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Boolean algebra
and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean domain. The
Two-element_Boolean_algebra
Algebraic structure modeling logical operations
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties
Boolean_algebra_(structure)
Algebraic manipulation of "true" and "false"
mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables
Boolean_algebra
Every Boolean algebra is isomorphic to a certain field of sets
pointwise convergence of nets of homomorphisms into the two-element Boolean algebra. For every Boolean algebra B, S(B) is a compact totally disconnected Hausdorff
Stone's representation theorem for Boolean algebras
Stone's_representation_theorem_for_Boolean_algebras
1969 non-fiction book by G. Spencer-Brown
Boolean arithmetic; The primary algebra (Chapter 6 of LoF), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean
Laws_of_Form
Algebraic ring that need not have additive negative elements
distributive lattices. The smallest semiring that is not a ring is the two-element Boolean algebra, for instance with logical disjunction ∨ {\displaystyle \lor
Semiring
Algebraic structure used in logic
Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with least element 0 and
Heyting_algebra
Topics referred to by the same term
of operations on a set Two-element Boolean algebra, Boolean algebra whose underlying set has two elements Boolean ring Boolean (disambiguation) This disambiguation
Boolean algebra (disambiguation)
Boolean_algebra_(disambiguation)
Function returning one of only two values
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {−1,1})
Boolean_function
polynomial Boolean domain Complete Boolean algebra Interior algebra Two-element Boolean algebra Derivative algebra (abstract algebra) Free Boolean algebra Monadic
List of Boolean algebra topics
List_of_Boolean_algebra_topics
Mathematical topics based on the works of George Boole
values (usually "true" and "false") Boolean algebra, a logical calculus of truth values or set membership Boolean algebra (structure), a set with operations
Boolean
Technical treatment of Boolean algebras
Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued
Boolean algebras canonically defined
Boolean_algebras_canonically_defined
mathematics, a Boolean matrix is a matrix with entries from a Boolean algebra. When the two-element Boolean algebra is used, the Boolean matrix is called
Boolean_matrix
Topics referred to by the same term
semi-truck tractor unit ² (square in algebra), multiplying a number by itself 2 (algebra), the two-element Boolean algebra, for which Paul Halmos introduced
2_(disambiguation)
Example of a Semigroup
semilattice with two elements and the only non-null semigroup with zero of order two, also a monoid, and ultimately the two-element Boolean algebra; this is also
Semigroup_with_two_elements
Algebraic structure providing a semantics of Łukasiewicz logic
1] MV-algebra characterizes all possible MV-algebras parallels the well-known fact that identities holding in the two-element Boolean algebra hold in
MV-algebra
Index of articles associated with the same name
or Off, 1 or 0) referring to two-element Boolean algebra (the Boolean domain), e.g. Boolean-valued function or Boolean data type in mathematics: something
Boolean-valued
Reasoning by means of visual representations
existential graphs: alpha – isomorphic to sentential logic and the two-element Boolean algebra; beta – isomorphic to first-order logic with identity, with all
Diagrammatic_reasoning
Type of diagrammatic notation for propositional logic
existential graphs: alpha, isomorphic to propositional logic and the two-element Boolean algebra; beta, isomorphic to first-order logic with identity, with all
Existential_graph
Boolean algebra generated by a set with no relations beyond Boolean laws
free Boolean algebra is a Boolean algebra with a distinguished set of elements, called generators, such that: Each element of the Boolean algebra can be
Free_Boolean_algebra
Algebraic concept in measure theory, also referred to as an algebra of sets
every finite Boolean algebra can be represented as a power set – the power set of its set of atoms; each element of the Boolean algebra corresponds to
Field_of_sets
Boolean algebra with all operators and laws forming a complete logical system
mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound). Complete Boolean algebras are used to construct
Complete_Boolean_algebra
Mathematical ring whose elements are matrices
the Boolean semiring (the two-element Boolean algebra R = {0, 1} with 1 + 1 = 1), then Mn(R) is the semiring of binary relations on an n-element set with
Matrix_ring
