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Mathematical logic concept
In computability theory, a set S of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidable
Computably_enumerable_set
Study of computable functions and Turing degrees
every computably enumerable set is many-one reducible to the halting problem, and thus the halting problem is the most complicated computably enumerable set
Computability_theory
Ordered listing of items in collection
countable sets. However it is also often used for computably enumerable sets, which are the countable sets for which an enumeration function can be computed with
Enumeration
Set with algorithmic membership test
both computably enumerable(c.e.). The preimage of a computable set under a total computable function is computable. The image of a computable set under
Computable_set
{\mathcal {O}}} ; and given any notation for an ordinal, there is a computably enumerable set of notations that contains one element for each smaller ordinal
Kleene's_O
Mathematical function that can be computed by a program
if n is in the set. Thus a set is computably enumerable if and only if it is the domain of some computable function. The word enumerable is used because
Computable_function
Formal language
recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable subset
Recursively enumerable language
Recursively_enumerable_language
Solution of some Diophantine equation
states that a set of integers is Diophantine if and only if it is computably enumerable. A set of integers S is computably enumerable if and only if
Diophantine_set
Theorem in computability theory
{\displaystyle \Sigma _{n+1}^{0}} if and only if B {\displaystyle B} is computably enumerable by an oracle Turing machine with an oracle for ∅ ( n ) {\displaystyle
Post's_theorem
In computability theory, a maximal set is a coinfinite computably enumerable subset A of the natural numbers such that for every further computably enumerable
Maximal set (computability theory)
Maximal_set_(computability_theory)
Halting probability of a random computer program
recognize. The domain of any universal computable function is a computably enumerable set but never a computable set. The domain is always Turing equivalent
Chaitin's_constant
In computability theory, the assignment of natural numbers to a set of objects
same computably enumerable set under W. A numbering is total if it is a total function. If the domain of a partial numbering is computably enumerable then
Numbering (computability theory)
Numbering_(computability_theory)
Limitative results in mathematical logic
Saul Kripke. Boolos's proof proceeds by constructing, for any computably enumerable set S of true sentences of arithmetic, another sentence which is true
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
In computability theory, a Friedberg numbering is a computable numbering (enumeration) of the set of all computably enumerable sets that has no repetitions:
Friedberg_numbering
Method of comparing problems by transforming one into another in computability theory
for a non-computable, computably enumerable set that the halting problem could not be Turing reduced to. As he could not construct such a set in 1944,
Reduction (computability theory)
Reduction_(computability_theory)
Whether a decision problem has an effective method to derive the answer
consequence of, and thus a member of, the theory. Every complete computably enumerable first-order theory is decidable. An extension of a decidable theory
Decidability_(logic)
In computability theory, a subset of the natural numbers is called simple if it is computably enumerable (c.e.) and co-infinite (i.e. its complement is
Simple_set
Attempt to formalize all of mathematics, based on a finite set of axioms
complete, consistent extension of even Peano arithmetic based on a computably enumerable set of axioms. A theory such as Peano arithmetic cannot even prove
Hilbert's_program
Solovay). Informally, a computably enumerable real set A {\displaystyle A} is s-reducible to another computably enumerable real set B {\displaystyle B} if
Enumeration_reducibility
Theorem that arithmetical truth cannot be defined in arithmetic
arithmetic defining the set of codes for arithmetic sentences, and for provable arithmetic sentences (a computably enumerable set). The undefinability theorem
Tarski's undefinability theorem
Tarski's_undefinability_theorem
Russian mathematician and computer scientist
Hilary Putnam had shown that this suffices to prove that every computably enumerable set is Diophantine, a result which solves Hilbert's tenth problem
