Parole in English per '(complex analysis, of a complex function) Complex-differentiable on all of ℂ.'
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adj
- (complex analysis, of a complex function) Complex-differentiable on all of ℂ.
- (sometimes postpositive) Whole; complete.
- Internal; interior.
- (of a male animal) Not gelded.
- Morally whole; pure; sheer.
- (botany) Having a smooth margin without any indentation.
- (botany) Consisting of a single piece, as a corolla.
- (of leaves or petals) having a smooth edge; not broken up into teeth or lobes
- constituting the full quantity or extent; complete
- (used of domestic animals) sexually competent
- constituting the undiminished entirety; lacking nothing essential especially not damaged
noun
noun
- (complex analysis) A form of complex number, proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities.
- (modular arithmetic) A representative element of an equivalence class modulo some base, conventionally in the half-open interval from zero to the base; the nonnegative remainder after dividing a number by a base.
- (biochemistry) A molecule that is released from a polymer after bonds between neighbouring monomers are broken, such as an amino acid in a polypeptide chain.
- (law) Whatever property or effects are left in an estate after payment of all debts, other charges and deduction of what is specifically bequeathed by the testator.
- (chemistry) The substance that remains after evaporation, distillation, filtration or any similar process.
- That which persists or remains following the removal or elimination of other elements.
- something left after other parts have been taken away
- matter that remains after something has been removed
adj
- (complex analysis, of a family of continuous functions) Which is pre-compact.
- (topology, of a topology or topological space) In which disjoint closed sets can be separated by disjoint neighborhoods.
- (linear algebra, of a matrix) Which commutes with its conjugate transpose.
- (commutative algebra, of a domain) Integrally closed: equal its own integral closure in its field of fractions.
- (functional analysis, of a Hilbert space operator) Which commutes with its adjoint.
- (probability theory, statistics, of a distribution, random variable, etc.) Which has a very specific bell curve shape; that is or has the qualities of a normal distribution.
- (physics, of a mode in an oscillating system) In which all parts of an object vibrate at the same frequency (a normal mode).
- (rail transport, of points) In the default position, set for the most frequently used route.
- (chemistry) Of, relating to, or being a solution containing one equivalent weight of solute per litre of solution.
- (category theory, of a category) Which contains only normal morphisms.
- (organic chemistry) Describing a straight chain isomer of an aliphatic hydrocarbon, or an aliphatic compound in which a substituent is in the 1- position of such a hydrocarbon.
- (fandom slang, sarcastic, with “about”) Fervently interested in a subject; obsessed.
- (algebraic geometry, of a variety or scheme) Such that the local ring at every point is an integrally closed domain.
- (category theory, of a morphism) Which is the kernel or cokernel of some morphism, respectively.
- (number theory, of a real number) In whose representation in a given base b ≥ 2, for every positive integer n, the bⁿ possible strings of n digits follow a uniform distribution.
- Usual, healthy; not sick or ill or unlike oneself.
- (set theory, of a function from the ordinals to the ordinals) Which is strictly monotonically increasing and continuous with respect to the order topology.
- (algebra, of a field extension of a field K) Which is the splitting field of a family of polynomials in K.
- (algebra, of a subgroup) With cosets which form a group.
- (commutative algebra, of a ring) Such that all of its localizations at prime ideals are integrally closed domains.
- (education, of a school) Teaching teachers how to teach; teaching teachers the norms of education.
- According to norms or rules or to a regular pattern.
- (geometry) Perpendicular to a tangent of a curve or tangent plane of a surface.
- in accordance with scientific laws
- conforming with or constituting a norm or standard or level or type or social norm; not abnormal
- forming a right angle
- being approximately average or within certain limits in e.g. intelligence and development
noun
- (geometry, countable) A line or vector that is perpendicular to another line, surface, or plane.
- (medicine, countable) A person who is healthy, normal, as opposed to one who is morbid.
- (slang, countable) A person who is normal, who fits into mainstream society, as opposed to those who live alternative lifestyles.
