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Circuit theorem
The Extra Element Theorem (EET) is an analytic technique developed by R. D. Middlebrook for simplifying the process of deriving driving point and transfer
Extra_element_theorem
signal-flow analysis by John Choma, and was made popular in the extra element theorem by R. D. Middlebrook and the asymptotic gain model of Solomon Rosenstark
Blackman's_theorem
Theorem in electrical circuit analysis
impedances, connected in wye or in delta. Extra element theorem Maximum power transfer theorem Millman's theorem Source transformation von Helmholtz, Hermann
Thévenin's_theorem
DC circuit analysis technique
law Millman's theorem Source transformation Superposition theorem Thévenin's theorem Maximum power transfer theorem Extra element theorem Mayer, Hans Ferdinand
Norton's_theorem
See Figure 2. The asymptotic gain model is a special case of the extra element theorem. As follows directly from limiting cases of the gain expression
Asymptotic_gain_model
developed many of the tools of D-OA including the Extra element theorem and the General Feedback Theorem. His goal with D-OA was to fundamentally change
R._D._Middlebrook
Product of any collection of compact topological spaces is compact
Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named
Tychonoff's_theorem
Topics referred to by the same term
technology Electronic energy transfer Epoxyeicosatrienoic acid Extra element theorem School of Engineering of Terrassa (Catalan: Escola d'Enginyeria
EET
Numerical method for solving physical or engineering problems
problems with boundary layers. The mixed finite element method is a type of finite element method in which extra independent variables are introduced as nodal
Finite_element_method
Type of electronic amplifier
transistor amplifying stage with negative feedback Extra element theorem Frequency compensation Miller theorem is a powerful tool for determining the input/output
Negative-feedback_amplifier
Mathematical result in differential geometry
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential
Atiyah–Singer_index_theorem
Classification theorem in group theory
In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved in the early 1960s
Feit–Thompson_theorem
On the intersection form of a smooth, closed 4-manifold with a spin structure
form is even. By a theorem of Cahit Arf, any even unimodular lattice has signature divisible by 8, so Rokhlin's theorem forces one extra factor of 2 to divide
Rokhlin's_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
On polynomial rings over fields
In mathematics, Hilbert's syzygy theorem is one of the three fundamental theorems about polynomial rings over fields, first proved by David Hilbert in
Hilbert's_syzygy_theorem
ISBN 0-13-436049-4. Richard R Spencer & Ghausi MS (2003). Example 10.7 pp. 723-724. ISBN 0-201-36183-3. Asymptotic gain model Blackman's theorem Extra element theorem
Return_ratio
Theorem in quantum information science
Hilbert space only up to a phase factor i.e. as an element of projectivised Hilbert space. To prove the theorem, we select an arbitrary pair of states | ϕ ⟩
No-cloning_theorem
Geometric theorem
The Banach–Tarski paradox is a theorem in set-theoretic geometry that states the following: Given a solid ball in three-dimensional space, there exists
Banach–Tarski_paradox
Square matrices satisfy their characteristic equation
In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix
Cayley–Hamilton_theorem
Subfield of automated reasoning and mathematical logic
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving
Automated_theorem_proving
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
On algebraic independence of logarithms
easier to state. For example, the Hermite–Lindemann theorem becomes the statement that any nonzero element of L {\displaystyle \mathbb {L} } is transcendental
Baker's_theorem
Planar graph drawn by relaxing springs
the equations geometrically produces a planar embedding. Tutte's spring theorem, proven by W. T. Tutte (1963), states that this unique solution is always
Tutte_embedding
Concept in differential geometry
closely related to the curvature of the connection, via the Ambrose–Singer theorem. The study of Riemannian holonomy has led to a number of important developments
Holonomy
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
Number divisible only by 1 and itself
than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself
Prime_number
Bound lattice in which every element has a complement
bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element b satisfying a ∨ b = 1 and a ∧ b = 0
Complemented_lattice
Streaming algorithm
than k different values. The following theorem is easy to prove: Theorem 1. Each heavy-hitter of b is an element of a k-reduced bag for b. The first pass
Misra–Gries heavy hitters algorithm
Misra–Gries_heavy_hitters_algorithm
Theorem about a certain class of control-flow graphs
programming language theory, the structured program theorem, generally called the Böhm–Jacopini theorem, states that a class of control-flow graphs (historically
Structured_program_theorem
Key result in general relativity
