# generalization

## Definitions

• General Tool rack in a School Shop
• WordNet 3.6
• n generalization (psychology) transfer of a response learned to one stimulus to a similar stimulus
• n generalization reasoning from detailed facts to general principles
• n generalization the process of formulating general concepts by abstracting common properties of instances
• n generalization an idea or conclusion having general application "he spoke in broad generalities"
• ***

Major General James Wolfe
Lieut. General Sir William Pepperell, Bart
Major-General Sir Isaac Barre
General the Marquis de Montcalm
General Sir Jeffery Amherst
General Hospital
General Gage
General Sir A. P. Irving

Webster's Revised Unabridged Dictionary
• Interesting fact: Although the outsides of a bone are hard, they are generally light and soft inside. They are about 75% water
• Generalization A general inference.
• Generalization The act or process of generalizing; the act of bringing individuals or particulars under a genus or class; deduction of a general principle from particulars. "Generalization is only the apprehension of the one in the many."
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Century Dictionary and Cyclopedia
• Interesting fact: The lifespan of a rhinoceros is generally 50 years
• n generalization The act of generalizing; recognition of a character as being common to two or more objects; also, the process of forming a general notion.
• n generalization Induction; an inference from the possession of a character by each individual or by some of the individuals of a class to its possession by all the individuals of that class; the observation that the known individuals of a species, or the known species of a genus, have a character in common, and the consequent attribution of that character to the whole class; also, a conclusion so reached.
• n generalization In mathematics, the process or result of modifying a proposition so as to obtain another having wider subject and predicate, but such that a limitation which, if applied to the new subject, gives the old subject, will reproduce the old predicate when applied to the new. For example, Fermat's theorem is that if ρ is any positive prime number and a any number not divisible by ρ, then the division of αρ by ρ leaves 1 as the remainder. A generalization of this is, that if κ is any positive integer, and φκ the number of numbers as small as κ and prime to it, and α is any number relatively prime to κ, then the division of αφκ by κ leaves 1 as the remainder; for when κ is a prime number, φκ = κ—1, and every number not divisible by κ is prime to it. The language of mathematics differs from that of logic in that from every generalization of a proposition the proposition itself is immediately deducible, which is not true in the logicians' sense of the word. The distinction between generalization and extension in mathematical language is not very clear, but the latter term applies primarily to a conception or function which has received a new and wider definition; also, the modification of a proposition concerning two dimensions so as to make it apply to three is called an extension.
• n generalization Also spelled generalisation.
• n generalization In pathology, the involvement of the entire system in a morbid process which was at first local.
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## Quotations

• Edmund Burke
“We must not always judge of the generality of the opinion by the noise of the acclamation.”
• Gilbert K. Chesterton
“People generally quarrel because they cannot argue.”
• Napoleon Bonaparte
“The greatest general is he who makes the fewest mistakes.”
• Edmond and Jules De Goncourt
“As a general truth, it is safe to say that any picture that produces a moral impression is a bad picture.”
• Barbara Tuchman
• Samuel Johnson
“What is written without effort is in general read without pleasure.”