- (countable, uncountable) The usual state.
- something regarded as a normative example
noun
- (mathematics, complex analysis, always plural) Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the criteria that f be complex-differentiable.
- (complex analysis) The equivalent single equation (∂f)/(∂x)+i(∂f)/(∂y)=0.
noun
- (specifically, complex analysis) A meromorphic function on the complex plane that is not a rational function.
- (mathematical analysis) Any function that is algebraically independent of its variable(s); a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials.
adj
- (mathematics, algebra) Whose coefficients are complex numbers; defined over the field of complex numbers.
- (mathematics, mathematical analysis, of a function) Whose range is a subset of the complex numbers.
- Made up of multiple parts; composite; not simple.
- (geometry) A curve, polygon or other figure that crosses or intersects itself.
- Not simple, easy, or straightforward; complicated.
- (mathematics, of a number) Having the form a + bi, where a and b are real numbers and i is (by definition) the imaginary square root of −1.
- difficult to analyze or understand
- complicated in structure; consisting of interconnected parts
noun
- (mathematics) A complex number.
- (psychology) A group of emotionally charged ideas or mental factors, unconsciously associated by the individual with a particular subject, arising from repressed instincts, fears, or desires and often resulting in mental abnormality.
- (taxonomy) A group of closely related species, often distinguished only with difficulty by traditional morphological methods.
- (linguistics) A multimorphemic word, one with several parts, one with affixes.
- A collection of buildings with a common purpose, such as a university or military base.
- An organized cluster of thunderstorms.
- (chemistry) A structure consisting of a central atom or molecule weakly connected to surrounding atoms or molecules, as for example coordination compounds in inorganic chemistry and protein complexes in biochemistry.
- A fixed mental tendency or obsession.
- A cluster of wildfires burning in the same vicinity.
- An assemblage of related things; a collection.
- A network of interconnected systems.
- a conceptual whole made up of complicated and related parts
- a compound described in terms of the central atom to which other atoms are bound or coordinated
- a whole structure (as a building) made up of interconnected or related structures
- (psychoanalysis) a combination of emotions and impulses that have been rejected from awareness but still influence a person's behavior
verb
noun
- (algebra, of a complex number) A complex conjugate.
- (algebra) More generally, any of a set of irrational or complex numbers that are zeros of the same polynomial with integral coefficients.
- (mathematics) An explementary angle.
- (grammar) A word agreeing in derivation with another word, and therefore generally resembling it in meaning.
- (algebra, field theory, of an element of an extension field) Given a field extension L / K and an element α ∈ L, any other element β ∈ L that is another root of the minimal polynomial of α over K.
- (anatomy, obstetrics) A type of pelvic measurement.
- Any entity formed by joining two or more smaller entities together.
- (immunology) A weak and a strong antigen covalently linked together
- a mixture of two partially miscible liquids A and B produces two conjugate solutions: one of A in B and another of B in A
adj
- (grammar) Agreeing in derivation and radical signification; said of words.
- (botany) In single pairs; coupled.
- (chemistry) Containing two or more radicals supposed to act the part of a single one.
- United in pairs; yoked together; coupled.
- (mathematics) Presenting themselves simultaneously and having reciprocal properties; said of quantities, points, lines, axes, curves, etc.
- (of a pinnate leaflet) having only one pair of leaflets
- formed by the union of two compounds
- of an organic compound; containing two or more double bonds each separated from the other by a single bond
- joined together especially in a pair or pairs
verb
- (rare) To join together, to unite; to juxtapose.
- (biology, of bacteria and algae) To temporarily fuse, exchanging or transferring DNA.
- (grammar, transitive) To inflect (a verb) for each person, in order, for one or more tenses; to list or recite its principal parts.
- (mathematics) To multiply on the left by one element and on the right by its inverse.
- unite chemically so that the product is easily broken down into the original compounds
- undergo conjugation
- add inflections showing person, number, gender, tense, aspect, etc.
noun
- (mathematics, complex analysis) A horizontal line placed over a complex number or expression to denote its complex conjugate.