theorem states the following: Given an asymptotically flat initial data set, one can define the energy-momentum of each infinite region as an element
Positive_energy_theorem
Self-adjusting binary search tree
accesses. Static optimality theorem—Let q x {\displaystyle q_{x}} be the number of times element x is accessed in S. If every element is accessed at least once
Splay_tree
Reciprocal work theorem in engineering
theorem has applications in structural engineering where it is used to define influence lines and derive the boundary element method. Betti's theorem
Betti's_theorem
Conjecture on zeros of the zeta function
hypothesis is true, then the theorem is true. If the generalized Riemann hypothesis is false, then the theorem is true. Thus, the theorem is true!! Care should
Riemann_hypothesis
Study of rational collective decision-making
impossibility theorem is what often comes to mind when one thinks about impossibility theorems in voting. There are several famous theorems concerning social
Social_choice_theory
Measure of algorithmic complexity
describe the length of the string, before writing out the string itself. Theorem. (extra information bounds, subadditivity) K ( x | y ) ≤ K ( x ) ≤ K ( x ,
Kolmogorov_complexity
Set with associative invertible operation
third element within the same set and the following conditions must hold: the operation is associative, it has an identity element, and every element of
Group_(mathematics)
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
On linear-time algorithms for graph logic
In the study of graph algorithms, Courcelle's theorem is the statement that every graph property definable in the monadic second-order logic of graphs
Courcelle's_theorem
Berta Karlik discovered that the element 85 astatine is a product of the natural decay processes. Bohr–van Leeuwen theorem In her 1919 thesis, Hendrika Johanna
List of inventions and discoveries by women
List_of_inventions_and_discoveries_by_women
Algebraic structure with addition and multiplication
theorems concerning a PID, the most important one is the structure theorem for finitely generated modules over a principal ideal domain. The theorem may
Ring_(mathematics)
Theories in mathematical logic
for which the sentences of the theory are all true (by the completeness theorem, satisfiability is equivalent to consistency); be complete: for any statement
List_of_first-order_theories
Mathematical problem
and Gödel's incompleteness theorem in the 1920s and 1930s. First, note that Garrett Birkhoff proved with his HSP theorem that the equational theory of
Tarski's high school algebra problem
Tarski's_high_school_algebra_problem
originally given as a theorem by Brouwer (1975) containing no "extra" restriction on R {\displaystyle R} under the name The Bar Theorem. However, the proof
Bar_induction
Construction in algebra
identity 1 of H is required to be in A). The Nichols–Zoeller freeness theorem of Warren Nichols and Bettina Zoeller (1989) established that the natural
Hopf_algebra
Form of mathematical proof
1000 AD, who applied it to arithmetic sequences to prove the binomial theorem and properties of Pascal's triangle. Whilst the original work was lost
Mathematical_induction
10th episode of the 6th season of Futurama
episode by what David X. Cohen described in an interview as a mathematical theorem proved by Keeler, who has a Ph.D. in Mathematics. The title and the story's
The_Prisoner_of_Benda
Mathematical function between groups that preserves multiplication structure
this property, one can deduce that h maps the identity element eG of G to the identity element eH of H, h ( e G ) = e H {\displaystyle h(e_{G})=e_{H}}
Group_homomorphism
Theory of algebraic structures in general
of A and returns a single element of A. Thus, a 0-ary operation (or nullary operation) can be represented simply as an element of A, or a constant, often
Universal_algebra
Mathematical-logic system based on functions
– A virtual machine designed for the lambda calculus Scott–Curry theorem – A theorem about sets of lambda terms To Mock a Mockingbird – An introduction
Lambda_calculus
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
Statement that is taken to be true
knowledge. They are accepted without demonstration. All other assertions (theorems, in the case of mathematics) must be proven with the aid of these basic
Axiom
Set of functions between two fixed sets
cardinal dimension of a function space with no extra structure can be found by the Erdős–Kaplansky theorem. Function spaces appear in various areas of mathematics:
Function_space
Mergelyan's theorem — generalization of Stone–Weierstrass theorem for polynomials Müntz–Szász theorem — variant of Stone–Weierstrass theorem for polynomials
List of numerical analysis topics
List_of_numerical_analysis_topics
Commutative ring with no zero divisors other than zero
two nonzero elements is nonzero. In an integral domain, every nonzero element a has the cancellation property, that is, if a ≠ 0, ab = ac implies b =
Integral_domain
Field in which every sum of two squares is a square
of a field F {\displaystyle F} is an extension obtained by adjoining an element 1 + λ 2 {\displaystyle {\sqrt {1+\lambda ^{2}}}} for some λ {\displaystyle
