AI & ChatGPT searches , social queriess for PRIMITIVE ELEMENT-THEOREM
Search references for PRIMITIVE ELEMENT-THEOREM. Phrases containing PRIMITIVE ELEMENT-THEOREM
See searches and references containing PRIMITIVE ELEMENT-THEOREM!
Search references for PRIMITIVE ELEMENT-THEOREM. Phrases containing PRIMITIVE ELEMENT-THEOREM
See searches and references containing PRIMITIVE ELEMENT-THEOREM!PRIMITIVE ELEMENT-THEOREM
Field theory theorem
theory, the primitive element theorem states that every finite separable field extension is simple, i.e. generated by a single element. This theorem implies
Primitive_element_theorem
Field extension generated by a one element
single element, called a primitive element. Simple extensions are well understood and can be completely classified. The primitive element theorem states
Simple_extension
Topics referred to by the same term
(free group), an element of a free generating set Primitive element (Lie algebra), a Borel-weight vector Primitive element theorem Primitive root (disambiguation)
Primitive_element
restrictive definition of primitive element than that mentioned above after the general normal basis theorem: one requires powers of the element to produce every
Normal_basis
Generator of the multiplicative group of a finite field
a primitive element of a finite field GF(q) is a generator of the multiplicative group of the field. In other words, α ∈ GF(q) is called a primitive element
Primitive element (finite field)
Primitive_element_(finite_field)
Algebraic structure with addition, multiplication, and division
theory from 1928 through 1942, eliminating the dependency on the primitive element theorem. A commutative ring is a set that is equipped with an addition
Field_(mathematics)
Gives the rank of the group of units in the ring of algebraic integers of a number field
0 or r2 = 0. Other ways of determining r1 and r2 are use the primitive element theorem to write K = Q ( α ) {\displaystyle K=\mathbb {Q} (\alpha )}
Dirichlet's_unit_theorem
Construction of a larger algebraic field by "adding elements" to a smaller field
0, every finite extension is a simple extension. This is the primitive element theorem, which does not hold true for fields of non-zero characteristic
Field_extension
Result due to Kummer on cyclic extensions of fields that leads to Kummer theory
'\mapsto \ell \otimes a\sigma ^{-1}(\ell ').\end{cases}}} The primitive element theorem gives L = K ( α ) {\displaystyle L=K(\alpha )} for some α {\displaystyle
Hilbert's_Theorem_90
(polynomials) Polynomial remainder theorem (polynomials) Primitive element theorem (field theory) Rational root theorem (algebra, polynomials) Solutions
List_of_theorems
Theorem in algebraic geometry
simple proofs use Gauss's lemma on primitive polynomials as a main step. Primitive element theorem — another theorem asserting that certain field extensions
Lüroth's_theorem
Theorem in linear algebra
In matrix theory, the Perron–Frobenius theorem, proved in its first part by Oskar Perron (1907) and extended by Georg Frobenius (1912), asserts that a
Perron–Frobenius_theorem
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Theorems that help decompose a finite group based on prime factors of its order
order of G, then there exists an element (and thus a cyclic subgroup generated by this element) of order p in G. Theorem (2)—Given a finite group G and
Sylow_theorems
Filtration of the Galois group of a local field extension
integers of K {\displaystyle K} . (This is stronger than the primitive element theorem.) Then, for each integer i ≥ − 1 {\displaystyle i\geq -1} , we
Ramification_group
Complex number that solves a monic polynomial with integer coefficients
algebraic number θ ∈ C {\displaystyle \theta \in \mathbb {C} } by the primitive element theorem. α ∈ K is an algebraic integer if there exists a monic polynomial
Algebraic_integer
Theorem about natural numbers
In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein
Goodstein's_theorem
Theorem in mathematical logic
strengthened finite Ramsey theorem is then a computable function of n, m, k, but grows extremely fast. In particular it is not primitive recursive, but it also
Paris–Harrington_theorem
Computational method
over Q {\displaystyle \mathbb {Q} } with high probability by the primitive element theorem. If this is the case, we can compute the minimal polynomial q
Factorization_of_polynomials
Type of algebraic field extension
The equivalence of 3. and 1. is known as the primitive element theorem or Artin's theorem on primitive elements. Properties 4. and 5. are the basis of
Separable_extension
In mathematics, element that equals its square
mathematics, an idempotent element or simply idempotent of a ring is an element a such that a2 = a. That is, the element is idempotent under the ring's
Idempotent_(ring_theory)
Relation between sides of a right triangle