- (logic, electronics) A horizontal line placed over a symbol or expression to denote logical negation (complement).
- (anatomy) A ligament that limits the movement of an organ or part.
- (Australia, surveying) A symbol in the shape of an elongated letter "S" (∫) or pair of hooks (⌠⌡) drawn on plans to join non-contiguous sections of land that are to be treated as a single parcel.
- (arithmetic, historical) A horizontal line placed over the characteristic (integer part) of a common logarithm to indicate that the characteristic is negative while the mantissa (decimal part) remains positive. Historically used to simplify the use of logarithm tables.
- (arithmetic) A horizontal line placed over one or more digits of a decimal expansion to indicate that those digits repeat indefinitely (the repetend).
- (arithmetic) The horizontal line between the numerator and denominator in a fraction.
- (mathematics, geometry) A horizontal line drawn over two letters to denote the line segment joining them.
- (arithmetic) A horizontal line over the top of some of the terms in an expression, indicating that that part of the calculation is to be done before other parts (in modern mathematical notation confined to use in radicals: √).
noun
- (mathematics) A function which negates the non-real part of a complex or hypercomplex number; a complex conjugation.
- (grammar, sometimes proscribed) The inflection of nouns or other words besides verbs; a declension.
- (grammar) The product of that act: the conjugated forms of a verb, collected into a list or recitation.
- (mathematics) A mapping sending x to gxg⁻¹, where g and x are elements of a group; an inner automorphism.
- (grammar) In some languages, one of several classifications of verbs categorized into distinct classes based on the specific inflectional patterns they exhibit.
- (grammar) The act or process of conjugating a verb.
- The coming together of things; a union.
- (law) Sexual relations within marriage.
- (chemistry) A system of delocalized orbitals consisting of alternating single bonds and double bonds.
- (biology) The temporary fusion of organisms, especially as part of sexual reproduction.
- the state of being joined together
- the act of pairing a male and female for reproductive purposes
- a class of verbs having the same inflectional forms
- the act of making or becoming a single unit
- the complete set of inflected forms of a verb
- the inflection of verbs
adj
- (computing, complexity theory) Bounded above by a constant.
- Consistently recurring over time; persistent.
- Firm; solid; not fluid.
- Unchanged through time or space; permanent.
- Steady in purpose, action, feeling, etc.
- unvarying in nature
- uninterrupted in time and indefinitely long continuing
- steadfast in purpose or devotion or affection
noun
- That which is permanent or invariable.
- (sciences) Any property of an experiment, determined numerically, that does not change under given circumstances.
- (computing) An identifier that is bound to an invariant value; a fixed value given a name to aid in readability of source code.
- (algebra) A quantity that remains at a fixed value throughout a given discussion or operation.
- a quantity that does not vary
- a number representing a quantity assumed to have a fixed value in a specified mathematical context
noun
- a complex of concurrent things
- a pattern of symptoms indicative of some disease
- (pathology) A recognizable pattern of signs, symptoms and/or behaviours, especially of a disease or medical or psychological condition.
- Any set of characteristics regarded as identifying a certain type, condition, etc., usually adverse.
noun
- the absolute value of a complex number
- an integer that can be divided without remainder into the difference between two other integers
- (physics) a coefficient that expresses how much of a specified property is possessed by a specified substance
- (physics) A coefficient that expresses how much of a certain property is possessed by a certain substance.
- (computing, programming) An operator placed between two numbers, to get the remainder of the division of those numbers.
- (physics) A scalar field controlling the shape and size of extra dimensions in a compactification.
- (mathematics) The absolute value of a complex number.
- (mathematics) The base with respect to which a congruence is computed.
noun
- the analysis of complex things into simpler constituents
- a theory that all complex systems can be completely understood in terms of their components
- An approach to studying complex systems or ideas by reducing them to a set of simpler components.
- (philosophy) A philosophical position which holds that a complex system is nothing but the sum of its parts, and that an account of it can be reduced to accounts of individual constituents. In a reductionist framework, the phenomena that can be explained completely in terms of relations between other more fundamental phenomena are called "epiphenomena".
name
- Initialism of Computability and Complexity in Analysis, a book.
