# inverse

## Definitions

• WordNet 3.6
• adj inverse reversed (turned backward) in order or nature or effect
• adj inverse opposite in nature or effect or relation to another quantity "a term is in inverse proportion to another term if it increases (or decreases) as the other decreases (or increases)"
• n inverse something inverted in sequence or character or effect "when the direct approach failed he tried the inverse"
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Webster's Revised Unabridged Dictionary
• Inverse (Bot) Inverted; having a position or mode of attachment the reverse of that which is usual.
• Inverse (Math) Opposite in nature and effect; -- said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity; as, multiplication is the inverse operation to division. The symbol of an inverse operation is the symbol of the direct operation with -1 as an index. Thus sin-1x means the arc or angle whose sine is x.
• Inverse Opposite in order, relation, or effect; reversed; inverted; reciprocal; -- opposed to direct.
• n Inverse That which is inverse. "Thus the course of human study is the inverse of the course of things in nature."
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Century Dictionary and Cyclopedia
• inverse Turned end for end, or in the opposite direction; having a contrary course or tendency; inverted: opposed to direct.
• inverse In mathematics, opposite in nature and effect: said with reference to any two operations which, when both performed in succession upon the same quantity, leave it unaltered: thus, subtraction is inverse to addition, division to multiplication, extraction of roots to the raising of powers, etc. A direct operation produces an unambiguous and possible value, and between two operations the one which combines quantities symmetrically is preferably considered as direct. Addition, multiplication, involution, and differentiation are considered as direct operations; subtraction, division, evolution, and integration as inverse operations. Corresponding to every direct operation there are, generally speaking, two inverse operations: thus, if F(x, y) be the direct operation, the two inverse operations are the one which gives x from F(x, y) and y, and the one which gives y from F(x, y) and x.
• n inverse An inverted state or condition; a direct opposite; something directly or absolutely contrary to something else: as, the inverse of a proposition.
• inverse In logic, with conclusion as hypothesis and hypothesis as conclusion.
• n inverse In logic, a proposition made by simply interchanging the hypothesis and conclusion of another, without any restriction.
• n inverse In mathematics, an inverse point, curve, function, ratio, proportion, etc.
• n inverse In rouge-et-noir, the triangular space in which bets are placed when wagering that the first card dealt for a color will not be the same color as the one that wins the coup: opposed to couleur. See rouge-et-noir.
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Chambers's Twentieth Century Dictionary
• adj Inverse in-vėrs′ inverted: in the reverse or contrary order: opposite, inverted—opp. to Direct:
• n Inverse an inverted state, a direct opposite
• adj Inverse in-vėrs′ (math.) opposite in effect, of one operation that annuls the effect of another, as subtraction to addition, &c
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## Quotations

• Aldous Huxley
“Official dignity tends to increase in inverse ratio to the importance of the country in which the office is held.”
• C. Northcote Parkinson
“The Law of Triviality... briefly stated, it means that the time spent on any item of the agenda will be in inverse proportion to the sum involved.”
• Bertrand Russell
“The degree of one's emotions varies inversely with one's knowledge of the facts- the less you know the hotter you get.”
• Aldous Huxley
“The quality of moral behavior varies in inverse ratio to the number of human beings involved.”
• David Searles
“The tendency of an event to occur varies inversely with one's preparation for it.”
• Eric Hoffer
“The compulsion to take ourselves seriously is in inverse proportion to our creative capacity. When the creative flow dries up, all we have left is our importance.”

## Etymology

Webster's Revised Unabridged Dictionary
L. inversus, p. p. of invertere,: cf. F. inverse,. See Invert

## Usage

### In literature:

Also the further fact that its accuracy is in inverse ratio to its rapidity, which does not need so much explanation.
"Desert Conquest" by A. M. Chisholm
It takes him down a bit, and (inversely) elevates his rival.
"The House with the Green Shutters" by George Douglas Brown
The angle which the diameter of a heavenly body subtends at any time, varying inversely with its distance.
"The Sailor's Word-Book" by William Henry Smyth
Vary by inversion of the colors in ground and darker vase.
"A Color Notation" by Albert H. Munsell
We must now examine more closely the inversion whose consequences we have just described.
"Creative Evolution" by Henri Bergson
This communication was an inversion of that paradox.
"The Machine That Saved The World" by William Fitzgerald Jenkins
The tendency is to condemn the violation of these commandments, not in proportion to the injury done, but rather in inverse proportion.
"New York Times Current History; The European War, Vol 2, No. 4, July, 1915" by Various
After these come the women-folk in order of precedence, carrying loads in inverse ratio thereto.
"Pan-Islam" by George Wyman Bury
Now the dignity and virtue of the plates is in the exactly inverse ratio of their fullness in chiaroscuro.
But, inversely, if all art is concentrated upon the representation, what matters the subject?
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### In news:

Norman Mailer , Warhol's Inverse, Helped Invent Modern Fame.
The worth of the personal finance industry is inversely proportional to its ubiquity, according to Forbes.com blogger Olen in his breezy romp through recent financial history.
INVERSE PRESETS USE THE SAME DEFAULT PRE-DELAY TIME.
Namco Bandai Games' new release, "Inversion," for the Xbox 360, PlayStation 3 and PC.
Peak error, integrated error, and rise time are inversely proportional to PID gain.
With all of its numerical symmetries, subdivisions and inversions, it could easily be the subject of a brainteaser from puzzle master Will Shortz.
Inversely, difficult short-term choices lead to easy long-term consequences.
Held in California and New York, the tests evaluated ways to recover people in the water and right dinghies from capsize and inversion.
What an inversion last night's vice presidential debate represented.
Set in Banks's far-future interstellar civilization known as the Culture, this highly literate novel from this celebrated British SF author ( Inversions ) centers on an act of revenge.
The post-WWII vision of a free Europe was hijacked by the ruling classes and gradually became the inversion of what was originally promised.
Inversion over the Wasatch Front Sunday, Dec 18, 2011 looking west from South Mounatin.
It also represents a fascinating, social-media-age inversion between the censor and the censored .
The investment seeks to replicate, net of expenses, three times the opposite (inverse) of the S&P GSCI Crude Oil Index ER.
Inversion layers have ups, downs.
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### In science:

It is clear that if f is a MP-inverse of e then e is a MP-inverse of f .
Moore-Penrose inverse, parabolic subgroups, and Jordan pairs
Baltes H P 1980 Progress in inverse optical problems, in Inverse Scattering Problems in Optics ed. H. P.
Design of one-dimensional Lambertian diffusers of light
We only need to prove that Φ is bijective with inverse Ψ on ob jects since Ψ is obviously the inverse of Φ on morphisms.
The categorical theory of relations and quantizations
We still have some uncertainty on the type inversion point. However from Fig. 12 we can see that, after type inversion, the slope is similar for both oxygenated and non-oxygenated sensors.
Characterization of Prototype BTeV Silicon Pixel Sensors Before and After Irradiation
For average connectivity greater than 1, the inverse participation ratio decreases with increasing N ; however, we do not observe a clear 1/N scaling of the inverse participation ratio for an average connectivity of 2.
Random Vibrational Networks and Renormalization Group
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