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See searches and references containing IDENTITY ELEMENT!IDENTITY ELEMENT
Specific element of an algebraic structure
In mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied
Identity_element
Algebraic ring without a multiplicative identity
multiplicative identity. The term rng is meant to suggest that it is a ring without i, that is, without the requirement for an identity element. There is no
Rng_(algebra)
Topics referred to by the same term
up identity in Wiktionary, the free dictionary. Identity may refer to: Identity document Identity (philosophy) Identity (social science) Identity (mathematics)
Identity
Function that returns its argument unchanged
{\displaystyle X} is always the same as the input element x {\displaystyle x} in the domain X {\displaystyle X} . The identity function on X {\displaystyle X} is clearly
Identity_function
Value that makes no change when added
mathematics, the additive identity of a set that is equipped with the operation of addition is an element which, when added to any element x in the set, yields
Additive_identity
Algebraic structure
monoid. A semigroup without an identity element can be easily turned into a monoid by just adding an identity element. Consequently, monoids are studied
Semigroup
Algebraic structure with an associative operation and an identity element
an identity element. For example, the natural numbers with addition form a monoid, the identity element being 0. Monoids are semigroups with identity. Such
Monoid
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)
Any one of the distinct objects that make up a set in set theory
{\displaystyle \ni } is a subset of P(U) × U. Identity element Singleton (mathematics) Weisstein, Eric W. "Element". mathworld.wolfram.com. Retrieved 2020-08-10
Element_of_a_set
Theorem relating a group with the image and kernel of a homomorphism
preservation of the group operation, and their mapping of the identity element to the identity element. We need to show that if f : G → H {\displaystyle f:G\to
Fundamental theorem on homomorphisms
Fundamental_theorem_on_homomorphisms
Property of operations
(G,\cdot )} , the identity element e {\displaystyle e} is the only idempotent element. Indeed, if x {\displaystyle x} is an element of G {\displaystyle
Idempotence
Structure-preserving map between two algebraic structures of the same type
homomorphism maps the identity element of the first group to the identity element of the second group, and maps the inverse of an element of the first group
Homomorphism
Arithmetic operation
the number. In other words, zero is the identity element for addition, and is also known as the additive identity. In symbols, for every a {\displaystyle
Addition
Generalization of additive and multiplicative inverses
inverse element generalises the concepts of opposite (−x) and reciprocal (1/x) of numbers. Given an operation denoted here ∗, and an identity element denoted
Inverse_element
Mathematical proofs of basic properties of addition of the natural numbers
The base case b = 0 follows immediately from the identity element property (0 is an additive identity), which has been proved above: a + 0 = a = 0 + a
Proofs involving the addition of natural numbers
Proofs_involving_the_addition_of_natural_numbers
Repeated application of an operation to a sequence
has a unique right identity. If f is associative, then Fl equals Fr, and we can simply write F. Moreover, if an identity element e exists, then it is
Iterated_binary_operation
Net in a normed algebra
approximate identity is a net in a Banach algebra or ring (generally without an identity) that acts as a substitute for an identity element. A right approximate
Approximate_identity
Algebraic structure with addition and multiplication
distributive over the addition operation, and has a multiplicative identity element. Some authors apply the term ring to a further generalization, often
Ring_(mathematics)
Set with operations obeying given axioms
common existential axioms. Identity element A binary operation ∗ {\displaystyle *} has an identity element if there is an element e such that x ∗ e = x and
Algebraic_structure
Cardinality of a mathematical group, or of the subgroup generated by an element
the order of an element a of a group, is thus the smallest positive integer m such that am = e, where e denotes the identity element of the group, and
Order_(group_theory)
Square matrix with ones on the main diagonal and zeros elsewhere
identity matrix serves as the multiplicative identity of the matrix ring of all n × n {\displaystyle n\times n} matrices, and as the identity element
Identity_matrix
Magma obeying the Latin square property
