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Notations

Listing of the Mathematical Notations used in the Mathematical Functions Website












Notations





Numbers, variables, and functions


The set of natural numbers : .

The set of positive natural numbers : .

The set of integer numbers : .

The set of rational numbers : .

The set of real numbers : .

The set of complex numbers : .

The set of prime numbers : .

The empty set.

The finite set of elements .

A sequence of elements listElement. Inside a list the construction is understood to splice all occurences of listElement into the list.

A (potentially infinite) sequence of terms defined by . is typically used as a sequence of an infinite or an undetermined number of elements in a list.

The Cartesian product of copies of sets . (Tensor product of sets .)

The Cartesian product of the sets , , ….

The ordered set of sets , ,….

As a rule, the following notation style is supported for all variables, numbers, and indices.

Generic complex variables.

Generic real variables. (Relations of the form imply that and are real.)

Integer variables.

Dummy variables used in sums and products.

Integration dummy variables in definite integrals or integral transforms.

The element does belong to the set .

The element does not belong to the set .

The number lies within the specified interval (excluding and ). It is True if the number lies within the specified interval (including its ends), and False otherwise.

The number lies within the specified interval (including and excluding ).

The number does not belong to the specified interval .

The inverse of the function . The value of for which the function : .

The function defined on the set is continuous and has all derivatives of orders .

The characteristic function of a set has the value 1 when its argument is an element of the specified set 𝔸, and the value 0 otherwise.

Gives 1 if cond is true, and 0 if it is false.

Gives expr if cond is true, and 0 otherwise.





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