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example and field
For example, there are persons who are in physical science, in the field of mineralogy, trained in crystallography, who use only X-rays, applying only the powder technique of X-ray diffraction, to clay minerals only, and who have spent the last fifteen years concentrating on the montmorillonites ; ;
Combinatorics is an example of a field of mathematics which does not, in general, follow the axiomatic method.
Another example of an algebraically closed field is the field of ( complex ) algebraic numbers.
This is an example of renormalization in quantum field theory — the field theory being necessary because the number of particles changes from one to two and back again.
For example, the number of solutions of an equation over a finite field reflects the topological nature of its solutions over the complex numbers.
Scientists dismiss these mechanisms as implausible since, for example, the magnetic field, when measured from earth, of a large but distant planet such as Jupiter is far smaller than that produced by ordinary household appliances.
For example, the field extension R / Q, that is the field of real numbers as an extension of the field of rational numbers, is transcendental, while the field extensions C / R and Q (√ 2 )/ Q are algebraic, where C is the field of complex numbers.
If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.
An example is the field of complex numbers.
For example, if K is a field of characteristic p and if X is transcendental over K, is a non-separable algebraic field extension.
For example, it also predicts the variation of the particle density in a gravitational field with height, if.
For example, the CIA World Factbook uses the word in its " Country name " field to refer to " a wide variety of dependencies, areas of special sovereignty, uninhabited islands, and other entities in addition to the traditional countries or independent states ".< sup id = Note_1 >
For example, a 1039 bit integer was factored with the special number field sieve using 400 computers over 11 months.
For example, if an electric field is placed across a solution of Na < sup >+</ sup > and Cl < sup >−</ sup > ( and conditions are right ) the sodium ions move towards the negative electrode ( cathode ), while the chloride ions move towards the positive electrode ( anode ).
The authors of the study interpreted this as being the result of the ease by which primary commodities may be extorted or captured compared to other forms of wealth, for example, it is easy to capture and control the output of a gold mine or oil field compared to a sector of garment manufacturing or hospitality services.

example and real
For example, suppose that X is the set of all non-empty subsets of the real numbers.
For example, while the axiom of choice implies that there is a well-ordering of the real numbers, there are models of set theory with the axiom of choice in which no well-ordering of the reals is definable.
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.
An example of such a number is the unique real root of the polynomial ( which is approximately 1. 167304 ).
Some have survived and others may be deduced from accurate landscapes of real places in his later work, for example his engraving Nemesis.
For example, if a bank, operating under the Basel I accord, has to hold 8 % capital against default risk, but the real risk of default is lower, it is profitable to securitise the loan, removing the low risk loan from its portfolio.
For example, a boom in the real estate market started around 2003.
For example, the spectrum of an element of a complex Banach algebra can never be empty, whereas in a real Banach algebra it could be empty for some elements.
* In anime Bleach is an example, Ikkaku Madarame carries a bokken when in his Gigai as he wasn't allowed to carry a real sword in public.
On the other hand, some other jurisdictions have sufficiently developed bodies of law so that parties have no real motivation to choose the law of a foreign jurisdiction ( for example, England and Wales, and the state of California ), but not yet so fully developed that parties with no relationship to the jurisdiction choose that law.
For example, a perfect crystal of diamond would only contain carbon atoms, but a real crystal might perhaps contain a few boron atoms as well.
For example, Georg Cantor ( who introduced this concept ) demonstrated that the real numbers cannot be put into one-to-one correspondence with the natural numbers ( non-negative integers ), and therefore that the set of real numbers has a greater cardinality than the set of natural numbers.
An example of a compact space is the unit interval of real numbers.
The given example sequence shows the importance of including the boundary points of the interval, since the limit points must be in the space itself: an open ( or half-open ) interval of the real numbers is not compact.
For example, the real line equipped with the discrete topology is closed and bounded but not compact, as the collection of all singleton points of the space is an open cover which admits no finite subcover.
An even more prominent example is that of Cardinal Richelieu, whose power was so great that he was for many years the real ruler of France.
Construction of a map in real time, for example by using Field-Map technology, improves productivity and quality of the result.
An example is given by the real numbers, which are complete but homeomorphic to the open interval ( 0, 1 ), which is not complete.
Another example is given by the irrational numbers, which are not complete as a subspace of the real numbers but are homeomorphic to N < sup > N </ sup > ( see the sequence example in Examples above ).

example and numbers
Nomia melanderi can be found in tremendous numbers in certain parts of the United States west of the Great Plains, for example, in Utah and central Washington.
For example, in accordance with the fashion of the times, most transitional societies have announced economic development plans of varying numbers of years ; ;
For example, suppose that each member of the collection X is a nonempty subset of the natural numbers.
For example an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces.
The divisibility order of the natural numbers is another example of an antisymmetric relation.
A simple example is that almost all prime numbers are odd.
For example, the prime number theorem states that the number of prime numbers less than or equal to N is asymptotically equal to N / ln N. Therefore the proportion of prime integers is roughly 1 / ln N, which tends to 0.
For example, if the numbers involved in a computation may be arbitrarily large, the time required by a single addition can no longer be assumed to be constant.
The canonical example for accumulator use is summing a list of numbers.
For example, the smallest pair of amicable numbers is ( 220, 284 ); for the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284 ; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.
An example is the " divides " relation between the set of prime numbers P and the set of integers Z, in which every prime p is associated with every integer z that is a multiple of p ( and not with any integer that is not a multiple of p ).
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.

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