associative and identity element properties are optional. In fact, a nonempty associative quasigroup is a group. A quasigroup that has an identity element is called
Quasigroup
Algebraic structure with a binary operation
these commutative magmas are not associative; nor do they have an identity element. This morphism of magmas has been used in economics since 1863 when
Magma_(algebra)
Group that is a topological space with continuous group operations
commutative topological group G of the identity element, there exists a symmetric neighborhood M of the identity element such that M−1 M ⊆ N, where note that
Topological_group
ELEMENT coord_sys (#PCDATA) <!ELEMENT datum (#PCDATA) <!ELEMENT format (#PCDATA)> <!ELEMENT lat (#PCDATA)> <!ELEMENT ll_point (lat, long)> <!ELEMENT long
Mobile_Location_Protocol
Branch of mathematics
S is linearly dependent (that is not linearly independent), then some element w of S is in the span of the other elements of S, and the span would remain
Linear_algebra
Vector space equipped with a bilinear product
nonassociative, satisfying the Jacobi identity instead. An algebra is unital or unitary if it has an identity element with respect to the multiplication
Algebra_over_a_field
Branch of elementary mathematics
another element. For example, the identity element of addition is 0 since any sum of a number and 0 results in the same number. The inverse element is the
Arithmetic
Branch of mathematics
operation has an identity element or a neutral element if one element e exists that does not change the value of any other element, i.e., if a ∘ e
Algebra
Number used for counting
+ ) {\displaystyle (\mathbb {N} ,+)} is a commutative monoid with identity element 0. It is a free monoid on one generator. This commutative monoid satisfies
Natural_number
Mathematical set containing no elements
negative infinity is the identity element for the maximum and supremum operators, while positive infinity is the identity element for the minimum and infimum
Empty_set
Concept in group theory
largest connected subgroup of G containing the identity element. In point set topology, the identity component of a topological group G is the connected
Identity_component
Semiring with minimum and addition replacing addition and multiplication
multiplication respectively. The identity element for ⊕ {\displaystyle \oplus } is + ∞ {\displaystyle +\infty } , and the identity element for ⊗ {\displaystyle \otimes
Tropical_semiring
Integer
of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less
−1
Generalizations of '"`UNIQ--math-00000046-QINU`"' in algebraic structures
on the context. An additive identity is the identity element in an additive group or monoid. It corresponds to the element 0 {\displaystyle 0} such that
Zero_element
Group that is also a differentiable manifold with group operations that are smooth
an element v of the tangent space at the identity is the vector field defined by v^g = Lg*v. This identifies the tangent space TeG at the identity with
Lie_group
Cryptographic algorithm for digital signatures
follows: Check that Q A {\displaystyle Q_{A}} is not equal to the identity element O, and its coordinates are otherwise valid. Check that Q A {\displaystyle
Elliptic Curve Digital Signature Algorithm
Elliptic_Curve_Digital_Signature_Algorithm
Property of some binary operations
operation, and let 0 {\displaystyle 0} be the identity element for + {\displaystyle +} . The Jacobi identity is x × ( y × z ) + y × ( z × x ) + z
Jacobi_identity
Algebraic structure used in analysis
more detail: for any Lie group, the multiplication operation near the identity element 1 is commutative to first order. In other words, every Lie group G
Lie_algebra
{\displaystyle (M,V)} there exists an identity element P {\displaystyle P} for the symplectic sum. Such identity elements have been used both in establishing
Symplectic_sum
Elements taken to zero by a homomorphism
contains the identity if and only if the homomorphism is injective, that is if the inverse image of every element consists of a single element. This means
Kernel_(algebra)
Mathematical function between groups that preserves multiplication structure
From 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
Set of elements that commute with every element of a group
Z(G) contains the identity element of G, because it commutes with every element of g, by definition: eg = g = ge, where e is the identity; If x and y are
Center_(group_theory)
Theorem on the orders of subgroups
the order of any element a of a finite group (i.e. the smallest positive integer number k with ak = e, where e is the identity element of the group) divides
Lagrange's theorem (group theory)
Lagrange's_theorem_(group_theory)
Symbol representing a mathematical object