Logical connective
Boolean algebra of propositional logic. Example of a 4-element Boolean algebra: the 4 divisors {1,2,3,6} of 6 with 1 as zero and 6 as unity element,
Converse_nonimplication
Algebraic structure in mathematics
An example is the ring of integers modulo 2. Every Boolean ring gives rise to a Boolean algebra, with ring multiplication corresponding to conjunction
Boolean_ring
English Mathematician (1923-2016)
algebra is essentially an elegant minimalist notation for the two-element Boolean algebra. One core aspect of the text is the 'observer dilemma' that arises
G._Spencer-Brown
Topics referred to by the same term
from a two-element set Boolean operation (Boolean algebra), a logical operation in Boolean algebra (AND, OR and NOT) Boolean operator (computer programming)
Boolean_operation
Overview of and topical guide to logic
Boolean algebra Free Boolean algebra Monadic Boolean algebra Residuated Boolean algebra Two-element Boolean algebra Modal algebra Derivative algebra (abstract
Outline_of_logic
Algebraic structure
what Boolean algebras are to set theory and ordinary propositional logic. Interior algebras form a variety of modal algebras. An interior algebra is an
Interior_algebra
Symbol connecting formulas in logic
from Boole's interpretation of logic as an elementary algebra over the two-element Boolean algebra; other notations include V {\displaystyle \mathrm {V}
Logical_connective
Computation modulo a fixed integer
Serial number arithmetic (a special case of modular arithmetic) Two-element Boolean algebra Topics relating to the group theory behind modular arithmetic:
Modular_arithmetic
Set theory concept
"true" and "false", but instead take values in some fixed complete Boolean algebra. Boolean-valued models were introduced by Dana Scott, Robert M. Solovay
Boolean-valued_model
Overview of and topical guide to algebraic structures
lattices, under their two operations. Heyting algebras are a special example of boolean algebras. Peano arithmetic Boundary algebra MV-algebra In computer science:
Outline of algebraic structures
Outline_of_algebraic_structures
Maximal proper filter
poset is a Boolean algebra. In this case, ultrafilters are characterized by containing, for each element x {\displaystyle x} of the Boolean algebra, exactly
Ultrafilter
Reasoning about equations with free variables
like the representation theorem for Boolean algebras and Stone duality fall under the umbrella of classical algebraic logic (Czelakowski 2003). Works in
Algebraic_logic
Property of operations
application. The concept of idempotence arises in a number of places in abstract algebra (in particular, in the theory of projectors and closure operators) and
Idempotence
Mathematical set of all subsets of a set
the Boolean algebra of the power set of a finite set. For infinite Boolean algebras, this is no longer true, but every infinite Boolean algebra can be
Power_set
Data having only values "true" or "false"
intended to represent the two truth values of logic and Boolean algebra. It is named after George Boole, who first defined an algebraic system of logic in the
Boolean_data_type
Class of formal logics
an arbitrary Boolean algebra; "true" corresponds to the maximal element of the algebra, and "false" corresponds to the minimal element. Intermediate
Classical_logic
Specific element of an algebraic structure
identity element of the addition of real numbers. This concept is used in algebraic structures such as groups and rings. The term identity element is often
Identity_element
Ideals in a Boolean algebra can be extended to prime ideals
In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement
Boolean_prime_ideal_theorem
Identities and relationships involving sets
Any set of sets closed under the set-theoretic operations forms a Boolean algebra with the join operator being union, the meet operator being intersection
Algebra_of_sets
Type of logical system
Quine. These algebras are all lattices that properly extend the two-element Boolean algebra. Tarski and Givant (1987) showed that the fragment of first-order
First-order_logic
In Boolean algebra, the inclusion relation a ≤ b {\displaystyle a\leq b} is defined as a b ′ = 0 {\displaystyle ab'=0} and is the Boolean analogue to the
Inclusion_(Boolean_algebra)
Set with operations obeying given axioms
operations that combine two elements of a set to produce a third element of the same set. These operations obey several algebraic laws. For example, a +
Algebraic_structure
Set whose pairs have minima and maxima
universal algebra. The class of lattices can be generalized to semilattices, and some notable subclasses of lattices are Heyting algebras, Boolean algebras, distributive