## Etymology

Webster's Revised Unabridged Dictionary
Cf. F. généralisation,

## Usage

### In literature:

The third, General Robert E. Lee, had been commissioned by the State of Virginia as major-general and commander of her army.
"The Rise and Fall of the Confederate Government, Vol. 1 (of 2)" by Jefferson Davis
His services were recognized by the brevets of brigadier-general and major-general in the regular army.
"Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4" by Various
The men would salute their old General, the General salute his old regiment.
"Mary Gray" by Katharine Tynan
General Mitchell has been made a Major-General.
"The Citizen-Soldier" by John Beatty
Some days later the 3rd Brigade under General Gatacre arrived, followed by General Low and the headquarter staff.
"Through Three Campaigns" by G. A. Henty
General Ashley and Major Henry set the pace.
"Pluck on the Long Trail" by Edwin L. Sabin
I called on General Cooper, Adjutant-General to the Confederate forces, and senior general in the army.
"Three Months in the Southern States, April-June 1863" by Arthur J. L. (Lieut.-Col.) Fremantle
This general, who struck so hard and never ceased striking, was her general.
"Before the Dawn" by Joseph Alexander Altsheler
October 30, General Buell was succeeded by General Rosecrans.
"Comic History of the United States" by Bill Nye
January 13, 1815... 240 General Jackson to the Secretary of War.
"The Medallic History of the United States of America 1776-1876" by J. F. Loubat
The 53rd Division will remain at the disposal of the General Commanding as general reserve.
"Gallipoli Diary, Volume 2" by Ian Hamilton
They are generally slightly nest stained.
"The Bird Book" by Chester A. Reed
You lead down from the more general to the less general.
"Logic, Inductive and Deductive" by William Minto
The Union right was commanded by General Sigel, the left by General Carr, and the centre by General Jefferson C. Davis.
"The Greater Republic" by Charles Morris
We were passed by General Hamilton and staff, also General Grant and suite.
"An Artilleryman's Diary" by Jenkin Lloyd Jones
In view of these losses, Campos welcomed the arrival of 30,000 additional troops from Spain, under General Pando and General Marin.
"The History of Cuba, vol. 4" by Willis Fletcher Johnson
A general emulation takes place which causes good humor, sociability, good manners and good morals to be general.
"Sages and Heroes of the American Revolution" by L. Carroll Judson
It is now generally believed that General Washington has killed and taken at least two thousand of Mr. Howe's army since Christmas.
Branes are generally supozed tew be lokated in the hed, but investigashun satisfys me that they are planted all over the boddy.
"The Complete Works of Josh Billings" by Henry W. Shaw
When ready, these are generally announced by ringing a bell, beating a gong, or by bugle call.
"Seven Legs Across the Seas" by Samuel Murray
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### In poetry:

Peace for mine own self I could never find,
And still my presence marred the general peace,
And when I parted, leaving them behind,
They felt, and I, release.
"The Solitary" by Robert Fuller Murray
And the Banker, inspired with a courage so new
It was matter for general remark,
In his zeal to discover the Snark
"The Hunting Of The Snark " by Lewis Carroll
A mighty general-- a nation's pride--
Thou givest again a rocking-horse to ride,
And wildly glad he groweth as the grim
Old jurist with the drum thou givest him:
"To Santa Claus" by James Whitcomb Riley
So, dull and damp, and another day;
But the night of that, mist lifting, rain ceasing,
Silent as a ghost, while they thought they were sure of him, my
General retreated.
"The Centerarian's Story" by Walt Whitman
And in the general joy of heart
The blind Boy's little dog took part;
He leapt about, and oft did kiss
His master's hands in sign of bliss,
With sound like lamentation.
"Memorials Of A Tour In Scotland, 1803" by William Wordsworth
" —— was born to spread the general joy;
By virtue rapt, by party uncontroll'd;
Britons for Britain shall the crook employ;
Britons for Britain's glory shear the fold."
"Elegy XVIII. He Repeats the Song of Colin, a Discerning Shepherd" by William Shenstone

### In news:

Walla — Adventist Health Medical Group at Walla Walla General Hospital is welcoming a new pediatrician to the group this month.
For accounting and general information.
Ashish Verma, The Lowell's General Manager.
Little to no construction has been started on general aviation facilities at the new Panama City—Bay County International Airport in Panama City, Fla.
Ted Thompson has pulled off four trades this weekend, which brings his total in four drafts as Packers general manager to a whopping 13 trades.
First-run shows are generally blessed with having a full season to prove their worth.
When you sink to the level of tequila shots, you generally think college bar or Tex-Mex dive.
Monson made the announcement Saturday at the faith's 182nd Semiannual General Conference in Salt Lake City.
SportsNation generally is adamantly opposed to limiting Team USA in any way, but would the squad still be the team to beat.
Former NBA player and general manager Steve Kerr wrote a piece for ESPN's Grantland.com in which he makes a case for the league raising the age limit from 19 to 20.
In a recent story on Grantland.com, five-time NBA champion and former general manager Steve Kerr attempts to answer one question: Would the NBA's business be stronger by raising the age requirement.
General managers will tell you it's one of the hardest decisions they have to make, knowing when to say goodbye to a popular player whose skills have succumbed to Father Time -- or knowing how to handle the phasing-out of that player.
Former Franklin County Sheriff Ewell Hunt (right) is joined in General District Court on Tuesday by defense attorney Bill Stanley.
Posted on May 17, 2011 at 10:56 am by Steve Campbell in Astros, Astros/MLB, General.
The investment seeks investment results that correspond generally to the price and yield performance, before fees and expenses, of the Barclays US Aggregate Bond Index (the "underlying index").
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### In science:

