different between sheaf vs group

English

Etymology

From Middle English scheef, from Old English s??af, from Proto-Germanic *skauba- (“sheaf”). Akin to West Frisian skeaf (“sheaf”), Dutch schoof (“sheaf”), German Schaub, Old Norse skauf (“a fox's tail”). Compare further Gothic ???????????????????? (skuft, “hair of the head”), German Schopf (“tuft”).

Pronunciation

• enPR: sh?f, IPA^(key): /?i?f/
• Rhymes: -i?f

Noun

sheaf (plural sheaves or sheafs)

1. A quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw.

   Synonym: reap

   • 1593, William Shakespeare, Titus Andronicus, Act V, Scene III, line 70:

     O, let me teach you how to knit again / This scattered corn into one mutual sheaf, / These broken limbs again into one body.

   • c. 1697, John Dryden, “Georgic I”, in The Works of Virgil:

     E’en while the reaper fills his greedy hands, / And binds the golden sheaves in brittle bands

2. Any collection of things bound together.

   Synonym: bundle
3. A bundle of arrows sufficient to fill a quiver, or the allowance of each archer.
4. A quantity of arrows, usually twenty-four.
   • 1786, Francis Grose, A Treatise on Ancient Armour and Weapons, page 34:

     Arrows were anciently made of reeds, afterwards of cornel wood, and occasionally of every species of wood: but according to Roger Ascham, ash was best; arrows were reckoned by sheaves, a sheaf consisted of twenty-four arrows.

5. (mechanical) A sheave.
6. (mathematics) An abstract construct in topology that associates data to the open sets of a topological space, together with well-defined restrictions from larger to smaller open sets, subject to the condition that compatible data on overlapping open sets corresponds, via the restrictions, to a unique datum on the union of the open sets.

Derived terms

• indsheaf

Translations

Verb

sheaf (third-person singular simple present sheafs, present participle sheafing, simple past and past participle sheafed)

1. (transitive) To gather and bind into a sheaf; to make into sheaves

2. (intransitive) To collect and bind cut grain, or the like; to make sheaves.
   • 1599, William Shakespeare, As You Like It, Act III, Scene II, line 107:

     They that reap must sheaf and bind; Then to cart with Rosalind.

Anagrams

• SHAEF, Shefa

English

Alternative forms

• groop (non-standard)
• groupe (obsolete)

Etymology

From French groupe (“cluster, group”), from Italian gruppo, groppo (“a knot, heap, group, bag (of money)”), from Vulgar Latin *cruppo, Renaissance Latin grupus, from Proto-Germanic *kruppaz (“lump, round mass, body, crop”), from Proto-Indo-European *grewb- (“to crumple, bend, crawl”). Cognate with German Kropf (“crop, craw, bunch”), Old English cropp, croppa (“cluster, bunch, sprout, flower, berry, ear of corn, crop”), Dutch krop (“craw”), Icelandic kroppr (“hump, bunch”). Doublet of crop and croup.

Pronunciation

• enPR: gro?op, IPA^(key): /??u?p/
• Rhymes: -u?p

Noun

group (plural groups)

1. A number of things or persons being in some relation to one another.

2. (group theory) A set with an associative binary operation, under which there exists an identity element, and such that each element has an inverse.
   • 1977, Roger C. Lyndon, Paul E. Schupp, Combinatorial Group Theory, Springer, page 192,

     Throughout this section, we shall assume the existence of finitely presented groups with unsolvable word problem.

   • 1992, Svetlana Katok, Fuchsian Groups, University of Chicago Press, page 112,

     In this chapter we give some examples of Fuchsian groups. The most interesting and important ones are the so-called "arithmetic" Fuchsian groups, i.e., discrete subgroups of PSL(2,R) obtained by some "arithmetic" operations. One such construction we have already seen: if we choose all matrices of SL(2,R) with integer coefficients, then the corresponding elements of PSL(2,R) form the modular group PSL(2,Z).

   • 2007, Zhong-Qi Ma, Group Theory for Physicists, World Scientific, page 277,

     In Chap. 4 the fundamental concepts on Lie groups have been introduced through the SO(3) group and its covering group SU(2).

3. (geometry, archaic) An effective divisor on a curve.
4. A (usually small) group of people who perform music together.

5. (astronomy) A small number (up to about fifty) of galaxies that are near each other.
6. (chemistry) A column in the periodic table of chemical elements.
7. (chemistry) A functional group.

8. (sociology) A subset of a culture or of a society.
9. (military) An air force formation.
10. (geology) A collection of formations or rock strata.
11. (computing) A number of users with same rights with respect to accession, modification, and execution of files, computers and peripherals.
12. An element of an espresso machine from which hot water pours into the portafilter.
13. (music) A number of eighth, sixteenth, etc., notes joined at the stems; sometimes rather indefinitely applied to any ornament made up of a few short notes.
14. (sports) A set of teams playing each other in the same division, while not during the same period playing any teams that belong to other sets in the division.
15. (business) A commercial organization.

Synonyms

• (number of things or persons being in some relation to each other): collection, set
• (people who perform music together): band, ensemble
• See also Thesaurus:group

Hypernyms

• (in group theory): monoid

Hyponyms

Derived terms

• subgroup

Related terms

Descendants

• ? Gulf Arabic: ?????
• ? Japanese: ???? (gur?pu)
• ? Korean: ?? (geurup)
• ? Tongan: kulupu

Translations

References

• group on Wikipedia.Wikipedia

Verb

group (third-person singular simple present groups, present participle grouping, simple past and past participle grouped)

1. (transitive) To put together to form a group.

   group the dogs by hair colour

2. (intransitive) To come together to form a group.

Synonyms

• (put together to form a group): amass, categorise/categorize, classify, collect, collect up, gather, gather together, gather up; see also Thesaurus:round up
• (come together to form a group): assemble, begather, foregather, throng; see also Thesaurus:assemble

Translations

Further reading

• group in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
• group in The Century Dictionary, New York, N.Y.: The Century Co., 1911.