different between preimage vs fiber

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

• fibre (chiefly British)

Etymology

From French fibre, from Old French, from Latin fibra

Pronunciation

• (General American) IPA^(key): /?fa?.b?/
• (Received Pronunciation) IPA^(key): /?fa?.b?/
• Rhymes: -a?b?(r)

Noun

fiber (countable and uncountable, plural fibers) (American spelling)

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

2. (uncountable) A material in the form of fibers.

3. (textiles) A material whose length is at least 1000 times its width.

4. Dietary fiber.

5. (figuratively) Moral strength and resolve.

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

   Holonyms: bundle, fiber bundle

   Meronym: germ

7. (category theory) Said to be of a morphism over a global element: The pullback of the said morphism along the said global element.
8. (computing) A kind of lightweight thread of execution.

Derived terms

Translations

Anagrams

• FBIer, brief, fibre

Danish

Noun

fiber c (definite singular fiberen, indefinite plural fibre, definite plural fibrene)

1. fibre (UK), fiber (US)

Latin

Etymology

From Proto-Indo-European *b?éb?rus. Doublet of beber.

Pronunciation

• (Classical) IPA^(key): /?fi.ber/, [?f?b?r]
• (Ecclesiastical) IPA^(key): /?fi.ber/, [?fi?b?r]

Noun

fiber m (genitive fibr?); second declension

1. beaver

Declension

Second-declension noun (nominative singular in -er).

Synonyms

• castor (more common), beber (Late Latin)

Derived terms

• fibr?nus

References

• fiber in Charlton T. Lewis and Charles Short (1879) A Latin Dictionary, Oxford: Clarendon Press

Norwegian Bokmål

Etymology

From Latin fibra (“fiber, filament”), possibly from *fidber or *findber, from Proto-Indo-European *b?eyd- (“to split”).

Noun

fiber m (definite singular fiberen, indefinite plural fibere or fibre or fibrer, definite plural fiberne or fibrene)

1. fibre (UK), fiber (US)

Derived terms

References

• “fiber” in The Bokmål Dictionary.

Norwegian Nynorsk

Noun

fiber m (definite singular fiberen, indefinite plural fibrar, definite plural fibrane)

1. fibre (UK), fiber (US)

Derived terms

• fiberoptisk
• fiberrik
• karbonfiber
• naturfiber

References

• “fiber” in The Nynorsk Dictionary.

Swedish

Noun

fiber c

1. fibre (UK), fiber (US)

Declension