For it is clear that the total number of ordinary intersections of C and Af must be even ( otherwise, starting in the interior of C, Af could not finally return to the interior ), and the center of rotation at T is the argument of the function, not a value.

For a statement of costs per kilowatt-hour would ignore the fact that many of these costs are not a function of kilowatt-hour output ( or consumption ) of energy.

Algorithm versus function computable by an algorithm: For a given function multiple algorithms may exist.

: For any set X of nonempty sets, there exists a choice function f defined on X.

: For any set A, the power set of A ( with the empty set removed ) has a choice function.

: For any set A there is a function f such that for any non-empty subset B of A, f ( B ) lies in B.

For example, if we abbreviate by BP the claim that every set of real numbers has the property of Baire, then BP is stronger than ¬ AC, which asserts the nonexistence of any choice function on perhaps only a single set of nonempty sets.

For a reader to assign the title of author upon any written work is to attribute certain standards upon the text which, for Foucault, are working in conjunction with the idea of " the author function ".

For example, the parent function y = 1 / x has a horizontal and a vertical asymptote, and occupies the first and third quadrant, and all of its transformed forms have one horizontal and vertical asymptote, and occupies either the 1st and 3rd or 2nd and 4th quadrant.

For small values of m like 1, 2, or 3, the Ackermann function grows relatively slowly with respect to n ( at most exponentially ).

For curves given by the graph of a function, horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to Vertical asymptotes are vertical lines near which the function grows without bound.

For example, for the function

For example the arctangent function satisfies

For example, the function has a horizontal asymptote at y = 0 when x tends both to −∞ and +∞ because, respectively,

For example, the function has

For example, the division example above may also be interpreted as a partial binary function from Z and N to Q, where N is the set of all natural numbers, including zero.

For instance, division of real numbers is a partial function, because one can't divide by zero: a / 0 is not defined for any real a.

For example, one definition of bandwidth could be the range of frequencies beyond which the frequency function is zero.

For example, methods to locate a gene within a sequence, predict protein structure and / or function, and cluster protein sequences into families of related sequences.

For each K, the function E < sub > K </ sub >( P ) is required to be an invertible mapping on

For integer order α = n, J < sub > n </ sub > is often defined via a Laurent series for a generating function:

For example, kinship and leadership function both as symbolic systems and as social institutions.

For his part, Thompson had explained in a previous letter that there would be nothing but an honorable friendship between Katie and himself.

For some time the Communists honored the distinction between the Soviet zone of Germany and the Soviet sector of Berlin by promulgating separately the laws for the two areas.

For the States which maintain two separate agencies -- one for the vocational rehabilitation of the blind, and one for the rehabilitation of persons other than the blind -- the Act specifies that their minimum ( base ) allotment shall be divided between the two agencies in the same proportion as it was divided in fiscal year 1954.

For four of the six ( the anaconda and the amethystine python cannot be included for lack of data ) there is also a correlation between size at maturity and maximum length, the boa constrictor being the smallest and the Indian python the next in size at the former stage.

For some forms of philosophy, this very division between the empirical and the rational becomes a sign of the metaphysical superiority of the latter.

For the illusion of depth created by the contrast between the affixed material and everything else gives way immediately to an illusion of forms in bas-relief, which gives way in turn, and with equal immediacy, to an illusion that seems to contain both -- or neither.

For the convenience of guests bundle centers have been established throughout the city and suburbs where the donations may be deposited between now and the date of the big event.

For example, the 2nd Academy Awards presented on April 3, 1930, recognized films that were released between August 1, 1928 and July 31, 1929.

For example, the randomization-based analysis results in a small but ( strictly ) negative correlation between the observations.

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

For such an online algorithm, a recurrence relation is required between quantities from which the required statistics can be calculated in a numerically stable fashion.

For blacklip abalone, the size limit varies from between 138 mm for the southern end of the state and 127 mm for the northern end of the state.

For example, the main crossover of the Andes between Argentina and Chile is still accomplished through the Paso Internacional Los Libertadores.

For example, if the water is 25 ft ( 8 m ) deep, and the anchor roller is 3 ft ( 1 m ) above the water, the scope is the ratio between the amount of cable let out and 28 ft ( 9 m ).

For the first time a conceptual and procedural distinction was made between laws and decrees.

For instance, antibacterial resistance genes can be exchanged between different bacterial strains or species via plasmids that carry these resistance genes.

For very large distances, cosmological redshift complicates the relation between absolute and apparent magnitude, and an additional k correction might be required.

For Friedrich Wilhelm Joseph Schelling, the philosophy of art is the " organon " of philosophy concerning the relation between man and nature.

For some, aesthetics is considered a synonym for the philosophy of art since Hegel, while others insist that there is a significant distinction between these closely related fields.

For according to them, there were seven islands in that sea in their time, sacred to Persephone, and also three others of enormous size, one of which was sacred to Hades, another to Ammon, and another one between them to Poseidon, the extent of which was a thousand stadia ; and the inhabitants of it — they add — preserved the remembrance from their ancestors of the immeasurably large island of Atlantis which had really existed there and which for many ages had reigned over all islands in the Atlantic sea and which itself had like-wise been sacred to Poseidon.

For example, using Cartesian coordinates on the plane, the distance between two points ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) and ( x < sub > 2 </ sub >, y < sub > 2 </ sub >) is defined by the formula

( For the famous relationship between Mozart and Salieri please see below.

For example between 1985 and 1989, 5, 000 civilians were killed in fighting between the two parties.

For example, the Barony of Grey of Codnor was in abeyance for over 490 years between 1496 and 1989, and the Barony of Hastings was similarly in abeyance for over 299 years from 1542 to 1841.