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relation and defined
The concept of function is defined as a special kind of binary relation.
A binary relation R is usually defined as an ordered triple ( X, Y, G ) where X and Y are arbitrary sets ( or classes ), and G is a subset of the Cartesian product X × Y.
Unlike other C-suite positions, which tend to be defined according to commonly designated responsibilities across most companies, the COO job tends to be defined in relation to the specific CEO with whom he / she works, given the close working relationship of these two individuals.
These rights lay outside feudalism, which defined authority in a hierarchy of personal relations, with only a loose relation to territory.
He continued arguing how problematic it was establishing the relation between " normal ", " nonfiction or standard discourse " and " fiction ", defined as its " parasite, “ for part of the most originary essence of the latter is to allow fiction, the simulacrum, parasitism, to take place-and in so doing to " de-essentialize " itself as it were ”.
* The relation " is approximately equal to " between real numbers, even if more precisely defined, is not an equivalence relation, because although reflexive and symmetric, it is not transitive, since multiple small changes can accumulate to become a big change.
However, if the approximation is defined asymptotically, for example by saying that two functions f and g are approximately equal near some point if the limit of f-g is 0 at that point, then this defines an equivalence relation.
The equivalence kernel of a function f is the equivalence relation ~ defined by.
" Let X be the unit Cartesian square ×, and let ~ be the equivalence relation on X defined bya, b ∈ (( a, 0 ) ~ ( a, 1 )( 0, b ) ~ ( 1, b )).
* Symmetric and transitive: The relation R on N, defined as aRb ↔ ab ≠ 0.
* Reflexive and symmetric: The relation R on Z, defined as aRb ↔ " a − b is divisible by at least one of 2 or 3.
In mathematical terms, the sequence F < sub > n </ sub > of Fibonacci numbers is defined by the recurrence relation
Currently, physics is traditionally defined as the study of matter, energy, and the relation between them.
In terms of set theory, where a function is defined as a particular kind of binary relation, the identity function is given by the identity relation, or diagonal of M.
He also defined the exponential function for complex numbers, and discovered its relation to the trigonometric functions.
In 1964, at the 12th CGPM conference, the original definition was reverted to, and thus the litre was once again defined in exact relation to the metre, as another name for the cubic decimetre, that is, exactly 1 dm < sup > 3 </ sup >.
The harmonic mean is an average which is useful for sets of numbers which are defined in relation to some unit, for example speed ( distance per unit of time ).
Finding a goal defined by its relation to the surroundings
* The relation defined by iff, where f is a function into some preorder.
* The relation defined by iff there exists some injection from x to y. Injection may be replaced by surjection, or any type of structure-preserving function, such as ring homomorphism, or permutation.
For a preorder "", a relation "<" can be defined as a < b if and only if ( a b and not b a ), or equivalently, using the equivalence relation introduced above, ( a b and not a ~ b ).

relation and by
A useful comment on his relation to his region may be made, I think, by noting briefly how in handling Southern materials and Southern problems he has deviated from the pattern set by other Southern authors while remaining faithful to the essential character of the region.
In conformance with the maximization principle we affirm that Gentile-Jewish relations will be harmonious or inharmonious to the degree that one relation or the other is expected by the active participants to yield the greatest net advantage, taking all value outcomes and effects into consideration.
The problem in the policy officer's mind thus begins to take shape as a galaxy of utterly complicated factors -- political, military, economic, financial, legal, legislative, procedural, administrative -- to be sorted out and handled within a political system which moves by consent in relation to an external environment which cannot be under control.
The mean temperature of the surface was then computed according to the following relation: Af where x is the fraction of the plug area covered by the hot spot.
The threat of effective anti-trust action, provoked by `` gouging the public '' through price increases not justified by cost increases, and fears of endangering relations with customers, Congress, the general public and the press, all operate to keep price increases in some relation to cost increases.
that is, by being placed in such relation to the forms depicted within the illusion that these forms left no room for the typography except near the surface.
At the same time, the wallpaper strips themselves seem to be pushed into depth by the lines and patches of shading charcoaled upon them, and by their placing in relation to the block capitals ; ;
The luminous efficiency Af of a photocathode depends on the maximum radiant sensitivity Af and on the spectral distribution of the incident light Af by the relation: Af where Af is normalized radiant photocathode sensitivity.
It is not disturbing them by thoughts of their Christian responsibility in relation to the world.
When there are only two means to compare, the t-test and the ANOVA F-test are equivalent ; the relation between ANOVA and t is given by F = t < sup > 2 </ sup >.
Related to this is lexicostatistics, which attempts to determine the degree of relation between a set of languages by comparing the percentage of basic vocabulary ( words like " I ", " you ", " heart ", " stone ", " two ", " be ", " and ") they share in common.
AM works by varying the strength of the transmitted signal in relation to the information being sent.
The harmonics are the more readily obtained by reason of the small diameter of the bore in relation to the length.
The buyout, secretly negotiated by Charles M. Schwab ( no relation to Charles R. Schwab ), was the largest such industrial takeover in United States history to date.
The Minḥat Ḳenaot is instructive reading for the historian because it throws much light upon the deeper problems which agitated Judaism, the question of the relation of religion to the philosophy of the age, which neither the zeal of the fanatic nor the bold attitude of the liberal-minded could solve in any fixed dogmatic form or by any anathema, as the independent spirit of the congregations refused to accord to the rabbis the power possessed by the Church of dictating to the people what they should believe or respect.
The constancy of a '/ a necessary for this relation to hold was pointed out by R. H. Bow ( Brit.
George Gummerman and Miranda Warburton view archaeoastronomy as part of an archaeology informed by cultural anthropology and aimed at understanding a " group's conception of themselves in relation to the heavens ', in a word, its cosmology.
The relation between electric current, magnetic fields and physical forces was first noted by Hans Christian Ørsted who, in 1820, observed a compass needle was deflected from pointing North when a current flowed in an adjacent wire.
The close relationship of alternative algebras and composition algebras was given by Guy Roos in 2008: He shows ( page 162 ) the relation for an algebra A with unit element e and an involutive anti-automorphism such that a + a * and aa * are on the line spanned by e for all a in A.
In 1988 it produced a translation of the Apostles ' Creed, distinguished among other things by its avoidance of the word " his " in relation to God.

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