- Initialism of Centre for Contemporary Arts.
- Initialism of California Culinary Academy.
- Initialism of Coca-Cola Amatil.
- Initialism of Canadian Construction Association.
- Initialism of Call Centre Association.
- Initialism of Caribbean Contemporary Arts.
- Initialism of Canadian Cartographic Association.
- Initialism of Calgary Construction Association.
- Initialism of C Code Analyzer.
- Initialism of Colon Cancer Alliance.
- Initialism of Computer Corporation of America, a computing company founded in 1965 and acquired in 2010 by Rocket Software.
- Initialism of Center for Computational Aesthetics.
- Initialism of Conference of Consulting Actuaries.
- Initialism of Canadian Conference of the Arts, discontinued in 2012.
- Initialism of Centre for Creative Arts.
- Initialism of Corrections Corp of America.
- Initialism of Canadian Cat Association.
- Initialism of Canadian Council of Archives.
- Initialism of Coastal Conservation Association.
- Initialism of Canadian Chiropractic Association.
- Initialism of Common Component Architecture.
- (Australia) Initialism of Commonwealth Copyright Administration.
- Initialism of Chandigarh College of Architecture.
- Initialism of Continental Chess Association.
- Initialism of Career College Association.
- Initialism of Centre for Corporate Accountability, closed down in 2009.
- Initialism of Christian Conference of Asia.
- Initialism of California College of the Arts.
- Initialism of Corporate Council on Africa.
- Initialism of Canadian Cycling Association, former name of Cycling Canada Cyclisme.
noun
- Initialism of certified cropadvisor.
- Initialism of consumer and corporate affairs.
- Initialism of congenital contractural arachnodactyly.
- Initialism of controller of certifying/certification authorities.
- Initialism of customer care assistant.
- Initialism of cold cranking amperes.
- Initialism of chromated copper arsenate.
- (computing) Initialism of continuous configuration automation.
- (anatomy) Initialism of common carotid artery.
- (military, aviation) Initialism of collaborative combat aircraft: a combat drone wingman
- (Singapore, education) Initialism of cocurricular activity.
- Initialism of clear channel assessment.
- Initialism of Citrix certified administrator.
adj
- (computing theory, of a problem) That is in a given complexity class and is such that every other problem in the class can be reduced to it (usually in polynomial time or logarithmic space).
- (algebra, of a lattice) In which every set with a lower bound has a greatest lower bound.
- With all parts included; with nothing missing; full.
- (logic, of a proof system of a formal system with respect to a given semantics) In which every semantically valid well-formed formula is provable.
- Generic intensifier.
- Finished; ended; concluded; completed.
- (ring theory, of a local ring) Complete as a topological group with respect to its m-adic topology, where m is its unique maximal idea.
- (mathematics, of a category) In which all small limits exist.
- (mathematical analysis, of a metric space or topological group) In which every Cauchy sequence converges to a point within the space.
- having every necessary or normal part or component or step
- highly skilled
- without qualification; used informally as (often pejorative) intensifiers
- having come or been brought to a conclusion
- perfect and complete in every respect; having all necessary qualities
noun
verb
- (transitive) To make whole or entire.
- (poker) To call from the small blind in an unraised pot.
- (ambitransitive) To finish; to make done; to reach the end.
- come or bring to a finish or an end
- write all the required information onto a form
- complete or carry out
- bring to a whole, with all the necessary parts or elements
- complete a pass
noun
- (topology, complex analysis) The complex numbers extended with the number ∞; the complex plane (representation of the complex numbers as a Euclidean plane) extended with a single idealised point at infinity and consequently homeomorphic to a sphere in 3-dimensional Euclidean space.
- (topology, complex analysis) The 2-sphere embedded in Euclidean three-dimensional space and often represented as a unit sphere, regarded as a homeomorphic representation of the extended complex plane and thus the extended complex numbers.
noun
- (complex analysis, broad sense) A number of the form a + bi, where a and b are real numbers and b is nonzero.
