different between preimage vs primage

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

Etymology 1

From Late Latin primagium. (The French word post-dates the English.)

Noun

primage (countable and uncountable, plural primages)

1. (archaic) A payment made for loading or unloading a ship, or for care of goods during transit by ship.
   • 1818, John Adolphus, The Political State of the British Empire, Volume 3, page 197,

     By the bill of lading the ma?ter undertakes to deliver the goods on payment of freight with primage and average accu?tomed.

2. (archaic, Britain) An import duty levied by a guild of harbour pilots (especially at Kingston-upon-Hull and Newcastle-upon-Tyne).
3. (Australia, New Zealand) An additional import duty levied by customs.
   • 1932, E. T. McPhee (Commonwealth Statistician), Official Year Book of the Commonwealth of Australia: No. 25 - 1932,

     The rate of primage duty was subsequently increased to 4 per cent. as from the 6th November, 1930.

External links

• Primage in the Encyclopædia Britannica (11th edition, 1911)

Etymology 2

From prime +? -age.

Noun

primage (countable and uncountable, plural primages)

1. (engineering, rare) Droplets of water suspended in steam (especially in the cylinder of a steam engine).
   • 1883, Emory Edwards, Modern American Locomotive Engines: Their Design, Construction and Management, page 75,

     Of these temperatures, only one, the second, indicates primage; all others exhibit a slight superheat.

Anagrams

• epigram