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A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates. [1] In a sense, these are nullary (i.e. 0- arity) predicates.
In mathematics, a codomain or set of destination of a function is a set into which all of the output of the function is constrained to fall. It is the set Y in the notation f: X → Y. The term range is sometimes ambiguously used to refer to either the codomain or the image of a function. A codomain is part of a function f if f is defined as a ...
In mathematics, change of base can mean any of several things: Changing numeral bases, such as converting from base 2 (binary) to base 10 (decimal). This is known as base conversion. The logarithmic change-of-base formula, one of the logarithmic identities used frequently in algebra and calculus. The method for changing between polynomial and ...
Counting measure. In mathematics, specifically measure theory, the counting measure is an intuitive way to put a measure on any set – the "size" of a subset is taken to be the number of elements in the subset if the subset has finitely many elements, and infinity if the subset is infinite. [1]
Enumerative combinatorics. Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations. More generally, given an infinite collection of finite sets Si indexed by the natural numbers ...
where E is the expected value operator. Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables. If Y always takes on the same values as X, we have the covariance of a variable with itself (i.e. ), which is called the variance and is more commonly denoted as the square of the ...
Wikipedia's contents: Mathematics and logic. edit · watch. Mathematics is the study of topics such as quantity (numbers), structure, space, and change. It evolved through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects.
In mathematics, the equidistribution theorem is the statement that the sequence. a, 2 a, 3 a, ... mod 1. is uniformly distributed on the circle , when a is an irrational number. It is a special case of the ergodic theorem where one takes the normalized angle measure .