oldest extant axiomatic proof of the theorem is presented, along with Euclid's formula for generating all primitive Pythagorean triples. With contents known
Pythagorean_theorem
Every set is smaller than its power set
question marks, boxes, or other symbols. In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A {\displaystyle
Cantor's_theorem
Gives information about the Galois module structure of class groups of cyclotomic fields
Stickelberger element of F {\displaystyle F} and the Stickelberger ideal of F {\displaystyle F} can be defined. By the Kronecker–Weber theorem there is an
Stickelberger's_theorem
In algebra, a primitive element of a co-algebra C (over an element g) is an element x that satisfies μ ( x ) = x ⊗ g + g ⊗ x {\displaystyle \mu (x)=x\otimes
Primitive element (co-algebra)
Primitive_element_(co-algebra)
Aspect of algebraic number theory
generated over K by θ (such a θ is guaranteed to exist by the primitive element theorem), and then to examine the minimal polynomial H(X) of θ over K;
Splitting of prime ideals in Galois extensions
Splitting_of_prime_ideals_in_Galois_extensions
Field theory is the branch of algebra that studies fields
single element, called a primitive element, or generating element. The primitive element theorem classifies such extensions. Normal extension An extension
Glossary_of_field_theory
Permutation group that preserves no non-trivial partition
\{1,\ldots ,n\}} is primitive for every n > 2. Block (permutation group theory) Jordan's theorem (symmetric group) O'Nan–Scott theorem, a classification
Primitive_permutation_group
Finite extension of the rationals
some element x ∈ K {\displaystyle x\in K} . By the primitive element theorem, there exists such an x {\displaystyle x} , called a primitive element. If
Algebraic_number_field
On prime divisors of differences two nth powers
a^{n}+b^{n}} has at least one primitive prime divisor with the exception 2 3 + 1 3 = 9 {\displaystyle 2^{3}+1^{3}=9} . Zsigmondy's theorem is often useful, especially
Zsigmondy's_theorem
In algebra, Weyl's theorem on complete reducibility is a fundamental result in the theory of Lie algebra representations (specifically in the representation
Weyl's theorem on complete reducibility
Weyl's_theorem_on_complete_reducibility
Modular arithmetic concept
1 in the ring Z n {\displaystyle \mathbb {Z} _{n}} ), or simply a primitive element of Z n × {\displaystyle \mathbb {Z} _{n}^{\times }} . When Z n × {\displaystyle
Primitive_root_modulo_n
Three results in the representation theory of finite groups
Brauer's main theorems are three theorems in representation theory of finite groups linking the blocks of a finite group (in characteristic p) with those
Brauer's_three_main_theorems
Fundamental combinatorial result of Ramsey theory
hypercube that is the subject of the theorem. A variable word w(x) over WH n still has length H but includes the special element x in place of at least one of
Hales–Jewett_theorem
Theorem in set theory
In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there
Schröder–Bernstein_theorem
Describes statistically the splitting of primes in a given Galois extension of Q
mathematics, specifically in algebraic number theory, the Chebotarev density theorem, named after Nikolai Chebotarev, statistically describes the splitting
Chebotarev_density_theorem
Algebraic structure
Fermat's little theorem. If a {\displaystyle a} is a primitive element in G F ( q ) {\displaystyle \mathrm {GF} (q)} , then for any non-zero element x {\displaystyle
Finite_field
Number with an integer power equal to 1
{(z+1)^{n}-1}{(z+1)-1}},} and expanding via the binomial theorem. Every nth root of unity is a primitive dth root of unity for exactly one positive divisor
Root_of_unity
Subfield of automated reasoning and mathematical logic
proof for a theorem is certified valid. For this, it is generally required that each individual proof step can be verified by a primitive recursive function
Automated_theorem_proving
Function computable with bounded loops
primitive recursive. The Paris–Harrington theorem involves a total recursive function that is not primitive recursive. The Sudan function The Goodstein
Primitive_recursive_function
Mathematical theorem
Jacobson density theorem is a theorem concerning simple modules over a ring R. The theorem can be applied to show that any primitive ring can be viewed
Jacobson_density_theorem
On prime divisors in Fibonacci and Lucas sequences
A246556 in the OEIS) Zsigmondy's theorem Yabuta, Minoru (2001). "A simple proof of Carmichael's theorem on primitive divisors" (PDF). Fibonacci Quarterly
Carmichael's_theorem
by a theorem of Borel–Morozov on the conjugacy of solvable subalgebras.) Given a g {\displaystyle {\mathfrak {g}}} -module V, a primitive element of V
Borel_subalgebra
Mathematical proposition equivalent to the axiom of choice
the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space
Zorn's_lemma
