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In mathematical logic, an elementary definition is a definition that can be made using only finitary first-order logic, and in particular without reference
Elementary_definition
Topics referred to by the same term
Elementary definition, in mathematical logic elementary OS, a Linux distribution Elementary particle, in particle physics Elementary proof Elementary
Elementary
Measure of positive and negative charges
from the negative charge to the positive one. A stronger mathematical definition is to use vector algebra, since a quantity with magnitude and direction
Electric_dipole_moment
Type of discrete orthogonal polynomials
In mathematics, discrete Chebyshev polynomials, or Gram polynomials, are a type of discrete orthogonal polynomials used in approximation theory, introduced
Discrete Chebyshev polynomials
Discrete_Chebyshev_polynomials
Topics referred to by the same term
Intensional definition Elementary definition Recursive definition Field of definition A continuous function A well-defined function High-definition television
Definition_(disambiguation)
a categorical fibration. The definition of categorical fibration is credited to Grothendieck. An elementary definition of fibration can be easily derived:
Fibrations_of_graphs
Type of mathematical function
are elementary functions involved, in some sense, in the definition of the function. The Risch algorithm (1968) can decide whether an elementary function
Elementary_function
Charge carried by one proton or electron
The elementary charge, usually denoted by e, is a fundamental physical constant, defined as the electric charge carried by a single proton (+1 e) or, equivalently
Elementary_charge
Mathematical logic
theory of real closed fields Axiomization of Euclidean geometry Elementary definition Elementary theory of the reals Mac Lane and Moerdijk, Sheaves in Geometry
Elementary_theory
Conversion constant for amount of substance
the Avogadro constant. The fundamental definition of the Avogadro constant itself is therefore one per elementary amount (NA = 1/na), independent of any
Avogadro_constant
SI unit of amount of substance
system which contains as many elementary entities as there are atoms in 0.012 kilograms of carbon-12." Thus, by that definition, one mole of pure 12C had
Mole_(unit)
Something that has mass and volume
based on its structure or "building blocks". On the scale of elementary particles, a definition that follows this tradition can be stated as: "ordinary matter
Matter
Subatomic particle having no substructure
In the Standard Model of particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles
Elementary_particle
Collection of proofs of equations involving trigonometric functions
trigonometric identities between them depend on the chosen definition. The oldest and most elementary definitions are based on the geometry of right triangles and
Proofs of trigonometric identities
Proofs_of_trigonometric_identities
Basic concepts of algebra
{\overset {}{\underset {}{x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}}}} Elementary algebra, also known as high school algebra or college algebra, encompasses
Elementary_algebra
{\displaystyle {\mathsf {ELEMENTARY}}} consists of the decision problems that can be solved in time bounded by an elementary recursive function. Equivalently
ELEMENTARY
Concept in probability theory
disjunction of elementary events is just the number of events in the disjunction divided by the total number of elementary events. The classical definition of probability
Classical definition of probability
Classical_definition_of_probability
Theorem in vector calculus
see the coarea formula. In this article, we instead use a more elementary definition, based on the fact that a boundary can be discerned for full-dimensional
Stokes'_theorem
Particle smaller than an atom
particle or an elementary particle. A composite particle, such as a proton or a neutron, is composed of other particles while an elementary particle, such
Subatomic_particle
School for children
2017. Retrieved 9 November 2007. "Definition of GRADE SCHOOL". Merriam-Webster. 9 April 2024. "Definition of ELEMENTARY SCHOOL". Merriam-Webster. 5 April
Primary_school
SI base unit of electric current
fixing the elementary charge e to be exactly 1.602176634×10−19 C, which means an ampere is an electric current equivalent to 1019 elementary charges moving
Ampere
Numerical method for solving physical or engineering problems
in V {\displaystyle V} are not differentiable according to the elementary definition of calculus. Indeed, if v ∈ V {\displaystyle v\in V} then the derivative
Finite_element_method
Mathematical concept
numbers over the rationals, as described by Hewitt and Stromberg. Elementary definition by powers. Define the exponential function with base a > 0 {\displaystyle
