of mathematics), the Laplacian of the indicator is obtained by letting the Laplace operator work on the indicator function of some domain D. It is a generalisation of the derivative (or "prime function") of the Dirac delta function to higher dimensions ; it is non-zero only on the surface of D .
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