| # Functions and maps ## Functions In this course we define functions as objects which take an argument in , and return a value in . We use the notation to refer to a function with ‘‘input’’ space . The ‘‘output’’ space for functions is . Example: The function with values gives the distance from the point to . We allow for functions to take infinity values. The domain of a function , denoted , is defined as the set of points where the function is finite. Example: Define the logarithm function as the function , with values if , and otherwise. The domain of the function is thus (the set of positive reals). ## Maps We reserve the term map to refer to functions which return more than a single value, and use the notation to refer to a map with input space and output space . The components of the map are the (scalar-valued) functions , . Example: a map.