Pythagorean_field
that a theorem is beautiful when they really mean to say that it is enlightening. We acknowledge a theorem's beauty when we see how the theorem 'fits'
Glossary of mathematical jargon
Glossary_of_mathematical_jargon
Theories of higher-dimensional general relativity
appears in string theory and M-theory as a central element for mathematical consistency, where extra dimensions are essential for mathematical consistency
Higher-dimensional Einstein gravity
Higher-dimensional_Einstein_gravity
Differential form
{\displaystyle n} , a volume form is an n {\displaystyle n} -form. It is an element of the space of sections of the line bundle ⋀ n ( T ∗ M ) {\displaystyle
Volume_form
British-Lebanese mathematician (1929–2019)
specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in
Michael_Atiyah
Type of binary relation
m)].} Some authors include an extra condition that R is set-like, i.e., that the elements less than any given element form a set. Equivalently, assuming
Well-founded_relation
Two-dimensional manifold
not be surfaces in the extrinsic sense. However, the Whitney embedding theorem asserts every surface can in fact be embedded homeomorphically into Euclidean
Surface_(topology)
Branch of mathematics that studies sets
uncountable, that is, one cannot put all real numbers in a list. This theorem is proved using Cantor's first uncountability proof, which differs from
Set_theory
Element of a unital algebra over the field of real numbers
number system. Hurwitz and Frobenius proved theorems that put limits on hypercomplexity: Hurwitz's theorem says finite-dimensional real composition algebras
Hypercomplex_number
Group in group theory and physics
the diagonal with −1.) By Bass's theorem, it has a polynomial growth rate of order 4. One can generate any element through ( 1 a c 0 1 b 0 0 1 ) = y
Heisenberg_group
Mathematical group
started with Camille Jordan's theorem that the projective special linear group PSL(2, q) is simple for q ≠ 2, 3. This theorem generalizes to projective groups
Group_of_Lie_type
Branch of numerical analysis
divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite
Numerical methods for partial differential equations
Numerical_methods_for_partial_differential_equations
Methods of mathematical approximation
polarisation Eigenvalue perturbation Homotopy perturbation method Interval finite element Lyapunov stability Method of dominant balance Order of approximation Perturbation
Perturbation_theory
Czech-Canadian mathematician
Mathematica, Extra Volume ICM III, archived from the original on 2020-07-27, retrieved 2017-03-22 Weisstein, Eric W. "Art Gallery Theorem." From MathWorld--A
Václav_Chvátal
Determinant of the matrix of first derivatives of a set of functions
Roth used this result about generalized Wronskians in his proof of Roth's theorem. For more general conditions under which the converse is valid see Wolsson
Wronskian
Category whose objects are sets and whose morphisms are functions
it is an element of some larger Grothendieck universe.) However, one does not work directly with the "category of all sets". Instead, theorems are expressed
Category_of_sets
Branch of mathematics
Königsberg problem and polyhedron formula are arguably the field's first theorems. The term topology was introduced by Johann Benedict Listing in the 19th
Topology
In arithmetic geometry, a Frobenioid is a category with some extra structure that generalizes the theory of line bundles on models of finite extensions
Frobenioid
Mathematics of real numbers and real functions
is an upper bound that is smaller than all of the others. Most of the theorems that are proved in real analysis rely on completeness in one way or another
Real_analysis
Pictorial representation of the behavior of subatomic particles
x = e i k x {\displaystyle A_{kx}=e^{ikx}\,} and the Fourier inversion theorem tells you the inverse: A k x − 1 = e − i k x {\displaystyle A_{kx}^{-1}=e^{-ikx}\
Feynman_diagram
Type of mathematical proof
method of exhaustion (e.g., the first computer-assisted proof of four color theorem in 1976), though such approaches can also be challenged on the basis of
Proof_by_exhaustion
Duality for locally compact abelian groups
bidual (the dual of its dual). The Fourier inversion theorem is a special case of this theorem. The subject is named after Lev Pontryagin, who laid down
Pontryagin_duality
Search algorithm finding the position of a target value within a sorted array
a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot
Binary_search
Theory in abstract algebra
Eduard Kummer around the 1840s in his pioneering work on Fermat's Last Theorem. The main statements do not depend on the nature of the field – apart from
Kummer_theory
Type of infinite structure
o-minimal structures. There is a cell decomposition theorem, Whitney and Verdier stratification theorems and a good notion of dimension and Euler characteristic
O-minimal_theory
Branch of mathematics that studies the properties of groups
is known that V above decomposes into irreducible parts (see Maschke's theorem). These parts, in turn, are much more easily manageable than the whole
Group_theory
