different between preimage vs fibre

English

Etymology

pre- +? image.

Pronunciation

• Rhymes: -?m?d?

Noun

preimage (plural preimages)

1. (mathematics) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X ? Y and a subset B ? Y, the set ƒ^?1(B) = {x ? X : ƒ(x) ? B}.
   • 1967 [Academic Press], Francois Treves, Topological Vector Spaces, Distributions and Kernels, 2006, Dover, page 22,

     The preimage of a neighborhood U of 0 in E must be a neighborhood of (0,x), since (0,x) is mapped into 0.

   • 2003, Sergei K. Lando, Alexander K. Zvonkin, Graphs on Surfaces and Their Applications, Springer, page 56,

     Previously, maps and hypermaps were constructed as the preimages of a segment joining two of the three critical values.

   • 2005, Oded Goldreich, Foundations of Cryptography: A Primer, now Publishers, page 24,

     Loosely speaking, saying that a function f is one-way implies that given y (in the range of f) it is infeasible to find a preimage of y under f.

Synonyms

• (set of all elements that map into a given subset of the codomain of a function): inverse image

Hyponyms

• (set of all elements that map into a given subset of the codomain of a function): kernel

Derived terms

• preimage attack

Related terms

• image

Translations

Further reading

• Image (mathematics) on Wikipedia.Wikipedia
• Kernel (linear algebra) on Wikipedia.Wikipedia

English

Alternative forms

• fiber (US)

Etymology

From French fibre, from Old French, from Latin fibra.

Pronunciation

• (UK) IPA^(key): /?fa?.b?(?)/
• Rhymes: -a?b?(?)
• Hyphenation: fi?bre
• Homophone: fiber

Noun

fibre (countable and uncountable, plural fibres) (Britain, Canada, Australia, Ireland, New Zealand, South Africa)

2. (countable) A single piece of a given material, elongated and roughly round in cross-section, often twisted with other fibres to form thread.

   The microscope showed several different fibres stuck to the sole of the shoe.

4. (uncountable) Material in the form of fibres.

   The cloth was made from strange, somewhat rough fibre.

5. Dietary fibre.

   Fresh vegetables are a good source of fibre.

6. Moral strength and resolve.
   • 1900, Joseph Conrad, Lord Jim, ch 2:

     He was gentlemanly, steady, tractable, with a thorough knowledge of his duties; and in time, when yet very young, he became chief mate of a fine ship, without ever having been tested by those events of the sea that show in the light of day the inner worth of a man, the edge of his temper, and the fibre of his stuff; that reveal the quality of his resistance and the secret truth of his pretences, not only to others but also to himself.

   The ordeal was a test of everyone’s fibre.

7. (mathematics) The preimage of a given point in the range of a map.

   Under this map, any two values in the fibre of a given point on the circle differ by 2?

8. (category theory) Said to be of a morphism over a global element: The pullback of the said morphism along the said global element.
9. (computing) A kind of lightweight thread of execution.
10. A long tubular cell found in muscle tissue; myocyte.

Related terms

Translations

Anagrams

• FBIer, brief, fiber

Danish

Noun

fibre c pl

1. indefinite plural of fiber

French

Etymology

From Old French fibre, borrowed from Latin fibra.

Pronunciation

• IPA^(key): /fib?/

Noun

fibre f (plural fibres)

1. fibre

Derived terms

• fibre de verre
• fibre optique

Related terms

Further reading

• “fibre” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

Italian

Noun

fibre f pl

1. plural of fibra

Norwegian Bokmål

Alternative forms

• fibere
• fibrer

Noun

fibre m pl

1. indefinite plural of fiber

Romanian

Pronunciation

• IPA^(key): [?fibre]

Noun

fibre f

1. indefinite plural of fibr?
2. indefinite genitive/dative singular of fibr?