And the best way to conceal and disguise the elements of an incest story is not to set out to write an incest story.

A set of tables containing spectral intensities for 39,000 lines of 70 elements, as observed in a copper matrix in a d-c arc, was completed and published.

This is not the most general situation of a Cartesian product of a family of sets, where a same set can occur more than once as a factor ; however, one can focus on elements of such a product that select the same element every time a given set appears as factor, and such elements correspond to an element of the Cartesian product of all distinct sets in the family.

The difficulty appears when there is no natural choice of elements from each set.

* In set theory, an automorphism of a set X is an arbitrary permutation of the elements of X.

Similarly, the subset order ⊆ on the subsets of any given set is antisymmetric: given two sets A and B, if every element in A also is in B and every element in B is also in A, then A and B must contain all the same elements and therefore be equal:

The repeating periodicity of the blocks of 2, 6, 10, and 14 elements within sections of the periodic table arises naturally from the total number of electrons which occupy a complete set of s, p, d and f atomic orbitals, respectively.

Another set of methods is the aromatization of cyclohexanes and other aliphatic rings: reagents are catalysts used in hydrogenation such as platinum, palladium and nickel ( reverse hydrogenation ), quinones and the elements sulfur and selenium.

* Consider a set with three elements, A, B, and C. The following operation:

The set of valid index tuples and the addresses of the elements ( and hence the element addressing formula ) are usually, but not always, fixed while the array is in use.

In addition to omitting the axiom of regularity, non-standard set theories have indeed postulated the existence of sets that are elements of themselves.

An abelian group is a set, A, together with an operation "•" that combines any two elements a and b to form another element denoted.

The set of all invertible elements is therefore closed under multiplication and forms a Moufang loop.

A partially ordered set ( poset ) P is said to satisfy the ascending chain condition ( ACC ) if every ascending chain of elements eventually terminates.

In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A.

In mathematics, a binary operation on a set is a calculation involving two elements of the set ( called operands ) and producing another element of the set ( more formally, an operation whose arity is two ).

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:

* Base ( group theory ), a sequence of distinct elements of a set

Bartók and Kodály quickly set about incorporating elements of such Magyar peasant music into their compositions.

Eight-bit machines ( with octets as the native data type ) that did not use parity checking typically set the eighth bit to 0.

The standard structure is where is the set of natural numbers, is the successor function and is naturally interpreted as the number 0.

In 1948 Australia set new standards, completely outplaying their hosts to win 4 – 0 with one draw.

Australia went 2 – 0 up after three Tests, but England won the Fourth Test by 3 runs ( after a 70-run last wicket stand ) to set up the final decider, which was drawn.

These states are labeled by a set of quantum numbers summarized in the term symbol and usually associated with particular electron configurations, i. e., by occupation schemes of atomic orbitals ( e. g., 1s < sup > 2 </ sup > 2s < sup > 2 </ sup > 2p < sup > 6 </ sup > for the ground state of neon -- term symbol: < sup > 1 </ sup > S < sub > 0 </ sub >).

* The current world record was set in 1999 at 100 picokelvins ( pK ), or 0. 000 000 000 1 of a kelvin, by cooling the nuclear spins in a piece of rhodium metal.

| ATA / ATAPI-7 || ATA-7, || UDMA 6aka UDMA / 133SATA / 150 || || SATA 1. 0, Streaming feature set, long logical / physical sector feature set for non-packet devices ||

in the ASCII character set, the digits 0 to 9 have sequential

A Bézier curve is defined by a set of control points P < sub > 0 </ sub > through P < sub > n </ sub >, where n is called its order ( n

A set S is called countable if there exists an injective function f from S to the natural numbers Since there is an obvious bijection between and it makes no difference whether one considers 0 to be a natural number of not.

If we set, then η is continuous at 0.

Given a set of integers, does some nonempty subset of them sum to 0?

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

If S is an arbitrary set, then the set S < sup > N </ sup > of all sequences in S becomes a complete metric space if we define the distance between the sequences ( x < sub > n </ sub >) and ( y < sub > n </ sub >) to be, where N is the smallest index for which x < sub > N </ sub > is distinct from y < sub > N </ sub >, or 0 if there is no such index.

But " having distance 0 " is an equivalence relation on the set of all Cauchy sequences, and the set of equivalence classes is a metric space, the completion of M. The original space is embedded in this space via the identification of an element x of M with the equivalence class of sequences converging to x ( i. e., the equivalence class containing the sequence with constant value x ).

In keeping with the concept of vacuous truth, when disjunction is defined as an operator or function of arbitrary arity, the empty disjunction ( OR-ing over an empty set of operands ) is often defined as having the result 0.

The characters allowed in a label are a subset of the ASCII character set, and includes the characters a through z, A through Z, digits 0 through 9, and the hyphen.

Assuming they form a set, the definable numbers form a field containing all the familiar real numbers such as 0, 1, π, e, et cetera.

While every computable number is definable, the converse is not true: the numeric representations of the Halting problem, Chaitin's constant, the truth set of first order arithmetic, and 0 < sup >#</ sup > are examples of numbers that are definable but not computable.

* The set N N of pairs of natural numbers can be made into a directed set by defining ( n < sub > 0 </ sub >, n < sub > 1 </ sub >) ≤ ( m < sub > 0 </ sub >, m < sub > 1 </ sub >) if and only if n < sub > 0 </ sub > ≤ m < sub > 0 </ sub > and n < sub > 1 </ sub > ≤ m < sub > 1 </ sub >.

* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )

* Consider the set K of all functions ƒ: → satisfying the Lipschitz condition | ƒ ( x ) − ƒ ( y )| ≤ | x − y | for all x, y ∈.

It is known that there exists a unique Delaunay triangulation for P, if P is a set of points in general position ; that is, there exists no k-flat containing k + 2 points nor a k-sphere containing k + 3 points, for 1 ≤ k ≤ d − 1 ( e. g., for a set of points in < big > ℝ </ big >< sup > 3 </ sup >; no three points are on a line, no four on a plane, no four are on a circle, and no five on a sphere ).

In mathematics, a directed set ( or a directed preorder or a filtered set ) is a nonempty set A together with a reflexive and transitive binary relation ≤ ( that is, a preorder ), with the additional property that every pair of elements has an upper bound: In other words, for any a and b in A there must exist a c in A with a ≤ c and b ≤ c.

* The set of natural numbers N with the ordinary order ≤ is a directed set ( and so is every totally ordered set ).

Then the Cartesian product set D < sub > 1 </ sub > D < sub > 2 </ sub > can be made into a directed set by defining ( n < sub > 1 </ sub >, n < sub > 2 </ sub >) ≤ ( m < sub > 1 </ sub >, m < sub > 2 </ sub >) if and only if n < sub > 1 </ sub > ≤ m < sub > 1 </ sub > and n < sub > 2 </ sub > ≤ m < sub > 2 </ sub >.