Yuri_Matiyasevich
Formula whose values are the prime numbers
matter of curiosity than of practical use. Because the set of primes is a computably enumerable set, by Matiyasevich's theorem, it can be obtained from a
Formula_for_primes
Branch of mathematics that studies sets
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any
Set_theory
Functions in computability theory
Grzegorczyk hierarchy. This implies in particular that every computably enumerable set is enumerable by some E 0 {\displaystyle {\mathcal {E}}^{0}} -function
Grzegorczyk_hierarchy
Concept in computability theory
In computability theory, two disjoint sets of natural numbers are called computably inseparable or recursively inseparable if they cannot be "separated"
Computably_inseparable
Mathematical logician and philosopher
but unprovable statement. That is, for any computably enumerable set of axioms for arithmetic (that is, a set that can in principle be printed out by an
Kurt_Gödel
Type of set in mathematics
Kučera and Terwijn. They built a computably enumerable set that is low for Martin-Löf-randomness but not computable. Their cost function was adaptive
K-trivial_set
On solvability of Diophantine equations
making the notion of recursive enumerability perfectly rigorous. It is evident that Diophantine sets are recursively enumerable (also known as semi-decidable)
Hilbert's_tenth_problem
Limit of a uniformly computable sequence of functions
As 0 ′ {\displaystyle 0'} is a [computably enumerable] set, it must be computable in the limit itself as the computable function can be defined r ^ ( x
Computation_in_the_limit
Classes of partial recursive functions
{\displaystyle W_{e}} be a computable enumeration of all c.e. sets. Let A {\displaystyle {\mathcal {A}}} be a class of partial computable functions. If A = {
Index_set_(computability)
Collection of mathematical objects
of a possibly larger set. Roster or enumeration notation is a notation introduced by Ernst Zermelo in 1908 that specifies a set by listing its elements
Set_(mathematics)
Yes-or-no question that cannot ever be solved by a computer
semi-decidable, solvable, or provable if A is a recursively enumerable set. In computability theory, the halting problem is a decision problem which can
Undecidable_problem
Standard system of axiomatic set theory
In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in
Zermelo–Fraenkel_set_theory
Axioms for the natural numbers
Hilbert's tenth problem, whose proof implies that all computably enumerable sets are diophantine sets, and thus definable by existentially quantified formulas
Peano_axioms
Fractal named after mathematician Benoit Mandelbrot
set is not computable, but its complement is computably enumerable. Many simple objects (e.g., the graph of exponentiation) are also not computable in
Mandelbrot_set
Measure of unsolvability
degree is called recursively enumerable (r.e.) or computably enumerable (c.e.) if it contains a recursively enumerable set. Every r.e. degree is below
Turing_degree
Mathematical set containing no elements
the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories
Empty_set
Set of the elements not in a given subset
In set theory, the complement of a set A, often denoted by A c {\displaystyle A^{c}} (or A′), is the set of elements not in A. When all elements in the
Complement_(set_theory)
Set of elements common to all of some sets
In set theory, the intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B , {\displaystyle A\cap B,} is the set containing
Intersection_(set_theory)
Informal set theories
Naive set theory is any of several set theories used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are defined
Naive_set_theory
Diagram that shows all possible logical relations between a collection of sets
delimits a set interleaves with previous curves, starting with the three-circle diagram. Venn's construction for four sets (use Gray code to compute, the digit
Venn_diagram
Computation model defining an abstract machine
recursively enumerable language. The Turing machine can equivalently be defined as a model that recognises valid input strings, rather than enumerating output
Turing_machine
Set of elements in any of some sets
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations
Union_(set_theory)
Concept in computability theory
run with oracle B, computes a partial function with domain A, then A is said to be B-recursively enumerable and B-computably enumerable. We say A {\displaystyle
Turing_reduction
