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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.
Nowhere continuous function: is not continuous at any point of its domain; for example, the Dirichlet function. Homeomorphism: is a bijective function that is also continuous, and whose inverse is continuous. Open function: maps open sets to open sets. Closed function: maps closed sets to closed sets.
For example, the gamma function is a function that satisfies the functional equation (+) = and the initial value () = There are many functions that satisfy these conditions, but the gamma function is the unique one that is meromorphic in the whole complex plane, and logarithmically convex for x real and positive ( Bohr–Mollerup theorem ).
The image of a function is the image of its entire domain, also known as the range of the function. [3] This last usage should be avoided because the word "range" is also commonly used to mean the codomain of f . {\displaystyle f.}
There is a larger class of number-theoretic functions that do not fit this definition, for example, the prime-counting functions. This article provides links to functions of both classes. An example of an arithmetic function is the divisor function whose value at a positive integer n is equal to the number of divisors of n.
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This is a list of some well-known periodic functions. The constant function f (x) = c, where c is independent of x, is periodic with any period, but lacks a fundamental period. A definition is given for some of the following functions, though each function may have many equivalent definitions.
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related to: functions example questions printable sheets free for adults picturesteacherspayteachers.com has been visited by 100K+ users in the past month