Multivalued Functions
Many functions do not have a unique inverse. For instance squaring a number gives a unique value, but there are two possible square roots of a positive number. The square root is multivalued. One value can be chosen by convention as the principal value, in the case of the square root the non-negative value is the principal value, but there is no guarantee that the square root function given by this principal value of the square of a number will be equal to the original number, e.g. the square root of the square of −2 is 2.
Read more about this topic: Mathematical Fallacy
Famous quotes containing the word functions:
“Let us stop being afraid. Of our own thoughts, our own minds. Of madness, our own or others’. Stop being afraid of the mind itself, its astonishing functions and fandangos, its complications and simplifications, the wonderful operation of its machinery—more wonderful because it is not machinery at all or predictable.”
—Kate Millett (b. 1934)