polynomial, and lifting the result to a factorization of the primitive part. Rational root theorem B. Hartley; T.O. Hawkes (1970). Rings, modules and linear
Primitive_part_and_content
Function that preserves distinctness
monomorphism differs from that of an injective homomorphism. This is thus a theorem that they are equivalent for algebraic structures; see Homomorphism § Monomorphism
Injective_function
element outside this union will generate L {\displaystyle L} . This theorem was found and proven in 1910 by Ernst Steinitz. Lemma 9.19.1 (Primitive element)
Steinitz's theorem (field theory)
Steinitz's_theorem_(field_theory)
Axioms for the natural numbers
Foundations of mathematics Frege's theorem Goodstein's theorem Neo-logicism Non-standard model of arithmetic Paris–Harrington theorem Presburger arithmetic Skolem
Peano_axioms
Numerical method for solving physical or engineering problems
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical
Finite_element_method
Theorem that arithmetical truth cannot be defined in arithmetic
metalanguage includes primitive notions, axioms, and rules of inference absent from the object language, so that there are theorems provable in the metalanguage
Tarski's undefinability theorem
Tarski's_undefinability_theorem
Existence and cardinality of models of logical theories
In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf
Löwenheim–Skolem_theorem
Group whose operation is composition of permutations
Each element of G can be thought of as a permutation in this way and so G is isomorphic to a permutation group; this is the content of Cayley's theorem. For
Permutation_group
Theorem in mathematical logic
compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important
Compactness_theorem
in the theorem is induced from an irreducible character of the inertial subgroup IG(μ). If, for example, the irreducible character χ is primitive (that
Clifford_theory
About products of primitive polynomials
irreducible in Q[X] and primitive in Z[X]. The proof is given below for the more general case. Note that an irreducible element of Z (a prime number) is
Gauss's_lemma_(polynomials)
Statement that is taken to be true
assertions (axioms, postulates, propositions, theorems) and definitions. One must concede the need for primitive notions, or undefined terms or concepts, in
Axiom
Undecidability of equality of real numbers
by other primitives than in Richardson's theorem, there exist algorithms that can determine whether an expression is zero. Richardson's theorem can be stated
Richardson's_theorem
Theorem for proving more complex theorems
also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to prove; however
Lemma_(mathematics)
theorem Goodstein's theorem Green's theorem (to do) Green's theorem when D is a simple region Heine–Borel theorem Intermediate value theorem Itô's lemma Kőnig's
List_of_mathematical_proofs
Standard system of axiomatic set theory
Informally, Zermelo–Fraenkel set theory is intended to formalize a single primitive notion, that of a hereditary well-founded set, so that all entities in
Zermelo–Fraenkel_set_theory
3-volume treatise on mathematics, 1910–1913
ideas and methods of mathematical logic and to minimise the number of primitive notions, axioms, and inference rules; to precisely express mathematical
Principia_Mathematica
Fundamental theorem in mathematical logic
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability
Gödel's_completeness_theorem
Fundamental theorem in condensed matter physics
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves
Bloch's_theorem
(Mathematical) decomposition into a product
when this is the case, the primitive part is generally easier to manipulate for further factorization. The factor theorem states that, if r is a root
Factorization
Symbol representing a property or relation in logic
{\displaystyle a} and b {\displaystyle b} . Predicates are considered a primitive notion of first-order, and higher-order logic and are therefore not defined
Predicate_(logic)
In mathematics, a statement that has been proven
mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses
Theorem
Function in mathematical number theory
abelian group, there must exist an element whose order equals the exponent, λ(n). Such an element is called a primitive λ-root modulo n. The Carmichael function
Carmichael_function
Transformations induced by a mathematical group
orbit–stabilizer theorem, |G| = |G ⋅ 1| |G1| = 8 |G1|. Applying the theorem now to the stabilizer G1, we can obtain |G1| = |(G1) ⋅ 2| |(G1)2|. Any element of G that
Group_action
Branch of mathematics that studies algebraic structures
density theorem Wedderburn's little theorem Lasker–Noether theorem Field (mathematics) Subfield (mathematics) Multiplicative group Primitive element (field
List of abstract algebra topics
List_of_abstract_algebra_topics
Computation modulo a fixed integer