Characterizations of the exponential function
Characterizations_of_the_exponential_function
One of the seven units of measurement that define the metric system
the current definitions and their values under the proposed new definition. He urged the CIPM to accept the proposed changes in the definition of the kilogram
SI_base_unit
Primary frequency standard
primary standard for the definition of the second in the International System of Units (SI), the modern metric system. By definition, radiation produced by
Caesium_standard
Algebraic manipulation of "true" and "false"
mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth
Boolean_algebra
1976 mathematics textbook by H. Jerome Keisler
definition of uniform continuity, and characterize Hrbacek's criticism as a "dubious lament". Between the first and second edition of the Elementary Calculus
Elementary Calculus: An Infinitesimal Approach
Elementary_Calculus:_An_Infinitesimal_Approach
Function defined on integers in number theory
In number theory, the Lagarias arithmetic derivative or number derivative is a function defined for integers, based on prime factorization, by analogy
Arithmetic_derivative
The definition of religion is a controversial and complicated subject in religious studies with scholars failing to agree on any one definition. Oxford
Definition_of_religion
Mathematics concept
the 256 elementary cellular automata, 64 are amphichiral. The second such transformation is to exchange the roles of 0 and 1 in the definition. The result
Elementary_cellular_automaton
2012 mass shooting in Connecticut, US
On December 14, 2012, a mass shooting occurred at Sandy Hook Elementary School in Newtown, Connecticut, United States. The perpetrator, 20-year-old Adam
Sandy Hook Elementary School shooting
Sandy_Hook_Elementary_School_shooting
Divergent series
finite answer for a series that diverges to +∞. Most of the more elementary definitions of the sum of a divergent series are stable and linear, and any
1_+_2_+_3_+_4_+_⋯
3-volume treatise on mathematics, 1910–1913
edition, below) begins with a definition of the sign "⊃" ✱1.01. p ⊃ q .=. ∾ p ∨ q. Df. ✱1.1. Anything implied by a true elementary proposition is true. Pp modus
Principia_Mathematica
Class in model theory
earlier definitions are still in use in finite model theory, where an elementary class may be called a Δ-elementary class, and the terms elementary class
Elementary_class
Axiom(s) of Set Theory
each n. In this way n = {0, 1, …, n − 1} for each natural number n. This definition has the property that n is a set with n elements. The first few numbers
Set-theoretic definition of natural numbers
Set-theoretic_definition_of_natural_numbers
Definition of the units kg, A, K and mol
2019 definition: The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge
2019_revision_of_the_SI
Type of mathematical measure
are integrable for all the elementary definitions of integrals. The measure (in the sense defined above) defined by elementary integration is precisely
Radon_measure
Instantaneous rate of change (mathematics)
vertical bars denote the absolute value. This is an example of the (ε, δ)-definition of limit. If the function f {\displaystyle f} is differentiable at a
Derivative
Defining elements of a set in terms of other elements in the set
In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements
Recursive_definition
Neighborhood in Houston, Texas
Dodson Elementary School in 1945; for a period it was the second-largest Black elementary school in the Third Ward area. In 1955 a new Allen elementary opened
Third_Ward,_Houston
Science of measurement and its application
1960. Metrology is divided into three basic overlapping activities: The definition of units of measurement The realisation of these units of measurement
Metrology
SI derived unit of electric charge
electric charge delivered by a 1 ampere current in 1 second, with the elementary charge e as a defining constant in the SI. The SI defines the coulomb
Coulomb
Group of two parents and their children
A nuclear family – also called an elementary family, atomic family, or conjugal family – is a family group consisting of two parents and their children
Nuclear_family
Modern form of the metric system
The seven defining constants are the most fundamental feature of the definition of the system of units. Each defining constant consists of an exact numerical
International_System_of_Units
Dictionary of 184 philosophical terms
Plato's and Aristotle's efforts in the area of definition, this collection seems to be an elementary text produced by second-rate philosophical study
Definitions_(Plato)
Relation between sine and cosine
horizontal side to its hypotenuse is the same, namely cos θ. The elementary definitions of the sine and cosine functions in terms of the sides of a right