Isomorphism type of ordered sets
Relevant theorems of this sort are expanded upon below. More examples can be given now: The set of positive integers (which has a least element), and that
Order_type
Observational basis of thermodynamics
now known as the first and second laws were established. Later, Nernst's theorem (or Nernst's postulate), which is now known as the third law, was formulated
Laws_of_thermodynamics
Set whose pairs have minima and maxima
greatest element (also called maximum, or top element, and denoted by 1 {\displaystyle 1} or ⊤ {\displaystyle \top } ) and a least element (also called
Lattice_(order)
How spheres of various dimensions can wrap around each other
representing maps, and any element of non-zero degree is nilpotent; the nilpotence theorem on complex cobordism implies Nishida's theorem.[citation needed] Example:
Homotopy_groups_of_spheres
Analysis of datasets using techniques from topology
first classification theorem for persistent homology appeared in 1994 via Barannikov's canonical forms. The classification theorem interpreting persistence
Topological_data_analysis
Particular class of sets which can be described entirely in terms of simpler sets
basic axioms of set theory, if ZF itself is consistent. Since many other theorems only hold in systems in which one or both of the propositions is true,
Constructible_universe
Element of a nonstandard model of the reals, which can be infinite or infinitesimal
h} . The transfer principle for ultrapowers is a consequence of Łoś's theorem of 1955. Concerns about the soundness of arguments involving infinitesimals
Hyperreal_number
Löwenheim–Skolem theorem states that if a first-order theory has an infinite model then it has a model of any given infinite cardinality lower bound An element of a
Glossary_of_set_theory
Type of physical quantity
Assignment of a tensor continuously varying across a region of space Noether's theorem – Statement relating differentiable symmetries to conserved quantities
Pseudotensor
Type of geometry
hexagon theorem. As a result, the points of each line are in one-to-one correspondence with a given field, F, supplemented by an additional element, ∞, such
Projective_geometry
Progression-free set of numbers
1942 that Salem–Spencer sets can have nearly-linear size. However a later theorem of Klaus Roth shows that the size is always less than linear. For k = 1
Salem–Spencer_set
Set of vectors used to define coordinates
of elements of a vector space V is called a basis (pl.: bases) if every element of V can be written in a unique way as a finite linear combination of elements
Basis_(linear_algebra)
Group of even permutations of a finite set
A4 is the smallest group demonstrating that the converse of Lagrange's theorem is not true in general: given a finite group G and a divisor d of |G|,
Alternating_group
Concept in math
K=\{(xk^{-1}x^{-1},k)\colon k\in K\}\cap H\times K.} (Orbit–stabilizer theorem) There is a bijection between HxK and (H × K) / (H × K)x under which hxk
Double_coset
Submodule of a mathematical ring
maximal left ideal); see Krull's theorem for more. A left (resp. right, two-sided) ideal generated by a single element x is called the principal left (resp
Ideal_(ring_theory)
In mathematics, invertible homomorphism
{\displaystyle 1+3=4.} This is a special case of the Chinese remainder theorem which asserts that, if m {\displaystyle m} and n {\displaystyle n}
Isomorphism
Probability distribution
which is positive. This is justified by considering the central limit theorem in the log domain (sometimes called Gibrat's law). The log-normal distribution
Log-normal_distribution
relies on the axiom of choice. This example can be extended into a general theorem about the existence of discontinuous linear maps on any infinite-dimensional
Discontinuous_linear_map
Algebraic structure used in topology
1954, pp. 62–63. Thom 1954, Theorem II.29. Hatcher 2001, Example 3.16. Hatcher 2001, Theorem 3.15. Hatcher 2001, Theorem 3.19. Hatcher 2001, p. 222. Hatcher
Cohomology
Class of mathematical sets
{\displaystyle X} . A Borel subset of X {\displaystyle X} is then simply an element of this σ-algebra. Borel sets are important in measure theory, since any
Borel_set
EXTRA ELEMENT-THEOREM
EXTRA ELEMENT-THEOREM
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.)
Girl/Female
Latin
Adroit; skillful.
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Boy/Male
Australian, British, Danish, Dutch, English, Finnish, French, German, Irish, Latin, Swedish
Gentle; Merciful; Mild; Form of Clement
Male
Polish
 Danish, German, Polish and Swedish form of Greek Klementos, KLEMENS means "gentle and merciful."
Male
Slovene
Slovene form of Greek Klementos, KLEMEN means "gentle and merciful."
Boy/Male
English American Danish
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Girl/Female
Arabic
Heavenly Smell
Girl/Female
Tamil
Extra ordinary
Boy/Male
English American Biblical Latin
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Male
English
English surname transferred to forename use, derived from Latin Clemens or Clement, CLEMENTS 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.)
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.
