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Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
A graph of the probability density functions of several normal distributions (from the same parametric family). For example, the probability density function f X of a random variable X may depend on a parameter θ. In that case, the function may be denoted (;) to indicate the dependence on the parameter θ.
Additionally, a family of sets may be defined as a function from a set , known as the index set, to , in which case the sets of the family are indexed by members of . [1] In some contexts, a family of sets may be allowed to contain repeated copies of any given member, [ 2 ] [ 3 ] [ 4 ] and in other contexts it may form a proper class .
A graph of three branches of the algebraic function y, where y 3 − xy + 1 = 0, over the domain 3/2 2/3 < x < 50. Furthermore, even if one is ultimately interested in real algebraic functions, there may be no means to express the function in terms of addition, multiplication, division and taking nth roots without resorting to complex numbers ...
Toggle Functions and sets subsection. 8.1 Definitions. 8.2 ... Toggle Sequences and collections of families of sets subsection. ... show that it is a Boolean algebra. ...
Let X and Y be two metric spaces, and F a family of functions from X to Y.We shall denote by d the respective metrics of these spaces.. The family F is equicontinuous at a point x 0 ∈ X if for every ε > 0, there exists a δ > 0 such that d(ƒ(x 0), ƒ(x)) < ε for all ƒ ∈ F and all x such that d(x 0, x) < δ.
Holomorphic function: complex-valued function of a complex variable which is differentiable at every point in its domain. Meromorphic function: complex-valued function that is holomorphic everywhere, apart from at isolated points where there are poles. Entire function: A holomorphic function whose domain is the entire complex plane.
The concept of parent function is less clear or inapplicable polynomials of higher degree because of the extra turning points, but for the family of n-degree polynomial functions for any given n, the parent function is sometimes taken as x n, or, to simplify further, x 2 when n is even and x 3 for odd n. Turning points may be established by ...
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