higher degree polynomials. Even the symbol 1 has been used to denote an identity element of an arbitrary field. These two notions are used almost identically
Variable_(mathematics)
Algebraic curve in mathematics
with respect to which it is an abelian group – and O serves as the identity element. If y2 = P(x), where P is any polynomial of degree three in x with
Elliptic_curve
Group obtained by aggregating similar elements of a larger group
For a congruence relation on a group, the equivalence class of the identity element is always a normal subgroup of the original group, and the other equivalence
Quotient_group
Subgroup invariant under conjugation
H {\displaystyle \phi :G\to H} whose fibers form a group where the identity element is N {\displaystyle N} and multiplication of any two fibers ϕ − 1 (
Normal_subgroup
Theory of algebraic structures in general
(x ∗ y) ∗ z; formally: ∀x,y,z. x∗(y∗z)=(x∗y)∗z. Identity element: There exists an element e such that for each element x, one has e ∗ x = x = x ∗ e; formally:
Universal_algebra
1969 non-fiction book by G. Spencer-Brown
identity element of that operation; or to put it in another way, an operand that is missing could be regarded as acting by default like the identity element)
Laws_of_Form
Group that has only one element
single element. All such groups are isomorphic, so one often speaks of the trivial group. The single element of the trivial group is the identity element and
Trivial_group
Existence of group elements of prime order
contains an element of order p. That is, there is x in G such that p is the smallest positive integer with xp = e, where e is the identity element of G. It
Cauchy's theorem (group theory)
Cauchy's_theorem_(group_theory)
Mathematical term
{\mathfrak {g}}=T_{e}G} is the tangent space at the origin e (e being the identity element of the group G). Since Ψ g {\displaystyle \Psi _{g}} is a Lie group
Adjoint_representation
Group of 𝑛 × 𝑛 invertible matrices
inverse of an invertible matrix is invertible, with the identity matrix as the identity element of the group. The group is so named because the columns
General_linear_group
Non-abelian group of order eight
{e}}^{2}=e,\;i^{2}=j^{2}=k^{2}=ijk={\bar {e}}\rangle ,} where e is the identity element and e commutes with the other elements of the group. These relations
Quaternion_group
Number
denote a zero element, which is the identity element for addition (if defined on the structure under consideration) and an absorbing element for multiplication
0
Skeletonized version of algebraic geometry
multiplication respectively. The identity element for ⊕ {\displaystyle \oplus } is + ∞ {\displaystyle +\infty } , and the identity element for ⊗ {\displaystyle \otimes
Tropical_geometry
Subset of a group that forms a group itself
trivial subgroup of any group is the subgroup {e} consisting of just the identity element. A proper subgroup of a group G is a subgroup H which is a proper subset
Subgroup
Special type of element of a set
absorbing element with any element of the set is the absorbing element itself. In semigroup theory, the absorbing element is called a zero element because
Absorbing_element
Approach to public-key cryptography
elliptic curves, is an abelian group, with the point at infinity as an identity element. The structure of the group is inherited from the divisor group of
Elliptic-curve_cryptography
Operation in group theory
product (also known as splitting extension). Given a group G with identity element e, a subgroup H, and a normal subgroup N ◃ G {\displaystyle N\triangleleft
Semidirect_product
Representation of groups by permutations
since T(g) = idG (the identity element of Sym(G)) implies that g ∗ x = x for all x in G, and taking x to be the identity element e of G yields g = g ∗
Cayley's_theorem
Commutative group (mathematics)
{\displaystyle (a\cdot b)\cdot c=a\cdot (b\cdot c)} holds. Identity element There exists an element e {\displaystyle e} in A {\displaystyle A} , such that
Abelian_group
(sending an element g to conjugation by g), is an isomorphism: injectivity implies that only conjugation by the identity element is the identity automorphism
Complete_group
just as the tangent space of the identity element of a Lie group forms a Lie algebra, the tangent space of the identity of a smooth Moufang loop forms a
Malcev_algebra
1997 film by Luc Besson
The Fifth Element (French: Le Cinquième Élément) is a 1997 English-language French science fiction-action film conceived and directed by Luc Besson, and
The_Fifth_Element
Group whose operation is a composition of braids
The above composition of braids is indeed a group operation. The identity element is the braid consisting of four parallel horizontal strands, and the
Braid_group
Graph structure studied in group theory