important theorems relating to modular arithmetic: Carmichael's theorem Chinese remainder theorem Euler's theorem Fermat's little theorem (a special
Modular_arithmetic
Axiom of set theory
{\displaystyle {\mathcal {A}}} has at least one element maximal with respect to inclusion. König's theorem: Informally, the sum of a sequence of cardinals
Axiom_of_choice
Equivalence of notions of density for sets of multiples of integers
Khachatrian, Levon H. (1997), "Classical results on primitive and recent results on cross-primitive sequences: Theorem 1.11", The Mathematics of Paul Erdős, I, Algorithms
Davenport–Erdős_theorem
On subsets of the integers in which no member of the set is a multiple of any other
\dots n\}} is called primitive if it has the property that no subset element is a multiple of any other element. Behrend's theorem states that the logarithmic
Behrend's_theorem
Problem in computer science
Minsky notes: ...the magnitudes involved should lead one to suspect that theorems and arguments based chiefly on the mere finiteness [of] the state diagram
Halting_problem
Indefinite integral
In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable
Antiderivative
Algebraic structure
Jacobson density theorem is a theorem concerning simple modules over a ring R. The theorem can be applied to show that any primitive ring can be viewed
Noncommutative_ring
Equation for radii of tangent circles
In geometry, Descartes' theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic
Descartes'_theorem
Concept in geometry
In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections. The product depends on the
Coxeter_element
Study of computable functions and Turing degrees
by Post's theorem. A weaker relationship was demonstrated by Kurt Gödel in the proofs of his completeness theorem and incompleteness theorems. Gödel's
Computability_theory
Equations of degree 5 or higher cannot be solved by radicals
In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial
Abel–Ruffini_theorem
One-to-one correspondence
function between two sets such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain). Given
Bijection
Basic framework of mathematics
organizing a field of knowledge by means of primitive concepts, axioms, postulates, definitions, and theorems. Aristotle took a majority of his examples
Foundations_of_mathematics
Mathematical set of all subsets of a set
power set must be larger than the original set). In particular, Cantor's theorem shows that the power set of a countably infinite set is uncountably infinite
Power_set
Impossible task in computing
impossible by Alonzo Church and Alan Turing in 1936. By the completeness theorem of first-order logic, a statement is universally valid if and only if it
Entscheidungsproblem
Theorem in transcendental number theory
Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following: Lindemann–Weierstrass theorem—if α1
Lindemann–Weierstrass_theorem
approach called domain theory, where they are considered as a kind of primitive element: the information represented by compact elements cannot be obtained
Compact_element
Set with associative invertible operation
Such an element a {\displaystyle a} is called a generator or a primitive element of the group. In additive notation, the requirement for an element to be
Group_(mathematics)
Size of a possibly infinite set
cannot happen with proper subsets of finite sets. However, a fundamental theorem due to Georg Cantor shows that it is possible for two infinite sets to
Cardinal_number
Type of logical system
to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem. First-order logic is the standard for the formalization
First-order_logic
Model of (first-order) Peano arithmetic that contains non-standard numbers
of arithmetic can be demonstrated by an application of the compactness theorem. To do this, a set of axioms P* is defined in a language including the
Non-standard model of arithmetic
Non-standard_model_of_arithmetic
System of mathematical set theory
finitely axiomatizable, while ZFC and MK are not. A key theorem of NBG is the class existence theorem, which states that for every formula whose quantifiers
Von Neumann–Bernays–Gödel set theory
Von_Neumann–Bernays–Gödel_set_theory
Proof by Alan Turing
to the Entscheidungsproblem". It was the second proof (after Church's theorem) of the negation of Hilbert's Entscheidungsproblem; that is, the conjecture
Turing's_proof
Mathematical connection between field theory and group theory
between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group
Galois_theory
Any one of the distinct objects that make up a set in set theory
In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. For example, given a set called A containing
Element_of_a_set
Number divisible only by 1 and itself
ISBN 978-1-4704-2849-5. Dudley 1978, Theorem 3, p. 28. Shahriari 2017, pp. 27–28. Ribenboim 2004, Fermat's little theorem and primitive roots modulo a prime, pp.
