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What is the difference between preimage and image?

preimage | image | Related terms |

Image is a derived term of preimage.

Image is a related term of preimage.



In mathematics terms the difference between preimage and image

is that preimage is the set containing exactly every member of the domain of a function such that the member is mapped by the function onto an element of a given subset of the codomain of the function. Formally, of a subset B of the codomain Y under a function ƒ, the subset of the domain X defined by while image is the subset of a codomain comprising those elements that are images of something.

As a verb image is

to represent symbolically.

preimage

English

(Function)

Noun

(en noun)
  • (mathematics) The set containing exactly every member of the domain of a function such that the member is mapped by the function onto an element of a given subset of the codomain of the function. Formally, of a subset B'' of the codomain ''Y'' under a function ƒ, the subset of the domain ''X defined by
  • f^{-1}(B) = \{x \in X : f(x) \in B\}.
    For example, the preimage of {4, 9} under the squaring function is the set {?3,?2,+2,+3}.

    Synonyms

    * inverse image

    image

    English

    (wikipedia image)

    Noun

    (en noun)
  • An optical or other representation of a real object; a graphic; a picture.
  • The Bible forbids the worship of graven images .
  • * {{quote-magazine, date=2012-03
  • , author=, title=Pixels or Perish , volume=100, issue=2, page=106, magazine=(American Scientist) citation , passage=Drawings and pictures are more than mere ornaments in scientific discourse. Blackboard sketches, geological maps, diagrams of molecular structure, astronomical photographs, MRI images , the many varieties of statistical charts and graphs: These pictorial devices are indispensable tools for presenting evidence, for explaining a theory, for telling a story.}}
  • A mental picture of something not real or not present.
  • * {{quote-magazine, date=2013-08-03, volume=408, issue=8847, magazine=(The Economist)
  • , title= Revenge of the nerds , passage=Think of banking today and the image is of grey-suited men in towering skyscrapers. Its future, however, is being shaped in converted warehouses and funky offices in San Francisco, New York and London, where bright young things in jeans and T-shirts huddle around laptops, sipping lattes or munching on free food.}}
  • (computing) A file that contains all information needed to produce a live working copy. (see disk image, executable image and image copy)
  • Most game console emulators do not come with any ROM images for copyright reasons.
  • A characteristic of a person, group or company etc., style, manner of dress, how one is, or wishes to be, perceived by others.
  • (mathematics) Something mapped to by a function.
  • The number 6 is the image of 3 under ''f'' that is defined as f(x) = 2*x.
  • (mathematics) The subset of a codomain comprising those elements that are images of something.
  • The image of this step function is the set of integers.
  • (obsolete) Show; appearance; cast.
  • * Dryden
  • The face of things a frightful image bears.

    Synonyms

    * (representation) picture * (mental picture) idea * (something mapped to) value * (subset of the codomain) range

    Derived terms

    * imagery * image magic * inverse image * macroimage * mental image * microimage * mirror image * preimage * real image * reimage * spitting image * virtual image

    Descendants

    * German: (l)

    Verb

    (imag)
  • To represent symbolically.
  • To reflect, .
  • * 1843 , (Thomas Carlyle), '', book 2, chapter 2, ''St. Edmundsbury :
  • we look into a pair of eyes deep as our own, imaging our own, but all unconscious of us; to whom we for the time are become as spirits and invisible!.
  • To create an image of.
  • * {{quote-magazine, year=2013, month=July-August, author= Fenella Saunders
  • , title= Tiny Lenses See the Big Picture, magazine=(American Scientist) , passage=The single-imaging optic of the mammalian eye offers some distinct visual advantages. Such lenses can take in photons from a wide range of angles, increasing light sensitivity. They also have high spatial resolution, resolving incoming images in minute detail.}}
  • (computing) To create a complete backup copy of a file system or other entity.