Fundamental theorem in mathematical logic
that it is possible to computably enumerate the semantic consequences of any computably enumerable first-order theory, by enumerating all the possible formal
Gödel's_completeness_theorem
American mathematician
proof of it, Tennenbaum had also studied Suslin's problem and computably enumerable sets. Over his academic career in the 1960s and 1970s, he switched
Stanley_Tennenbaum
System of mathematical set theory
connections between KP, computability theory, and the theory of admissible ordinals. KP can be studied as a constructive set theory by dropping the law
Kripke–Platek_set_theory
Mathematical set that can be enumerated
vary and care is needed respecting the difference with recursively enumerable. A set S {\displaystyle S} is countable if: Its cardinality | S | {\displaystyle
Countable_set
Robert I. (1987). Recursively enumerable sets and degrees. A study of computable functions and computably generated sets. Perspectives in Mathematical
Low_(computability)
Ability to solve a problem by an effective procedure
which are recursively enumerable, but not recursive? And, furthermore, are there languages which are not even recursively enumerable? The halting problem
Computability
axiomatic set theory by the axiom of infinity, which asserts the existence of the set N of natural numbers. Every infinite set which can be enumerated by natural
Paradoxes_of_set_theory
Size of a set in mathematics
different sizes of infinity. They defined three major classes of number: enumerable (finite numbers), unenumerable (asamkhyata, roughly, countably infinite)
Cardinality
recursively enumerable set is productive. The complement of the set T will not be recursively enumerable, and thus T is an example of a productive set whose
Creative_and_productive_sets
Real number that can be computed within arbitrary precision
showing that the computable numbers are subcountable. The set S {\displaystyle S} of these Gödel numbers, however, is not computably enumerable (and consequently
Computable_number
Function computable with bounded loops
functions. For example, the set of provably total functions (in Peano arithmetic) is also recursively enumerable, as one can enumerate all the proofs of the
Primitive_recursive_function
Any one of the distinct objects that make up a set in set theory
mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. For example, given a set called A containing the first four
Element_of_a_set
Collection of sets in mathematics that can be defined based on a property of its members
In set theory and its applications throughout mathematics, a class is a collection of mathematical objects (often sets) that can be unambiguously defined
Class_(set_theory)
System of mathematical set theory
of mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of
Morse–Kelley_set_theory
American mathematician
analytic sets then x# exists for all reals x, and proving with Saharon Shelah that the first-order theory of the partially ordered set of computably enumerable
Leo_Harrington
Abstract data type for storing distinct values
a given value is in the set, or enumerating the values in some arbitrary order. Other variants, called dynamic or mutable sets, allow also the insertion
Set_(abstract_data_type)
Automata that lists elements of some given set
times. An Enumerable Language is Turing Recognizable It's very easy to construct a Turing Machine M {\displaystyle M} that recognizes the enumerable language
Enumerator_(computer_science)
Mathematical set of all subsets of a set
such as the set of integers or rationals, but not possible for example if S is the set of real numbers, in which case we cannot enumerate all irrational
Power_set
Mathematical set containing all objects
In set theory, a universal set is a set that contains all of the objects in the theory, including itself. In set theory as usually formulated, it can
Universal_set
Yes/no problem in computer science
semidecidable, solvable, or provable if the set of inputs for which the answer is YES is a recursively enumerable set. Problems that are not decidable are undecidable
Decision_problem
Paradox in set theory
a set-theoretic paradox published by the British philosopher and mathematician, Bertrand Russell, in 1901. Russell's paradox shows that every set theory
Russell's_paradox
Problem in computer science
input x} represents the halting problem. This set is recursively enumerable, which means there is a computable function that lists all of the pairs (i, x)
Halting_problem
Identities and relationships involving sets