Lattice_(order)
Set of elements in any of some sets
given by union, intersection, and complementation, is a Boolean algebra. In this Boolean algebra, union can be expressed in terms of intersection and complementation
Union_(set_theory)
Algebraic structure with addition and multiplication
In mathematics, a ring is an algebraic structure consisting of a set with two binary operations typically called addition and multiplication and denoted
Ring_(mathematics)
True when either but not both inputs are true
description of a Boolean function as a polynomial in F 2 {\displaystyle \mathbb {F} _{2}} , using this basis, is called the function's algebraic normal form
Exclusive_or
Algebraic structure with an associative operation and an identity element
In abstract algebra, a monoid is a set equipped with an associative binary operation and an identity element. For example, the natural numbers with addition
Monoid
Vector space equipped with a bilinear product
it has an identity element with respect to the multiplication. The ring of real square matrices of order n forms a unital algebra since the identity matrix
Algebra_over_a_field
2-valued morphism is a homomorphism that sends a Boolean algebra B onto the two-element Boolean algebra 2 = {0,1}. It is essentially the same thing as an
2-valued_morphism
In mathematics, element that equals its square
of modules, and connected to homological properties of the ring. In Boolean algebra, the main objects of study are rings in which all elements are idempotent
Idempotent_(ring_theory)
Subset with finite complement
forms a Boolean algebra, which means that it is closed under the operations of union, intersection, and complementation. This Boolean algebra is the finite–cofinite
Cofiniteness
Pair of logical equivalences
In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid
De_Morgan's_laws
Product of a number by itself
A commutative ring in which every element is equal to its square (every element is idempotent) is called a Boolean ring; an example from computer science
Square_(algebra)
Theories in mathematical logic
axiom ¬0 = 1, to exclude the trivial algebra with one element. Tarski proved that the theory of Boolean algebras is decidable. We write x ≤ y as an abbreviation
List_of_first-order_theories
Concept in mathematical logic
functionally complete Boolean algebra. Algebra of sets – Identities and relationships involving sets Boolean algebra – Algebraic manipulation of "true"
Functional_completeness
Standard forms of Boolean functions
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form (CDNF), minterm canonical form, or Sum of Products (SoP
Canonical_normal_form
engineering. In 1935 he discovered the possible interpretation of Boolean algebra of logic in electro-mechanical relay circuits. He graduated from Moscow
Victor_Shestakov
Smallest integer n for which n equals 0 in a ring
have characteristic 0. The integers modulo n have characteristic n. Every Boolean ring has characteristic 2. The characteristic of a field is either 0 or
Characteristic_(algebra)
Elements in exactly one of two sets
as the neutral element of the group and every element in this group being its own inverse. The power set of any set becomes a Boolean ring, with symmetric
Symmetric_difference
Polish–American mathematician (1901–1983)
first-order logic what the two-element Boolean algebra is to classical sentential logic. This work culminated in the two monographs by Tarski, Henkin,
Alfred_Tarski
Boolean polynomials as sums of monomials
Algebraic normal form (ANF) is a representation of functions in boolean algebra. Formulas written in ANF are also known as ring sum normal form (RSNF
Algebraic_normal_form
Algebraic structure of set algebra
measure on X , {\displaystyle X,} the measure algebra of ( X , μ ) {\displaystyle (X,\mu )} is the Boolean algebra of all Borel sets modulo μ {\displaystyle
Σ-algebra
Encoded data represented in binary notation
Mathematical Analysis of Logic' that describes an algebraic system of logic, now known as Boolean algebra. Boole's system was based on binary, a yes-no,
Binary_code
importance because many algebraic structures are bounded lattices, including complete lattices, Heyting algebras, Boolean algebras, and others. A bounded
Bounded_lattice
Finite field of two elements
elements of GF(2) are seen as Boolean values, then the addition is the same as that of the logical XOR operation. Since each element equals its opposite, subtraction
GF(2)
these solutions. Pre-algebra Elementary algebra Boolean algebra Abstract algebra Linear algebra Universal algebra An algebraic equation is an equation
Outline_of_algebra
Algebraic ring without a multiplicative identity