Pythagorean trigonometric identity
Pythagorean_trigonometric_identity
In mathematics, cocompact embeddings are embeddings of normed vector spaces possessing a certain property similar to but weaker than compactness. Cocompactness
Cocompact_embedding
Set of the simplest pathways in a biochemical network
{\displaystyle \mathbf {v} _{irr}\geq 0.} A more formal definition is given by: An elementary mode, v i {\displaystyle \mathbf {v} _{i}} , is defined
Elementary_modes
First Lady of the United States from 2001 to 2009
at Longfellow Elementary School in the Dallas Independent School District. She then taught for three years at John F. Kennedy Elementary School, a Houston
Laura_Bush
Concept in model theory
in M. If N is an elementary substructure of M, then M is called an elementary extension of N. An embedding h: N → M is called an elementary embedding of N
Elementary_equivalence
Logical incompatibility between two or more propositions
the formal system in the definition of tautology. When Emil Post, in his 1921 "Introduction to a General Theory of Elementary Propositions", extended his
Contradiction
Proof that only uses basic techniques
In mathematics, an elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer
Elementary_proof
Type of representation of a linear semisimple Lie group
from Harish-Chandra's results that it is equivalent to the more elementary definition given above. Tempered representations also seem to play a fundamental
Tempered_representation
Type of integration
the space of elementary functions. These elementary functions and their elementary integrals may be any set of functions and definitions of integrals
Daniell_integral
syntax Alphabet Arity Automata Axiom schema Expression ground Extension by definition conservative Relation Formation rule Grammar Formula atomic closed ground
Saturated_set
generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions. All are controversial
Definitions_of_mathematics
Thesis on the nature of computability
Church and the British mathematician Alan Turing. Before the precise definition of computable function, mathematicians often used the informal term effectively
Church–Turing_thesis
Infinite cardinal number
{\displaystyle \aleph _{0},} the smallest infinite cardinality. The definition of ℵ 1 {\displaystyle \aleph _{1}} implies (in ZF, Zermelo–Fraenkel set
Aleph_number
Process of repeating items in a self-similar way
Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. Recursion is used in a variety of disciplines
Recursion
Subgroup of the group of invertible n×n matrices
is encoded in its set X(k) of k-rational points, which allows an elementary definition of a linear algebraic group. First, define a function from the abstract
Linear_algebraic_group
Technique used in mathematical logic
syntax Alphabet Arity Automata Axiom schema Expression ground Extension by definition conservative Relation Formation rule Grammar Formula atomic closed ground
Back-and-forth_method
Characterizing property of mathematical constructions
independently from the method chosen for constructing them. For example, the definitions of the integers from the natural numbers, of the rational numbers from
Universal_property
Event that contains only one outcome
probabilities. Under the measure-theoretic definition of a probability space, the probability of an elementary event need not even be defined. In particular
Elementary_event
Concept in computability theory
the ELEMENTARY complexity class deals with decision problems and Turing machine runtime, rather than total functions. The definitions of elementary recursive
Elementary_recursive_function
Measure of algorithmic complexity
bounded (a result called the invariance theorem, see below). There are two definitions of Kolmogorov complexity: plain and prefix-free. The plain complexity
Kolmogorov_complexity
Limitative results in mathematical logic
system, then one has to add either p or "not p" as axioms. But then the definition of "being a Gödel number of a proof" of a statement changes. which means
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Bohemian polymath (1781–1848)
mathematical analysis he contributed the introduction of a fully rigorous ε–δ definition of a mathematical limit. Bolzano was the first to recognize the greatest
Bernard_Bolzano
Logical principle
(All quotes are from van Heijenoort, italics added). Brouwer offers his definition of "principle of excluded middle"; we see here also the issue of "testability":
Law_of_excluded_middle
Mathematics taught in primary and secondary school
Elementary mathematics, also known as primary or secondary school mathematics, is the study of mathematics topics that are commonly taught at the primary
Elementary_mathematics
History of chemical crystallography to 1895