- (complex analysis, strict sense) A number of the form bi, where b is any real number and i denotes the imaginary unit.
- (mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1
noun
- a set of complex numbers that has a highly convoluted fractal boundary when plotted; the set of all points in the complex plane that are bounded under a certain mathematical iteration
- (mathematics) the set of complex numbers c for which the orbit of 0 under iteration of the complex quadratic polynomial zₙ₊₁ = zₙ² + c remains bounded. The boundary of this set is a fractal.
noun
- (complex analysis) A form of complex number, proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities.
- (modular arithmetic) A representative element of an equivalence class modulo some base, conventionally in the half-open interval from zero to the base; the nonnegative remainder after dividing a number by a base.
- (biochemistry) A molecule that is released from a polymer after bonds between neighbouring monomers are broken, such as an amino acid in a polypeptide chain.
- (law) Whatever property or effects are left in an estate after payment of all debts, other charges and deduction of what is specifically bequeathed by the testator.
- (chemistry) The substance that remains after evaporation, distillation, filtration or any similar process.
- That which persists or remains following the removal or elimination of other elements.
- something left after other parts have been taken away
- matter that remains after something has been removed
noun
- (mathematics, complex analysis, always plural) Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the criteria that f be complex-differentiable.
- (complex analysis) The equivalent single equation (∂f)/(∂x)+i(∂f)/(∂y)=0.
noun
- (specifically, complex analysis) A meromorphic function on the complex plane that is not a rational function.
- (mathematical analysis) Any function that is algebraically independent of its variable(s); a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials.
noun
- (algebra, of a complex number) A complex conjugate.
- (algebra) More generally, any of a set of irrational or complex numbers that are zeros of the same polynomial with integral coefficients.
- (mathematics) An explementary angle.
- (grammar) A word agreeing in derivation with another word, and therefore generally resembling it in meaning.
- (algebra, field theory, of an element of an extension field) Given a field extension L / K and an element α ∈ L, any other element β ∈ L that is another root of the minimal polynomial of α over K.
- (anatomy, obstetrics) A type of pelvic measurement.
- Any entity formed by joining two or more smaller entities together.
- (immunology) A weak and a strong antigen covalently linked together
- a mixture of two partially miscible liquids A and B produces two conjugate solutions: one of A in B and another of B in A
adj
- (grammar) Agreeing in derivation and radical signification; said of words.
- (botany) In single pairs; coupled.
- (chemistry) Containing two or more radicals supposed to act the part of a single one.
- United in pairs; yoked together; coupled.
- (mathematics) Presenting themselves simultaneously and having reciprocal properties; said of quantities, points, lines, axes, curves, etc.
- (of a pinnate leaflet) having only one pair of leaflets
- formed by the union of two compounds
- of an organic compound; containing two or more double bonds each separated from the other by a single bond
- joined together especially in a pair or pairs
verb
- (rare) To join together, to unite; to juxtapose.
- (biology, of bacteria and algae) To temporarily fuse, exchanging or transferring DNA.
- (grammar, transitive) To inflect (a verb) for each person, in order, for one or more tenses; to list or recite its principal parts.
- (mathematics) To multiply on the left by one element and on the right by its inverse.
- unite chemically so that the product is easily broken down into the original compounds
- undergo conjugation
- add inflections showing person, number, gender, tense, aspect, etc.
noun
- (mathematics, complex analysis) A horizontal line placed over a complex number or expression to denote its complex conjugate.
- (logic, electronics) A horizontal line placed over a symbol or expression to denote logical negation (complement).
- (anatomy) A ligament that limits the movement of an organ or part.
- (Australia, surveying) A symbol in the shape of an elongated letter "S" (∫) or pair of hooks (⌠⌡) drawn on plans to join non-contiguous sections of land that are to be treated as a single parcel.