power of a must be the group identity, which we denote either as e or 1; the lowest such power is the order of the element a, the number of distinct elements
Cycle_graph_(algebra)
Topics referred to by the same term
particle without electrical charge Neutral element or identity element, in mathematics, a special element with respect to a binary operation, such that
Neutral
Arithmetical operation
the inclusion of an identity element and inverses. A simple example is the set of non-zero rational numbers. Here the identity element is 1, as opposed to
Multiplication
Map from a Lie algebra to its Lie group
{\mathfrak {g}}} be its Lie algebra (thought of as the tangent space to the identity element of G {\displaystyle G} ). The exponential map is a map exp : g → G
Exponential_map_(Lie_theory)
Finite field of two elements
addition has an identity element (0) and an inverse for every element; multiplication has an identity element (1) and an inverse for every element but 0; addition
GF(2)
Type of group in mathematics
dimension n has two connected components. The one that contains the identity element is a normal subgroup, called the special orthogonal group, and denoted
Orthogonal_group
Equivalence relation in algebra
For a congruence on a group, the equivalence class containing the identity element is always a normal subgroup, and the other equivalence classes are
Congruence_relation
Algebraic structure
commutative semigroup is a medial magma, and a medial magma has an identity element if and only if it is a commutative monoid. The "only if" direction
Medial_magma
Arithmetic operation
without an identity element and hence without inverses. "Division" in the sense of "cancellation" can be done in any magma by an element with the cancellation
Division_(mathematics)
Mathematical abelian group
which each element is self-inverse (composing it with itself produces the identity) and in which composing any two of the three non-identity elements produces
Klein_four-group
Correspondence between topics in Lie theory
elements of the Hopf algebra of distributions on G with support at the identity element; for this, see Related constructions below. Suppose G is a closed subgroup
Lie group–Lie algebra correspondence
Lie_group–Lie_algebra_correspondence
Mathematical set of all subsets of a set
with the operation of symmetric difference (with the empty set as the identity element and each set being its own inverse), and a commutative monoid when
Power_set
Type of mathematical group
is residually finite or finitely approximable if for every element g that is not the identity in G there is a homomorphism h from G to a finite group, such
Residually_finite_group
Topics referred to by the same term
nutrients and drugs Unit number, the number 1 Unit, identity element Unit (ring theory), an element that is invertible with respect to ring multiplication
Unit
Natural number
A. (ed.). "Sequence A057771 (Number of loops (quasigroups with an identity element) of order n)". The On-Line Encyclopedia of Integer Sequences. OEIS
109_(number)
Algebraic structure in linear algebra
eigenvalue λ. Equivalently, v is an element of the kernel of the difference f − λ · Id (where Id is the identity map V → V). If V is finite-dimensional
Vector_space
Operation on the subsets of a set
operation, often called multiplication, with an identity element, such that every element has an inverse element. Here, the auxiliary operations are the nullary
Closure_(mathematics)
Set with exactly one element
Any singleton admits a unique group structure (the unique element serving as identity element). These singleton groups are zero objects in the category
Singleton_(mathematics)
Quality of zero being an even number
as even − even = even, require 0 to be even. Zero is the additive identity element of the group of even integers, and it is the starting case from which
Parity_of_zero
Branch of mathematics that studies abstract algebraic structures
2)\quad g_{1}\cdot (g_{2}\cdot v)=(g_{1}g_{2})\cdot v} where e is the identity element of G and g1g2 is the group product in G. The definition for associative
Representation_theory
Relationship between two sets, defined by a set of ordered pairs
(also denoted by R; S) is the relative product of R and S. The identity element is the identity relation. The order of R and S in the notation S ∘ R, used
Relation_(mathematics)
Center of the inscribed circle of a triangle
X(1), in Clark Kimberling's Encyclopedia of Triangle Centers, and the identity element of the multiplicative group of triangle centers. For polygons with
Incenter
Mathematical concept
associative. Identity The direct product has an identity element, namely (1G, 1H), where 1G is the identity element of G and 1H is the identity element of H.