mathematics, particularly in the study of set theory, the algebra of sets defines the properties and laws of sets, the set-theoretic operations of union, intersection
Algebra_of_sets
Axiomatic set theories based on the principles of mathematical constructivism
constitute sets, the next level being the computably enumerable ones at Σ 1 0 {\displaystyle \Sigma _{1}^{0}} . There is a large corpus of computability theory
Constructive_set_theory
Generalization of Turing computability
a set X of natural numbers: in the definition of an ordinal notation, the clause for limit ordinals is changed so that the computable enumeration of
Hyperarithmetical_theory
Hierarchy of complexity classes for formulas defining sets
are exactly the recursively enumerable sets. The set of natural numbers that are indices for Turing machines that compute total functions is Π 2 0 {\displaystyle
Arithmetical_hierarchy
System of mathematical set theory
Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces
Von Neumann–Bernays–Gödel set theory
Von_Neumann–Bernays–Gödel_set_theory
Mathematical logic hierarchy
a computably enumerable sequence of basic open sets. A code for such a set is a pair (0,e), where e is the index of a program enumerating the sequence
Borel_hierarchy
Maximal proper filter
In the mathematical field of set theory, an ultrafilter on a set X {\displaystyle X} is a maximal filter on the set X . {\displaystyle X.} In other words
Ultrafilter_on_a_set
Finite collection of distinct objects
(or the cardinal number) of the set. A set that is not a finite set is called an infinite set. For example, the set { 1 , 2 , 3 , … } {\displaystyle
Finite_set
Theorem in computability theory
provided), and produces an enumeration of A. See enumeration reducibility for a precise account. A set A is computably enumerable with oracle B (or simply
Selman's_theorem
Theorem about Turing reductions
density theorem—The computably enumerable degrees are dense. Post's problem Friedberg, Richard M. (1957). Two recursively enumerable sets of incomparable
Friedberg–Muchnik_theorem
Set theory concept
In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is the class of hereditary
Von_Neumann_universe
Named set of data type values
data type consisting of a set of named values called elements, members, enumeral, or enumerators of the type. The enumerator names are usually identifiers
Enumerated_type
Mathematical set formed from two given sets
In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is an
Cartesian_product
Non-contradiction of a theory
recursively enumerable, consistent theory of arithmetic can never be proven in that system itself. The same result is true for recursively enumerable theories
Consistency
Subfield of automated reasoning and mathematical logic
semantically valid well-formed formulas, so the valid formulas are computably enumerable: given unbounded resources, any valid formula can eventually be
Automated_theorem_proving
American logician (1933–2019)
Robert I. (1987), Recursively Enumerable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets, Perspectives in Mathematical
Gerald_Sacks
Theorem in set theory
In set theory, Kőnig's theorem states that if the axiom of choice holds, I is a set, κ i {\displaystyle \kappa _{i}} and λ i {\displaystyle \lambda _{i}}
Kőnig's_theorem_(set_theory)
Russian mathematician (1934–2019)
I. Soare, Recursively Enumberable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets. Springer-Verlag, 1999, ISBN 3-540-15299-7;
Albert_Muchnik
Convex hull of a finite set of points in a Euclidean space
vertex enumeration problem and the problem of the construction of a H-representation is known as the facet enumeration problem. While the vertex set of a
Convex_polytope
Category of mathematical proof
Turing: "... the set of solvable Diophantine equations is an example of a computably enumerable but not decidable set, and the set of unsolvable Diophantine
Proof_of_impossibility
Theory that allows sets to be elements of themselves
Non-well-founded set theories (sometimes unhyphenated, as nonwellfounded; or poorly founded) are variants of axiomatic set theory that allow sets to be elements
Non-well-founded_set_theory
Infinite set that is not countable
mathematics, an uncountable set, informally, is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related
Uncountable_set
Proof in set theory
So the uncountable 2 N {\displaystyle 2^{\mathbb {N} }} is also not enumerable and it can also be mapped onto N {\displaystyle {\mathbb {N} }} . Classically