Prime_number
Algebraic structure
to divisibility: any element of a PID has a unique factorization into prime elements (so an analogue of the fundamental theorem of arithmetic holds);
Principal_ideal_domain
Mathematical logic concept
arithmetic and that its consistency is therefore less controversial. Gentzen's theorem is concerned with first-order arithmetic: the theory of the natural numbers
Gentzen's_consistency_proof
Polynomial without nontrivial factorization
factorization domain the same theorem is true, but is more accurately formulated by using the notion of primitive polynomial. A primitive polynomial is a polynomial
Irreducible_polynomial
Concept in computability theory
Kleene's normal form theorem for computable functions (Soare 1987, p. 15; Kleene 1943, p. 52—53). This states there exists a fixed primitive recursive function
Kleene's_T_predicate
Process of repeating items in a self-similar way
this is a theorem guaranteeing that recursively defined functions exist. Given a set X, an element a of X and a function f: X → X, the theorem states that
Recursion
PRIMITIVE ELEMENT-THEOREM
PRIMITIVE ELEMENT-THEOREM
Male
English
English surname transferred to forename use, derived from Latin Clemens or Clement, CLEMENTS means "gentle and merciful."
Male
Polish
 Danish, German, Polish and Swedish form of Greek Klementos, KLEMENS means "gentle and merciful."
Surname or Lastname
English, French, and Dutch
English, French, and Dutch : from the Latin personal name Clemens meaning ‘merciful’ (genitive Clementis). This achieved popularity firstly through having been borne by an early saint who was a disciple of St. Paul, and later because it was selected as a symbolic name by a number of early popes. There has also been some confusion with the personal name Clemence (Latin Clementia, meaning ‘mercy’, an abstract noun derived from the adjective; in part a masculine name from Latin Clementius, a later derivative of Clemens). As an American family name, Clement has absorbed cognates in other continental European languages. (For forms, see Hanks and Hodges 1988.)
Boy/Male
English American Biblical Latin
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Boy/Male
English American Danish
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Surname or Lastname
English
English : patronymic from the personal name Clement.German, Dutch, and Danish : from the personal name Clemens (see Clement).Samuel Langhorne Clemens, better known by his pen name, Mark Twain, was descended from VA stock on his father’s side, from a Robert Clemens, who was born in Warwickshire, England, in 1634.
Boy/Male
Czechoslovakian, Danish, German, Greek, Latin, Polish
Giving Mercy; Mild; Merciful
Surname or Lastname
English
English : patronymic from the personal name Clement. As an American family name, this form has absorbed cognates in other continental European languages. (For forms, see Hanks and Hodges 1988.)
Male
English
Short form of Latin Clementius, CLEMENT means "gentle and merciful." meaning "gentle and merciful." In the bible, this is the name of a companion of Paul.
Girl/Female
Danish, Finnish, French, German, Latin, Swedish
Ancient; Primitive; Venerable
Male
Italian
 Italian, Portuguese and Spanish form of Latin Clementius, CLEMENTE means "gentle and merciful."