Direct_product_of_groups
Partial order with joins
meet-semilattice, the identity 1 is the greatest element of S. Similarly, an identity element in a join semilattice is a least element. An order theoretic
Semilattice
How spheres of various dimensions can wrap around each other
makes this set of equivalence classes into an abelian group whose identity element is the class of any constant map, i.e. a one that maps all of Si to
Homotopy_groups_of_spheres
Point, line, or plane about which a molecule or crystal is symmetric
points that remain unchanged make up a plane of symmetry. The identity symmetry element is found in all objects and is denoted E. It corresponds to an
Symmetry_element
Abelian group with no non-trivial torsion elements
group in which the group operation is commutative and the identity element is the only element with finite order. While finitely generated abelian groups
Torsion-free_abelian_group
Certain generalizations of groups
"group multiplication") e : 1 → G (thought of as the "inclusion of the identity element") inv : G → G (thought of as the "inversion operation") such that the
Group_object
Each word in S represents an element of G, namely the product of the expression. By convention, the unique identity element can be represented by the empty
Word_(group_theory)
Problem of inverting exponentiation in groups
operation by multiplication and its identity element by 1 {\displaystyle 1} . Let b {\displaystyle b} be any element of G {\displaystyle G} . For any positive
Discrete_logarithm
Mathematical group that can be generated as the set of powers of a single element
some element g, called a generator of G. For a finite cyclic group G of order n we have G = {e, g, g2, ... , gn−1}, where e is the identity element and
Cyclic_group
Set of finitely supported functions from a group to a ring
the multiplicative identity element of C[G] is 1⋅1G where the first 1 comes from C and the second from G. The additive identity element is zero. When G is
Group_ring
Mathematical form
has the value of 1 (the identity element of multiplication), just like the empty sum has the value of 0 (the identity element of addition). However, the
Product_(mathematics)
IDENTITY ELEMENT
IDENTITY ELEMENT
Surname or Lastname
English and Scottish
English and Scottish : habitational name from any of the numerous and widespread places so called. The majority of these are named with Old English middel ‘middle’ + tūn ‘enclosure’, ‘settlement’; a smaller group, with examples in Cumbria, Kent, Northamptonshire, Northumbria, Nottinghamshire, and Staffordshire, have as their first element Old English mylen ‘mill’.
Boy/Male
Indian, Sanskrit
Tendency to Identify Oneself with External Phenomena
Girl/Female
Muslim
Identity
Boy/Male
Muslim
Identity
Surname or Lastname
Americanized spelling of Swedish Ap(p)elberg, an ornamental name composed of the elements apel ‘apple tree’ + berg ‘mountain’.English
Americanized spelling of Swedish Ap(p)elberg, an ornamental name composed of the elements apel ‘apple tree’ + berg ‘mountain’.English : the surname Applebury is recorded in England in the 19th century, perhaps a habitational name from a lost place.
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : habitational name from a place in northern France, of which the identity is not clear. It is probably Sainville in Eure-et-Loire, so called from Old French saisne ‘Saxon’ + ville ‘settlement’.
Boy/Male
Arabic, Gujarati, Hindu, Indian, Kannada, Muslim
Identity
Girl/Female
Tamil
Higher, North the direction, Name of a start (Princess of Virata, pupil of Arjuna as Brihhannala (his disguised identity as the eunuch dance teacher during the Pandavas final year of exile).)
Girl/Female
Hindu, Indian
God Like; All Pervading Formless Entity
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Punjabi, Sikh, Sindhi, Tamil, Telugu
Glories; Love; Identity; Pride
Surname or Lastname
English (chiefly Gloucestershire and Worcestershire)
English (chiefly Gloucestershire and Worcestershire) : variant of Millward.French (northern) : from a Germanic personal name composed of the elements mil ‘good’, ‘gracious’ + hard ‘hardy’, ‘brave’, ‘strong’.Southern French : from a variant spelling of Occitan milhar ‘millet field’ (from mil ‘millet’).
Girl/Female
Indian
Identity
Surname or Lastname
English
English : metonymic occupational name for a felt maker, from Old English felt ‘felt’.Said to be an Americanized or Germanized spelling of a Hungarian name, of uncertain identity.