In general, if N is a generalized complex submanifold then the induced generalized complex need not have σ ′ = 0.
Generalized Complex Submanifolds
We are now ready to prove our last theorem, namely that these conditions are guaranteed to be satisﬁed by a generalized K ¨ahler structure and so our notion of generalized complex submanifold preserves generalized K ¨ahler structures.
Generalized Complex Submanifolds
Generalized K¨ahler manifolds are a special type of generalized complex manifolds, and as such many of their properties stem from general properties of generalized complex structures.
Formality in generalized Kahler geometry
It follows that a generalized bracket of two generalized vector ﬁelds can be deﬁned and generalized vector ﬁelds form a Lie algebra with this generalized bracket.
Generalized forms and vector fields
We could deﬁne a generalized vector as an ordered pair of a vector and a bivector, dual to a generalized one-form, referring either to the ring of real functions, or to the ring of generalized zero-forms.
Generalized forms and vector fields
Next we deﬁne the generalized contraction, or interior product IV , with respect to a generalized vector V = (v1 , v0), as a map from generalized p-forms to generalized (p − 1)-forms.
Generalized forms and vector fields
The generalized interior product, when restricted to the ordinary subspace of vector ﬁelds, i.e., to generalized vector ﬁelds of the type V = (v , 0) , is identical to the interior product of ordinary differential geometry, acting independently on the two ordinary forms which make up a generalized form.
Generalized forms and vector fields
We will generalize this formula to compute the generalized commutator of two generalized vector ﬁelds.
Generalized forms and vector fields
Also, the new generalized Lie derivative on generalized vector ﬁelds is not the generalized commutator.
Generalized forms and vector fields
It would be interesting to generalize our main results to the general setting of , i.e., to study the ﬂuctuations of HN in the general setting of .
Universality for the distance in finite variance random graphs: Extended version
Fomin introduced operators called generalized Schur operators, and generalized the Robinson-Schensted-Knuth correspondence for generalized Schur operators.
Pieri's Formula for Generalized Schur Polynomials
In particular, it is shown that for any such groupoid the general linear 2-group is always split (for the deﬁnition of split 2-group, see §2.8), generalizing the situation encountered for Kapranov and Voevodsky general linear 2-groups, which correspond to the case G is a ﬁnite discrete category.
Generalized 2-vector spaces and general linear 2-groups
Finally, in Section 5, the general linear 2-group of the generalized 2-vector space generated by a ﬁnite homogeneous groupoid is computed, recovering Kapranov and Voevodsky general linear 2-groups as particular cases.
Generalized 2-vector spaces and general linear 2-groups
Generalized free 2-vector spaces, as well as generalized free 2-vector spaces of ﬁnite rank, constitute a subclass of the class of all generalized 2-vector spaces which remains stable under ﬁnite products, i.e.
Generalized 2-vector spaces and general linear 2-groups
Finally, another important drawback of generalized 2vector spaces is that, for arbitrary categories C and D, the category of morphisms between the corresponding generalized 2-vector spaces Hom2GVECTK (VectK [C ], VectK [D]) may no longer be a generalized 2-vector space.
Generalized 2-vector spaces and general linear 2-groups
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