Given two unital algebras A and B, an algebra homomorphism f : A → B is unital if it maps the identity element of A to the identity element of B. If
Rng_(algebra)
{\displaystyle {\bf {3}}} , or Boolean type, iff M {\displaystyle \mathbb {M} } is polynomially equivalent to a two-element Boolean algebra. M {\displaystyle \mathbb
Minimal_algebra
Bound lattice in which every element has a complement
in fact a Boolean algebra. A complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement
Complemented_lattice
Algebraic structure with addition, multiplication, and division
generated by an element x, as above, is an algebraic extension of E if and only if x is an algebraic element. That is to say, if x is algebraic, all other
Field_(mathematics)
Set whose elements all belong to another set
partial order on sets. In fact, the subsets of a given set form a Boolean algebra under the subset relation, in which the join and meet are given by
Subset
Theory of algebraic structures in general
algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures
Universal_algebra
Branch of mathematics
this development, such as Boolean algebra, vector algebra, and matrix algebra. Influential early developments in abstract algebra were made by the German
Algebra
Collection of mathematical objects
the subset itself as the additive inverse. The powerset is also a Boolean algebra for which the join ∨ {\displaystyle \lor } is the union ∪ {\displaystyle
Set_(mathematics)
Representation of natural numbers and other data types in lambda calculus
derive them and operations on them, from first principles Some interactive examples of Church numerals Lambda Calculus Live Tutorial: Boolean Algebra
Church_encoding
Axiom of set theory
basis. There is a vector space with two bases of different cardinalities. There is a free complete Boolean algebra on countably many generators. There
Axiom_of_choice
so that every Boolean algebra and every distributive lattice forms a median algebra. Birkhoff and Kiss showed that a median algebra with elements 0
Median_algebra
Method in mathematical logic
Fraïssé limit of the class of nontrivial finite Boolean algebras is the unique countable atomless Boolean algebra. The class K {\displaystyle \mathbf {K} }
Fraïssé_limit
Device performing a Boolean function
introduced switching circuit theory in a series of papers showing that two-valued Boolean algebra, which they discovered independently, can describe the operation
Logic_gate
In mathematics, an algebraic structure
general concept, include Boolean algebras, Heyting algebras, residuated Boolean algebras, relation algebras, and MV-algebras. Residuated semilattices
Residuated_lattice
Logical connective OR
will come.' Affirming a disjunct Boolean algebra (logic) Boolean algebra topics Boolean domain Boolean function Boolean-valued function Conjunction/disjunction
Logical_disjunction
Process in digital electronics and integrated circuit design
structures on an integrated circuit. In terms of Boolean algebra, the optimization of a complex Boolean expression is a process of finding a simpler one
Logic_optimization
Function that outputs either true or false
f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted
Boolean-valued_function
Mathematical problem
In mathematical logic, Tarski's high school algebra problem was a question posed by Alfred Tarski. It asks whether there are identities involving addition
Tarski's high school algebra problem
Tarski's_high_school_algebra_problem
Branch of mathematics
establish other connections to algebra. An example is given by the correspondence between Boolean algebras and Boolean rings. Other issues are concerned
Order_theory
Vector operation
algebra, the outer product of two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in
Outer_product
In mathematics, vector subspace
operation does not turn the lattice of subspaces into a Boolean algebra (nor a Heyting algebra).[citation needed] Most algorithms for dealing with subspaces
Linear_subspace
Property involving two mathematical operations
polynomials, matrices, rings, and fields. It is also encountered in Boolean algebra and mathematical logic, where each of the logical and (denoted ∧ {\displaystyle
Distributive_property
Nonempty, upper-bounded, downward-closed subset
reserved for Boolean algebras, where a maximal filter (ideal) is a filter (ideal) that contains exactly one of the elements {a, ¬a}, for each element a of the
Ideal_(order_theory)
Idempotent semiring endowed with a closure operator
obtain a Kleene algebra. Every Boolean algebra with operations ∨ {\displaystyle \lor } and ∧ {\displaystyle \land } turns into a Kleene algebra if we use ∨
Kleene_algebra