Cantor's_diagonal_argument
Class of mathematical set whose elements are all subsets
In set theory, a branch of mathematics, a set A {\displaystyle A} is called transitive if either of the following equivalent conditions holds: whenever
Transitive_set
American mathematician (1948–2017)
work is highly cited in the fields of vector spaces, including computably enumerable sets and vector spaces. Robbins, Gary (October 6, 2017). "Renowned
Jeffrey_B._Remmel
Part of a machine instruction
In computing, an opcode (abbreviated from operation code) is an enumerated value that specifies the operation to be performed. Opcodes are employed in
Opcode
Mathematical construction of a set with an equivalence relation
setoid (X, ~) is a set (or type) X equipped with an equivalence relation ~. A setoid may also be called E-set, Bishop set, or extensional set. Setoids are studied
Setoid
Mathematical concept
arithmetical. Every recursively enumerable set is arithmetical. Every computable function is arithmetically definable. The set encoding the halting problem
Arithmetical_set
Low (computability) Soare, R. I. (1987). Recursively enumerable sets and degrees : a study of computable functions and computably generated sets. Berlin:
High_(computability)
Topics referred to by the same term
calculator that clears the last number entered Computably enumerable, a property of some sets in computability theory, abbreviated c.e. Computer engineering
CE
Set of all true first-order statements about the arithmetic of natural numbers
{R}}} ) of the recursively enumerable Turing degrees, in the signature of partial orders. In particular, there are computable functions S and T such that:
True_arithmetic
Proposition in mathematical logic
specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states: There is no set whose
Continuum_hypothesis
Robert I. (1987). Recursively enumerable sets and degrees. A study of computable functions and computably generated sets. Perspectives in Mathematical
Low_basis_theorem
Unicode character block
computers from the 1970s and 1980s, extending the set of characters provided by the Symbols for Legacy Computing block. It includes characters from Amstrad CPC
Symbols for Legacy Computing Supplement
Symbols_for_Legacy_Computing_Supplement
COMPUTABLY ENUMERABLE-SET
COMPUTABLY ENUMERABLE-SET
Male
English
Anglicized form of Hebrew Sheth, SETH means "buttocks." In the bible, this is the name of the third son of Adam and Eve. Compare with other forms of Seth.
Surname or Lastname
English
English : patronymic from Setter.
Surname or Lastname
English
English : habitational name from Mitcham in Surrey, so named from Old English micel ‘big’ + hÄm ‘homestead’, ‘settlement’.
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.
Surname or Lastname
English
English : habitational name from places in Cheshire and East Yorkshire, so named from Old English mylen ‘mill’ + tūn ‘enclosure’, ‘settlement’.
Surname or Lastname
English
English : habitational name from a place in Shropshire, so named from Welsh mynydd ‘hill’ + Old English tūn ‘enclosure’, ‘settlement’.
Female
Japanese
(節å) Japanese name SETSUKO means "temperate child."
Male
Greek
(Σήθος) Greek form of Egyptian Sutekh, possibly SETHOS means "one who dazzles." In mythology, this is the name of an ancient evil god of Chaos, storms, and the desert, who slew Osiris.Â
Surname or Lastname
English
English : habitational name from a place in North Yorkshire, so named from Old English setl ‘seat’, ‘dwelling’.
Surname or Lastname
English
English : from a medieval personal name, Latin Bart(h)olomaeus, from the Aramaic patronymic bar-Talmay ‘son of Talmay’, meaning ‘having many furrows’, i.e. rich in land. This was an extremely popular personal name in Christian Europe, with innumerable vernacular derivatives. It derived its popularity from the apostle St. Bartholomew (Matthew 10:3), the patron saint of tanners, vintners, and butlers. As an Irish name, it has been used as an Americanized form of Mac Pharthaláin (see McFarlane).
Surname or Lastname
English
English : habitational name from Milwich in Staffordshire, so named from Old English myln ‘mill’ + wīc ‘dairy farm’; ‘(trading) settlement’.
Surname or Lastname
English
English : habitational name from places called Merton in London, Devon, Norfolk, and Oxfordshire, named in Old English with mere ‘lake’, ‘pool’ + tūn ‘enclosure’, ‘settlement’. Compare Marton, Martin 2.
Male
Hindi/Indian
(सेठ) Hindi name derived from the Sanskrit word setu, SETH means "bridge." Compare with other forms of Seth.
