Information om | Engelska ordet DIVISIBILITY

Exempel på hur man kan använda DIVISIBILITY i en mening

• The divisibility relation on the natural numbers is an important example of an antisymmetric relation.
• Integral domains are generalizations of the ring of integers and provide a natural setting for studying divisibility.
• A large generalization of this formula applies to summation over an arbitrary locally finite partially ordered set, with Möbius' classical formula applying to the set of the natural numbers ordered by divisibility: see incidence algebra.
• Number theory looks at things like how numbers divide evenly (divisibility), or how prime numbers are spread out.
• Principal ideal domains are mathematical objects that behave like the integers, with respect to divisibility: any element of a PID has a unique factorization into prime elements (so an analogue of the fundamental theorem of arithmetic holds); any two elements of a PID have a greatest common divisor (although it may not be possible to find it using the Euclidean algorithm).
• There are divisibility rules that allow one to recognize certain divisors of a number from the number's digits.
• In contrast to fields, where every nonzero element is multiplicatively invertible, the concept of divisibility for rings is richer.
• This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime.
• As mathematical properties (such as divisibility) can confer practical utility, there may be interplay and connections between the cultural or practical significance of an integer and its mathematical properties.
• However, other tasks including many specialties in software projects are less divisible; Brooks points out this limited divisibility with another example: while it takes one woman nine months to make one baby, "nine women can't make a baby in one month".
• Like the Bernoulli irregularity, the weak regularity relates to the divisibility of class numbers of cyclotomic fields.
• It generalizes to commutative algebra the notion of size inherent in consideration of the degree of a pole or multiplicity of a zero in complex analysis, the degree of divisibility of a number by a prime number in number theory, and the geometrical concept of contact between two algebraic or analytic varieties in algebraic geometry.
• Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple and the infimum is the greatest common divisor.
• The origin of the idea in the Western tradition can be traced to the 5th century BCE starting with the Ancient Greek pre-Socratic philosopher Democritus and his teacher Leucippus, who theorized matter's divisibility beyond what can be perceived by the senses until ultimately ending at an indivisible atom.
• In another paper in 1897, Dedekind studied the lattice of divisors with gcd and lcm as operations, so that the lattice order is given by divisibility.
• For example, in the study of modern manufacturing (Milgrom and Roberts, 1990b), one would like to focus on the complementarity or substitutability across production inputs, without making assumptions on scale economies or divisibility (through a concavity condition on the production function).
• Artin–Tits monoids are eligible for Garside methods based on the investigation of their divisibility relations, and are well understood:.
• The three-volume History of the Theory of Numbers (1919–23) is still much consulted today, covering divisibility and primality, Diophantine analysis, and quadratic and higher forms.
• He then argues that since important geometric ideas (equality, straightness, flatness) do not have any precise and workable standard beyond common observation, corrective measurements, and the "imaginary" standards we are naturally prone to fabricate, it follows that the extremely subtle geometric demonstrations of infinite divisibility cannot be trusted.
• The Ax–Katz result has an interpretation in étale cohomology as a divisibility result for the (reciprocals of) the zeroes and poles of the local zeta-function.

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