Algebraic structure with a binary operation
In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with
Magma_(algebra)
Function that is its own inverse
varieties of algebras. For instance, involutive negation characterizes Boolean algebras among Heyting algebras. Correspondingly, classical Boolean logic arises
Involution_(mathematics)
Number that, when added to the original number, yields the additive identity
an algebraic structure defined under addition ( S , + ) {\displaystyle (S,+)} with an additive identity e ∈ S {\displaystyle e\in S} , an element x ∈
Additive_inverse
Logical connective AND
And-inverter graph AND gate Bitwise AND Boolean algebra Boolean conjunctive query Boolean domain Boolean function Boolean-valued function Conjunction/disjunction
Logical_conjunction
Mathematical table used in logic
mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional
Truth_table
Value indicating the relation of a proposition to truth
done in algebraic semantics. The algebraic semantics of intuitionistic logic is given in terms of Heyting algebras, compared to Boolean algebra semantics
Truth_value
Branch of mathematics
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations
Abstract_algebra
TWO ELEMENT-BOOLEAN-ALGEBRA
TWO ELEMENT-BOOLEAN-ALGEBRA
Boy/Male
Czechoslovakian, Danish, German, Greek, Latin, Polish
Giving Mercy; Mild; Merciful
Male
English
English surname transferred to forename use, derived from Latin Clemens or Clement, CLEMENTS means "gentle and merciful."
Male
Welsh
Welsh form of English Tom, TWM means "twin."
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'.
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 Danish
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
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.
Biblical
mild; good; merciful
Male
Hungarian
Hungarian form of Greek Klementos, KELEMEN means "gentle and merciful."
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Boy/Male
English American Biblical Latin
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.
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."
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
Turkish
Turkish name derived from the marines in the Ottoman military called Leventler ("the Levents"), LEVENT means "the lions."
Boy/Male
African, American, Australian, British, Chinese, Christian, Danish, English, French, German, Greek, Indian, Jamaican, Latin, Swedish, Swiss
Merciful; Mild; Gentle; Giving Mercy; Merciful in French
Male
Italian
 Italian, Portuguese and Spanish form of Latin Clementius, CLEMENTE means "gentle and merciful."
TWO ELEMENT-BOOLEAN-ALGEBRA
TWO ELEMENT-BOOLEAN-ALGEBRA
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : variant spelling of Pullen.
Boy/Male
Arabic, Muslim
Chosen; Name of a Sahabi (RA)
Girl/Female
French American Scottish
God is gracious.
Girl/Female
Hindu
Sharp
Surname or Lastname
English
English : from a pet form of Pott, a short form of Philpott.
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
Ocean; Related to Sea; Wave; Born in the Ocean; Beautiful; Goddess Durga
Boy/Male
British, Christian, English, French
Shining Pledge; Bright
Girl/Female
Muslim
This was the name of a very
Boy/Male
Tamil
Thathathan | ததாதாந
Lord Buddha
Girl/Female
Muslim
Sacrifice
TWO ELEMENT-BOOLEAN-ALGEBRA
TWO ELEMENT-BOOLEAN-ALGEBRA
TWO ELEMENT-BOOLEAN-ALGEBRA
TWO ELEMENT-BOOLEAN-ALGEBRA
TWO ELEMENT-BOOLEAN-ALGEBRA
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.
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.
To overlay or coat with cement; as, to cement a cellar bottom.
a.
Made of wool; consisting of wool; as, woolen goods.
v. t.
To constitute; to make up with elements.
n.
The four elements were, air, earth, water, and fire
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.
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.
a.
Of or pertaining to wool or woolen cloths; as, woolen manufactures; a woolen mill; a woolen draper.
n.
The simplest or fundamental principles of any system in philosophy, science, or art; rudiments; as, the elements of geometry, or of music.
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.
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.
Constituting one of eleven parts into which a thing is divided; as, the eleventh part of a thing.
v. t.
To compound of elements or first principles.
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.
Pertaining to the elements, first principles, and primary ingredients, or to the four supposed elements of the material world; as, elemental air.
n.
The quotient of a unit divided by eleven; one of eleven equal parts.
a.
Next after the tenth; as, the eleventh chapter.