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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.
Template: Functions. ... Download as PDF; Printable version; In other projects ... Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; ...
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
Graph of a linear function Graph of a polynomial function, here a quadratic function. Graph of two trigonometric functions: sine and cosine. A real function is a real-valued function of a real variable, that is, a function whose codomain is the field of real numbers and whose domain is a set of real numbers that contains an interval.
In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x 1/n).
linewidths: different line widths may be defined for each series of data with csv, if set to 0 with "showSymbols" results with points graph, eg.: linewidths=1, 0, 5, 0.2; showSymbols: show symbol on data point for line graphs, if a number is provided, the symbol size (default 2.5) may be defined for each data series, eg.: showSymbols=1, 2, 3, 4
If f : X → Y is any function, then f ∘ id X = f = id Y ∘ f, where "∘" denotes function composition. [4] In particular, id X is the identity element of the monoid of all functions from X to X (under function composition). Since the identity element of a monoid is unique, [5] one can alternately define the identity function on M to
Hypercomplex function: a function whose domain is hypercomplex (e.g. quaternions, octonions, sedenions, trigintaduonions etc.) p-adic function: a function whose domain is p-adic. Linear function; also affine function. Convex function: line segment between any two points on the graph lies above the graph. Also concave function.
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