Surname or Lastname
Partial translation of Swedish Sjöberg, an ornamental name composed of the elements sjö ‘sea’ + berg ‘mountain’, ‘hill’.English
Partial translation of Swedish Sjöberg, an ornamental name composed of the elements sjö ‘sea’ + berg ‘mountain’, ‘hill’.English : from a Middle English form of an Old English feminine personal name, Sǣburh, composed of the elements sǣ ‘sea’ + burh ‘fortified place’.Possibly also English : habitational name from Seaborough in Dorset (from Old English seofon ‘seven’ + beorg ‘hill’, ‘burial mound’) or possibly from Seaborough Hall in Essex.
Surname or Lastname
English
English : variant of Mills.Dutch : habitational name from Milheeze in the province of North Brabant.Dutch : from a short form of the personal name Amilius or Amelis (Latinized forms of a Germanic name with the initial element amal ‘strength’, ‘vigor’) or of the Latin personal name Aemilius (see Milian).
Boy/Male
Arabic, Muslim
One who can Identify Between Truth and Falsehood
Girl/Female
Hindu
Higher, North the direction, Name of a start (Princess of Virata, pupil of Arjuna as Brihhannala (his disguised identity as the eunuch dance teacher during the Pandavas final year of exile).)
Surname or Lastname
English and Scottish
English and Scottish : habitational name from any of the places so called. In over thirty instances from many different areas, the name is from Old English midel ‘middle’ + tūn ‘enclosure’, ‘settlement’. However, Middleton on the Hill near Leominster in Herefordshire appears in Domesday Book as Miceltune, the first element clearly being Old English micel ‘large’, ‘great’. Middleton Baggot and Middleton Priors in Shropshire have early spellings that suggest gem̄ðhyll (from gem̄ð ‘confluence’ + hyll ‘hill’) + tūn as the origin.A Scottish family of this name derives it from lands at Middleto(u)n near Kincardine. The Scottish physician Peter Middleton practiced in New York City after 1752 and was one of the founders of the medical school at King's College (now Columbia University) in 1767. One of the earliest of the Charleston, SC, Middleton family of prominent legislators was Arthur Middleton, born in Charleston in 1681.
Girl/Female
Arabic
Entity; Strong Existence
Girl/Female
African, American, Arabic, Australian, Gujarati, Indian, Jain, Japanese, Muslim, Sanskrit, Swahili, Tamil
Name; One's Self; The Victorious; Named Child; Identity
IDENTITY ELEMENT
IDENTITY ELEMENT
Male
Irish
Rare Irish variant form of German Herbert, HARBIN means "bright army."
Girl/Female
Gujarati, Indian, Kannada, Sanskrit
Heavenly Jewel
Girl/Female
Hindu, Indian, Tamil
Love; A Mark of Love
Girl/Female
Hindu, Indian, Traditional
Brindavan Friend of Radha
Boy/Male
Muslim
Obedient, Willing
Girl/Female
Muslim
Awake, Alert
Girl/Female
Tamil
Boy/Male
Hindu
A pleasure garden
Girl/Female
Hindu
Shailee means style
Girl/Female
Muslim
Bright, Shining, Pearl-like
IDENTITY ELEMENT
IDENTITY ELEMENT
IDENTITY ELEMENT
IDENTITY ELEMENT
IDENTITY ELEMENT
adv.
In an identical manner; with respect to identity.
pl.
of Identity
n.
Same as Identism.
imp. & p. p.
of Identify
n.
Sameness of name or designation; identity in relations.
n.
An identical equation.
pl.
of Entity
pl.
of Ideality
p. pr. & vb. n.
of Identify
n.
The doctrine taught by Schelling, that matter and mind, and subject and object, are identical in the Absolute; -- called also the system / doctrine of identity.
v. t.
To mistake for another; to identify falsely.
n.
The state or quality of being identical, or the same; sameness.
n.
A rare metallic element of doubtful identity.
adv.
In a consubstantial manner; with identity of substance or nature.
v. t.
To make to be the same; to unite or combine in such a manner as to make one; to treat as being one or having the same purpose or effect; to consider as the same in any relation.
n.
The condition of being the same with something described or asserted, or of possessing a character claimed; as, to establish the identity of stolen goods.
v. t.
To establish the identity of; to prove to be the same with something described, claimed, or asserted; as, to identify stolen property.
n.
Thickness; density; compactness.
n.
An identity or union of substance.
v. i.
To become the same; to coalesce in interest, purpose, use, effect, etc.