clarification of the concept of atomic weight (Stanislao Cannizzaro), the definition of the idea of valence (then known as atomicity), and new chemical structural
Chemical crystallography before X-rays
Chemical_crystallography_before_X-rays
Term in mathematical logic
syntax Alphabet Arity Automata Axiom schema Expression ground Extension by definition conservative Relation Formation rule Grammar Formula atomic closed ground
Spectrum_of_a_sentence
Area of mathematical logic
elementary classes, which are defined by a strong substructure relation generalising that of an elementary substructure. Even though its definition is
Model_theory
Branch of mathematics
including a definition of continuity in terms of infinitesimals, and a (somewhat imprecise) prototype of an (ε, δ)-definition of limit in the definition of differentiation
Calculus
example, ellipse or minimal surface) may have more than one definition. These definitions are equivalent in the context of a given mathematical structure
Equivalent definitions of mathematical structures
Equivalent_definitions_of_mathematical_structures
syntax Alphabet Arity Automata Axiom schema Expression ground Extension by definition conservative Relation Formation rule Grammar Formula atomic closed ground
Weakly_o-minimal_structure
Concept in model theory
syntax Alphabet Arity Automata Axiom schema Expression ground Extension by definition conservative Relation Formation rule Grammar Formula atomic closed ground
Amalgamation_property
Two-dimensional group theory table
− 1 {\displaystyle g\mapsto g^{-1}} , which is non-trivial except for elementary abelian 2-groups, and outer because abelian groups are precisely those
Character_table
First stage of education for children
primary teaching. SAGE. 4 August 2017. ISBN 9781473994034. "Elementary education | Definition, Goals, & Facts". Britannica. 2023-09-05. Retrieved 2023-09-22
Primary_education
precise inclusion criteria are disputed, and there is no broadly accepted definition. Only shootings that have Wikipedia articles of their own are included
List of mass shootings in the United States in the 2020s
List_of_mass_shootings_in_the_United_States_in_the_2020s
Ordered field that does not satisfy the Archimedean property
Leibniz Abraham Robinson Pierre de Fermat Augustin-Louis Cauchy Leonhard Euler Textbooks Analyse des Infiniment Petits Elementary Calculus Cours d'analyse
Non-Archimedean_ordered_field
Mathematical function with no sudden changes
only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity. Continuity is one of the core
Continuous_function
syntax Alphabet Arity Automata Axiom schema Expression ground Extension by definition conservative Relation Formation rule Grammar Formula atomic closed ground
Apartness_relation
is contained in the conductor. Indeed, for such a J, JB ⊆ J ⊆ A, so by definition J is contained in f ( B / A ) {\displaystyle {\mathfrak {f}}(B/A)} . Conversely
Conductor_(ring_theory)
In logic, defining a new symbol
first-order theories, an extension by definition formalizes the introduction of a new symbol by means of a definition. For example, it is common in naive
Extension_by_definition
Fictional character created by Sir Arthur Conan Doyle
ISBN 978-0-7624-3252-3. Look up elementary, my dear Watson in Wiktionary, the free dictionary. Sherlock Holmes at Wikipedia's sister projects Definitions from Wiktionary
Sherlock_Holmes
Electromagnetic property of matter
quantized: it comes in integer multiples of individual small units called the elementary charge, e, about 1.602×10−19 C, which is the smallest charge that can
Electric_charge
In geometry, a slab is a region between two parallel lines in the Euclidean plane, or between two parallel planes in three-dimensional Euclidean space
Slab_(geometry)
Collection of mathematical objects
define precisely what constitutes a "set" or "collection", because such a definition would have to be in terms of something else previously defined. Instead
Set_(mathematics)
Reasoning for mathematical statements
definition of a formal proof is intended to capture the concept of proofs as written in the practice of mathematics. The soundness of this definition
Mathematical_proof
Mathematical function
In mathematics, specifically in commutative algebra, the elementary symmetric polynomials are one type of basic building block for symmetric polynomials
Elementary symmetric polynomial
Elementary_symmetric_polynomial
syntax Alphabet Arity Automata Axiom schema Expression ground Extension by definition conservative Relation Formation rule Grammar Formula atomic closed ground
List_of_mathematical_proofs
Incidents involving multiple victims of firearm violence
victims of firearm related violence. Definitions vary, with no single, broadly accepted definition. One definition is an act of public firearm violence—excluding
Mass shootings in the United States