Male
Greek
(Σήθι) Greek form of Egyptian Seti, SETHI means "of Seth."Â
Surname or Lastname
English
English : habitational name from a place in Kent named Meopham, from an Old English personal name MÄ“apa + Old English hÄm ‘homestead’, ‘settlement’.
Surname or Lastname
English
English : occupational name for a stone- or bricklayer, from Middle English setter ‘one who lays stones or bricks in building’ (agent derivative of setten ‘to set’).English : occupational name from Old French saietier ‘silk weaver’ (an agent derivative of sayete, a kind of silk).English : from an agent derivative of Middle English setten ‘to place (decoration, on a garment or metal surface)’, probably an occupational name for an embroiderer.German : unexplained.Norwegian : unexplained.
Surname or Lastname
Scottish and English
Scottish and English : topographic name for someone who lived near a mill, Middle English mille, milne (Old English myl(e)n, from Latin molina, a derivative of molere ‘to grind’). It was usually in effect an occupational name for a worker at a mill or for the miller himself. The mill, whether powered by water, wind, or (occasionally) animals, was an important center in every medieval settlement; it was normally operated by an agent of the local landowner, and individual peasants were compelled to come to him to have their grain ground into flour, a proportion of the ground grain being kept by the miller by way of payment.English : from a short form of a personal name, probably female, as for example Millicent.
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’.
Surname or Lastname
English
English : topographic name for someone who lived in the center of a village, from Middle English midde ‘mid’ + toun ‘village’, ‘town’.English : habitational name from places in Lancashire, Worcestershire, and West Yorkshire, so named in Old English as ‘farmstead at a river confluence’, from (ge)m̄ðe ‘river confluence’ + tūn ‘farmstead’, ‘settlement’.
Male
Italian
Italian form of Roman Latin Septimus, SETTIMIO means "seventh."
COMPUTABLY ENUMERABLE-SET
COMPUTABLY ENUMERABLE-SET
Boy/Male
Gujarati, Hindu, Indian, Modern
Lord Shiva
Boy/Male
Indian, Sanskrit
Liberal; Generous; Virtuous
Girl/Female
American, Australian, British, Chinese, English, Greek
Pearl
Female
English
English short form of Latin Penelope, PEN means "weaver of cunning."
Girl/Female
Latin
Unwilling.
Boy/Male
Arabic
Blessed.
Boy/Male
Egyptian
Hunter.
Boy/Male
Indian, Punjabi, Sikh
Reflections on Excellence
Girl/Female
Arabic, Muslim
Exalted; High; Name of a Sahabi RA
Surname or Lastname
English
English : variant spelling of Hight.Americanized spelling of German Heit.
COMPUTABLY ENUMERABLE-SET
COMPUTABLY ENUMERABLE-SET
COMPUTABLY ENUMERABLE-SET
COMPUTABLY ENUMERABLE-SET
COMPUTABLY ENUMERABLE-SET
a.
Multiplied by millions; innumerable.
a.
Not computable.
n.
The quality of being commutable; interchangeableness.
imp. & p. p.
of Enumerate
a.
Surmountable; superable.
v. t.
To count; to tell by numbers; to count over, or tell off one after another; to number; to reckon up; to mention one by one; to name over; to make a special and separate account of; to recount; as, to enumerate the stars in a constellation.
a.
Innumerable; countless.
a.
Innumerable.
adv.
By imputation.
a.
Innumerable.
n.
State of being innumerable.
p. pr. & vb. n.
of Enumerate
a.
Capable of being commuted or interchanged.
a.
Not numbered; not counted or estimated; innumerable.
v. t.
Capable of being numbered or counted.
n.
The state or quality of being numerable or countable.
adv.
In a compatible manner.
n.
The quality of being commutable.
a.
Not capable of being counted, enumerated, or numbered, for multitude; countless; numberless; unnumbered, hence, indefinitely numerous; of great number.
a.
Capable of being computed, numbered, or reckoned.