More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.

More precisely, Ural – Altaic came to subgroup Finno-Ugric and Samoyedic as " Uralic " and Turkic, Mongolic, and Tungusic as " Altaic ", with Korean sometimes added to Altaic, and less often Japanese.

More precisely, if S

More precisely, a binary operation on a non-empty set S is a map which sends elements of the Cartesian product S × S to S:

More precisely, given any small positive distance, all but a finite number of elements of the sequence are less than that given distance from each other.

More precisely, objects can be reachable in only two ways:

More precisely, it tries to classify problems that can or cannot be solved with appropriately restricted resources.

More precisely:

More generally, to insist that all evidence converge precisely with no deviations would be naïve falsificationism, equivalent to considering a single contrary result to falsify a theory when another explanation, such as equipment malfunction or misinterpretation of results, is much more likely.

More precisely, the positions of the pixels and subpixels on the screen must be exactly known to the computer to which it is connected.

( More precisely, this is true of the sines of the angles.

More importantly, however, he went on to maintain the same high level of performance throughout the season, kicking precisely 100 goals for the year to become the first player to top the ton since Richmond's Jack Titus in 1940.

" More precisely, it is " the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference.

More precisely, a full moon occurs when the geocentric apparent ( ecliptic ) longitudes of the Sun and Moon differ by 180 degrees ; the Moon is then in opposition with the Sun .< ref >

More precisely, all known FFT algorithms require Θ ( N log N ) operations ( technically, O only denotes an upper bound ), although there is no known proof that better complexity is impossible.

More precisely, because of the relation between spin and statistics, a particle containing an odd number of fermions is itself a fermion: it will have half-integer spin.

More precisely, and technically, a Feynman diagram is a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory.

More precisely, he showed that a random graph on vertices, formed by choosing independently whether to include each edge with probability has, with probability tending to 1 as goes to infinity, at most cycles of length or less, but has no independent set of size Therefore, removing one vertex from each short cycle leaves a smaller graph with girth greater than in which each color class of a coloring must be small and which therefore requires at least colors in any coloring.

( More precisely, the nodes are spherical harmonics that appear as a result of solving Schrödinger's equation in polar coordinates.

More precisely, the square of x is not invertible because it is impossible to deduce from its output the sign of its input.

More precisely, the law states that alleles of different genes assort independently of one another during gamete formation.

More precisely, it returns a new list whose elements are in reverse order compared to the given list.

More precisely, these proofs have to be verifiable in polynomial time by a deterministic Turing machine.

More precisely, it is the instant when the Moon and the Sun have the same ecliptical longitude.

More explicitly, the action groupoid is the set with source and target maps s ( g, x )

More generally, one can define the fundamental groupoid on any subset A of X, using homotopy classes of paths joining points of A.

constructed from an inverse semigroup, and conversely .. More precisely, an inverse semigroup is precisely a groupoid in the category of posets which is an etale groupoid with respect to its ( dual ) Alexandrov topology and whose poset of objects is a meet-semilattice.

More generally, G can be a Lie groupoid.

*** More particularly following Lives and Comparisons ( D is Dryden translation ; G is Gutenberg ; P is Perseus Project ; L is LacusCurtius ):

More precisely, H is a subgroup of G if the restriction of * to H x H is a group operation on H. This is usually represented notationally by H ≤ G, read as " H is a subgroup of G ".

The English Roman Catholic writer G. K. Chesterton said of More that " He may come to be counted the greatest Englishman, or at least the greatest historical character in English history.

" H. G. Wells, in an unsigned review for the Pall Mall Gazette, called Earnest one of the freshest comedies of the year, saying " More humorous dealing with theatrical conventions it would be difficult to imagine.

More precisely, if A is a finite set of generators for G then the word problem is the membership problem for the formal language of all words in A and a formal set of inverses that map to the identity under the natural map from the free monoid with involution on A to the group G. If B is another finite generating set for G, then the word problem over the generating set B is equivalent to the word problem over the generating set A.

* Regan, G. More Military Blunders.

More strongly, if one wishes to prove that X and G ( X ) are not naturally isomorphic, without reference to a particular isomorphism, this requires showing that for any isomorphism η, there is some A with which it does not commute ; in some cases a single automorphism A works for all candidate isomorphisms η, while in other cases one must show how to construct a different A < sub > η </ sub > for each isomorphism.

More generally, if 〈 F, G, ε, η 〉 is an adjunction ( with counit-unit ( ε, η )) and

More precisely, there is an adjunction between F ′ F and G G ′ with unit and counit given by the compositions:

More formally an inner automorphism of a group G is a function:

More than half of the known F and G stars are binaries, and these are preferentially located within this central region.

More generally, if S is a subset of a group G, then < S >, the subgroup generated by S, is the smallest subgroup of G containing every element of S, meaning the intersection over all subgroups containing the elements of S ; equivalently, < S > is the subgroup of all elements of G that can be expressed as the finite product of elements in S and their inverses.

More recently, more sensitive tests have been developed, such as the immunoglobulin G ( IgG ) and immunoglobulin M ( IgM ) tests.

More precisely, the characteristic property of B ( m, n ) is that, given any group G with m generators g < sub > 1 </ sub >,…, g < sub > m </ sub > and of exponent n, there is a unique homomorphism from B ( m, n ) to G that maps the ith generator x < sub > i </ sub > of B ( m, n ) into the ith generator g < sub > i </ sub > of G. In the language of group presentations, free Burnside group B ( m, n ) has m generators x < sub > 1 </ sub >,…, x < sub > m </ sub > and the relations x < sup > n </ sup > = 1 for each word x in x < sub > 1 </ sub >,…, x < sub > m </ sub >, and any group G with m generators of exponent n is obtained from it by imposing additional relations.