Mass_shootings_in_the_United_States
Łukasiewicz–Moisil algebras (LMn algebras) were introduced in the 1940s by Grigore Moisil (initially under the name of Łukasiewicz algebras) in the hope
Łukasiewicz–Moisil_algebra
Basic integral in elementary calculus
In real analysis, the Riemann integral is a rigorous definition of the integral of a function on an interval. It defines the integral by approximating
Riemann_integral
Foundations of probability theory
by starting from a philosophical definition of probability and arguing that the axioms are satisfied by this definition. For example, Cox's theorem derives
Probability_axioms
Level of database normalisation
Elementary key normal form (EKNF) is a subtle enhancement on third normal form, thus EKNF tables are in 3NF by definition. This happens when there is
Elementary_key_normal_form
Relationship where one statement follows from another
consequence must be true in all cases, however this is an incomplete definition of formal consequence, since even the argument "P is Q's brother's son
Logical_consequence
ring k; see the articles on group theory and group ring for the elementary definitions). Let B be the group (sub)algebra of a normal subgroup H of index
Depth of noncommutative subrings
Depth_of_noncommutative_subrings
Branch of pure mathematics
the integers. Elementary number theory studies aspects of integers that can be investigated using elementary methods such as elementary proofs. Analytic
Number_theory
Property involving two mathematical operations
{\displaystyle x\cdot (y+z)=x\cdot y+x\cdot z} is always true in elementary algebra. For example, in elementary arithmetic, one has 2 ⋅ ( 1 + 3 ) = ( 2 ⋅ 1 ) + ( 2
Distributive_property
ELEMENTARY DEFINITION
ELEMENTARY DEFINITION
Biblical
savior; deliverer, The Greek form of the name Joshua or Jeshua, a contraction of Jehoshua, that is, help of Jehovah or saviour. Latin: Jesus, Iesus, Iesu, Josue. Greek: Ieous from Hebrew Yeshua. Also means safety, victory and who's help is Jehovah or it may be from the verb "Yasha", "to save," and = Jehovah Savior, or simply Savior; a late form of Hebrew "yehosua", the Jesus means of which is "YHWH is salvation" or "YHWH saves/has saved." Online definition of "savior." Latin term drove out Old English "hæland" which means "healer" as the preferred descriptive term for Jesus.
Girl/Female
Indian
Definition
Girl/Female
Hindu, Indian
Number; Definition
ELEMENTARY DEFINITION
ELEMENTARY DEFINITION
Surname or Lastname
English (East Midlands)
English (East Midlands) : occupational name from Middle English dyster ‘dyer’ (see Dyer).
Boy/Male
Muslim
Servant of the gatherer
Female
Slovene
 Slovene form of Latin Laura, LAVRA means "laurel." Compare with another form of Lavra.
Male
German
Short form of German Tillo, a pet form of names beginning with Diet-, TILL means "people, race."
Boy/Male
American, Australian, British, Christian, Dutch, English, French, German, Indian, Latin
Lame
Surname or Lastname
English (mainly South Wales and southwestern England)
English (mainly South Wales and southwestern England) : variant of Nead.
Male
English
English unisex name derived from Middle English haven (Old English hæfen), HAVEN means "haven, refuge."
Girl/Female
English
Bear or warrior maiden.
Boy/Male
Hindu
Boy/Male
Hindu
Supporter of Dharma, Observer of the right path
ELEMENTARY DEFINITION
ELEMENTARY DEFINITION
ELEMENTARY DEFINITION
ELEMENTARY DEFINITION
ELEMENTARY DEFINITION
a.
Pertaining to the elements, first principles, and primary ingredients, or to the four supposed elements of the material world; as, elemental air.
n.
Elementariness.
a.
Regulative.
n.
Unorganized material; elementary matter.
a.
Pertaining to aliment or food, or to the function of nutrition; nutritious; alimental; as, alimentary substances.
a.
Pertaining to rudiments or first principles; rudimentary; elementary.
n.
An elementary piece of the mechanism of a lock.
a.
Elementary.
adv.
According to elements; literally; as, the words, "Take, eat; this is my body," elementally understood.
a.
Elementary.
a.
Relating to hypostasis, or substance; hence, constitutive, or elementary.
n.
The doctrine of the elementary requisites of mere thought.
a.
Having only one principle or constituent part; consisting of a single element; simple; uncompounded; as, an elementary substance.
a.
Pertaining to, or treating of, the elements, rudiments, or first principles of anything; initial; rudimental; introductory; as, an elementary treatise.
a.
Pertaining to one of the four elements, air, water, earth, fire.
a.
Combined with arsenic; -- said some elementary substances or radicals; as, arseniureted hydrogen.
n.
The state of being elementary; original simplicity; uncompounded state.
a.
Capable of being leased; held by tenants.
n.
The whole alimentary, or enteric, canal.
a.
Elementary; rudimental.