In mathematics, a transformation is a function f that maps a set X to itself, i.e. f: X → X. In other areas of mathematics, a transformation may simply refer to any function, regardless of domain and codomain.

Verb. transform, metamorphose, transmute, convert, transmogrify, transfigure mean to change a thing into a different thing. transform implies a major change in form, nature, or function.

Some common synonyms of transform are convert, metamorphose, transfigure, transmogrify, and transmute.

To transform something or someone means to change them completely and suddenly so that they are much better or more attractive. ...

More to the point, though, neither word should be interpreted as exclusively positive or negative. These adjectives—like “transform,” the word they come from—merely have to do with change, and change can be for better or for worse. A magic spell, for instance, might transform a subject into a frog or a prince.

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