Girl/Female
British, English, Latin
Dyer; Skillful; Dexterous; Adroit; Right-handed
Male
Russian
(Климент) Russian form of Greek Klementos, KLIMENT means "gentle and merciful."
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
Indian
Extra ordinary
Male
Hungarian
Hungarian form of Greek Klementos, KELEMEN means "gentle and merciful."
Male
Italian
 Italian, Portuguese and Spanish form of Latin Clementius, CLEMENTE means "gentle and merciful."
EXTRA ELEMENT-THEOREM
EXTRA ELEMENT-THEOREM
Boy/Male
Celebrity, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
King of the Earth; Warrior
Girl/Female
British, English, French
From Germany
Girl/Female
Latin
Born seventh. Name given to the seventh child born to a large family.
Surname or Lastname
German
German : variant of Klaus, a reduced form of the personal name Nikolaus, German form of Nicholas.English : nickname for a flatterer, from Old French glose ‘flattery’.
Girl/Female
Arabic, Muslim
A Distinguished Woman of her Times was so Named and She was the Daughter of Saad Al-aslamiyah and She Offered Allegiance (Bayah) to the Prophet PBUH
Surname or Lastname
Irish
Irish : Anglicized form of Gaelic Ó hEarcáin ‘descendant of Earcán’, a byname or personal name formed from a diminutive of earc ‘red’, ‘bloody’; also meaning ‘pig’.English : from a pet form of a medieval personal name (see Harkey).
Boy/Male
Tamil
A non Aryan
Girl/Female
Tamil
Chitrini | சிதà¯à®°à¯€à®¨à¯€
Beautiful woman with artistic talents
Boy/Male
Indian, Sanskrit
Desirable; Acceptable
Surname or Lastname
English and Dutch
English and Dutch : from the personal name (Greek Nikolaos, from nikÄn ‘to conquer’ + laos ‘people’). Forms with -ch- are due to hypercorrection (compare Anthony). The name in various vernacular forms was popular among Christians throughout Europe in the Middle Ages, largely as a result of the fame of a 4th-century Lycian bishop, about whom a large number of legends grew up, and who was venerated in the Orthodox Church as well as the Catholic. In English-speaking countries, this surname is also found as an Americanized form of various Greek surnames such as Papanikolaou ‘(son of) Nicholas the priest’ and patronymics such as Nikolopoulos.The colonial official and revolutionary patriot Robert Carter Nicholas was from a prominent VA family on both sides. His father was a British navy surgeon who emigrated in about 1700 from Lancashire, England, to Williamsburg, VA.
EXTRA ELEMENT-THEOREM
EXTRA ELEMENT-THEOREM
EXTRA ELEMENT-THEOREM
EXTRA ELEMENT-THEOREM
EXTRA ELEMENT-THEOREM
v. t.
To constitute; to make up with elements.
n.
To overlay or coat with cement; as, to cement a cellar bottom.
n.
The quotient of a unit divided by eleven; one of eleven equal parts.
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.
Beyond what is due, usual, expected, or necessary; additional; supernumerary; also, extraordinarily good; superior; as, extra work; extra pay.
n.
Any outline or sketch, regarded as containing the fundamental ideas or features of the thing in question; as, the elements of a plan.
n.
Something in addition to what is due, expected, or customary; something in addition to the regular charge or compensation, or for which an additional charge is made; as, at European hotels lights are extras.
pl.
of Extra
n.
The simplest or fundamental principles of any system in philosophy, science, or art; rudiments; as, the elements of geometry, or of music.
n.
The elements of the alchemists were salt, sulphur, and mercury.
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.
v. t.
To compound of elements or first principles.
a.
Constituting one of eleven parts into which a thing is divided; as, the eleventh part of a thing.
n.
One of the ultimate parts which are variously combined in anything; as, letters are the elements of written language; hence, also, a simple portion of that which is complex, as a shaft, lever, wheel, or any simple part in a machine; one of the essential ingredients of any mixture; a constituent part; as, quartz, feldspar, and mica are the elements of granite.
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 four elements were, air, earth, water, and fire
a.
Acting with great force; furious; violent; impetuous; forcible; mighty; as, vehement wind; a vehement torrent; a vehement fire or heat.
n.
One of the ultimate, undecomposable constituents of any kind of matter. Specifically: (Chem.) A substance which cannot be decomposed into different kinds of matter by any means at present employed; as, the elements of water are oxygen and hydrogen.
a.
Pertaining to the elements, first principles, and primary ingredients, or to the four supposed elements of the material world; as, elemental air.
n.
One of the necessary data or values upon which a system of calculations depends, or general conclusions are based; as, the elements of a planet's orbit.