Girl/Female
German, Latin
Archaic; Ancient; Old; Primitive
Boy/Male
Australian, British, Danish, Dutch, English, Finnish, French, German, Irish, Latin, Swedish
Gentle; Merciful; Mild; Form of Clement
Male
Russian
(Климент) Russian form of Greek Klementos, KLIMENT means "gentle and merciful."
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Male
Hungarian
Hungarian form of Greek Klementos, KELEMEN means "gentle and merciful."
Girl/Female
American, Australian, Biblical, British, Chinese, Christian, Danish, English, Finnish, French, German, Gothic, Italian, Latin, Portuguese, Swedish
Ancient; Primitive; Venerable
Male
Slovene
Slovene form of Greek Klementos, KLEMEN means "gentle and merciful."
Girl/Female
American, Australian, Chinese, Finnish, French, Latin, Portuguese, Swedish
Ancient; Primitive; Venerable
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
PRIMITIVE ELEMENT-THEOREM
PRIMITIVE ELEMENT-THEOREM
Girl/Female
Christian & English(British/American/Australian)
Beloved
Girl/Female
Indian
Grace, Is of czech & slovak
Boy/Male
Gujarati, Hindu, Indian, Kannada, Telugu
Signs
Male
Russian
(Russian Иларион, Ukrainian: Іларіон):: Russian and Ukrainian form of Greek Hilarion, ILARION means "joyful, happy."
Boy/Male
Hindu, Indian, Punjabi, Sikh
Fragrance Like Sandalwood; Full of Fragrance
Boy/Male
Tamil
Fame, Bright
Boy/Male
African, Arabic, Egyptian, Swahili
Dignified; Creek; From Kikuyu
Boy/Male
Tamil
Janardan | ஜநாரà¯à®¤à®¨
Lord Krishna, One who helps people, Liberator from the cycle of birth and death
Boy/Male
Hindu, Indian
Full of Light
Boy/Male
Norse
Giver of feeling.
PRIMITIVE ELEMENT-THEOREM
PRIMITIVE ELEMENT-THEOREM
PRIMITIVE ELEMENT-THEOREM
PRIMITIVE ELEMENT-THEOREM
PRIMITIVE ELEMENT-THEOREM
v. t.
To compound of elements or first principles.
pl.
of Primitia
n.
The four elements were, air, earth, water, and fire
n.
An infinitesimal part of anything of the same nature as the entire magnitude considered; as, in a solid an element may be the infinitesimal portion between any two planes that are separated an indefinitely small distance. In the calculus, element is sometimes used as synonymous with differential.
n.
The simplest or fundamental principles of any system in philosophy, science, or art; rudiments; as, the elements of geometry, or of music.
n.
A privative prefix or suffix. See Privative, a., 3.
v. t.
To constitute; to make up with elements.
a.
Constituting one of eleven parts into which a thing is divided; as, the eleventh part of a thing.
a.
Being of the first production; primitive; original.
a.
Of or pertaining to a former time; old-fashioned; characterized by simplicity; as, a primitive style of dress.
n.
One out of several parts combined in a system of aggregation, when each is of the nature of the whole; as, a single cell is an element of the honeycomb.
n.
Sometimes a curve, or surface, or volume is considered as described by a moving point, or curve, or surface, the latter being at any instant called an element of the former.
a.
Original; primary; radical; not derived; as, primitive verb in grammar.
n.
The elements of the alchemists were salt, sulphur, and mercury.
a.
Involving a limit; as, a limitive law, one designed to limit existing powers.
a.
Pertaining to the elements, first principles, and primary ingredients, or to the four supposed elements of the material world; as, elemental air.
n.
Any outline or sketch, regarded as containing the fundamental ideas or features of the thing in question; as, the elements of a plan.
a.
Of or pertaining to the beginning or origin, or to early times; original; primordial; primeval; first; as, primitive innocence; the primitive church.
a.
Implying privation or negation; giving a negative force to a word; as, alpha privative; privative particles; -- applied to such prefixes and suffixes as a- (Gr. /), un-, non-, -less.
pl.
of Primitia