- (arithmetic, historical) A horizontal line placed over the characteristic (integer part) of a common logarithm to indicate that the characteristic is negative while the mantissa (decimal part) remains positive. Historically used to simplify the use of logarithm tables.
- (arithmetic) A horizontal line placed over one or more digits of a decimal expansion to indicate that those digits repeat indefinitely (the repetend).
- (arithmetic) The horizontal line between the numerator and denominator in a fraction.
- (mathematics, geometry) A horizontal line drawn over two letters to denote the line segment joining them.
- (arithmetic) A horizontal line over the top of some of the terms in an expression, indicating that that part of the calculation is to be done before other parts (in modern mathematical notation confined to use in radicals: √).
noun
- (mathematics) A function which negates the non-real part of a complex or hypercomplex number; a complex conjugation.
- (grammar, sometimes proscribed) The inflection of nouns or other words besides verbs; a declension.
- (grammar) The product of that act: the conjugated forms of a verb, collected into a list or recitation.
- (mathematics) A mapping sending x to gxg⁻¹, where g and x are elements of a group; an inner automorphism.
- (grammar) In some languages, one of several classifications of verbs categorized into distinct classes based on the specific inflectional patterns they exhibit.
- (grammar) The act or process of conjugating a verb.
- The coming together of things; a union.
- (law) Sexual relations within marriage.
- (chemistry) A system of delocalized orbitals consisting of alternating single bonds and double bonds.
- (biology) The temporary fusion of organisms, especially as part of sexual reproduction.
- the state of being joined together
- the act of pairing a male and female for reproductive purposes
- a class of verbs having the same inflectional forms
- the act of making or becoming a single unit
- the complete set of inflected forms of a verb
- the inflection of verbs
noun
- a complex of concurrent things
- a pattern of symptoms indicative of some disease
- (pathology) A recognizable pattern of signs, symptoms and/or behaviours, especially of a disease or medical or psychological condition.
- Any set of characteristics regarded as identifying a certain type, condition, etc., usually adverse.
noun
- the absolute value of a complex number
- an integer that can be divided without remainder into the difference between two other integers
- (physics) a coefficient that expresses how much of a specified property is possessed by a specified substance
- (physics) A coefficient that expresses how much of a certain property is possessed by a certain substance.
- (computing, programming) An operator placed between two numbers, to get the remainder of the division of those numbers.
- (physics) A scalar field controlling the shape and size of extra dimensions in a compactification.
- (mathematics) The absolute value of a complex number.
- (mathematics) The base with respect to which a congruence is computed.
adj
- (mathematics, algebra) Whose coefficients are complex numbers; defined over the field of complex numbers.
- (mathematics, mathematical analysis, of a function) Whose range is a subset of the complex numbers.
- Made up of multiple parts; composite; not simple.
- (geometry) A curve, polygon or other figure that crosses or intersects itself.
- Not simple, easy, or straightforward; complicated.
- (mathematics, of a number) Having the form a + bi, where a and b are real numbers and i is (by definition) the imaginary square root of −1.
- difficult to analyze or understand
- complicated in structure; consisting of interconnected parts
noun
- (mathematics) A complex number.
- (psychology) A group of emotionally charged ideas or mental factors, unconsciously associated by the individual with a particular subject, arising from repressed instincts, fears, or desires and often resulting in mental abnormality.
- (taxonomy) A group of closely related species, often distinguished only with difficulty by traditional morphological methods.
- (linguistics) A multimorphemic word, one with several parts, one with affixes.
- A collection of buildings with a common purpose, such as a university or military base.
- An organized cluster of thunderstorms.
- (chemistry) A structure consisting of a central atom or molecule weakly connected to surrounding atoms or molecules, as for example coordination compounds in inorganic chemistry and protein complexes in biochemistry.
- A fixed mental tendency or obsession.
- A cluster of wildfires burning in the same vicinity.
- An assemblage of related things; a collection.
- A network of interconnected systems.
- a conceptual whole made up of complicated and related parts
- a compound described in terms of the central atom to which other atoms are bound or coordinated
- a whole structure (as a building) made up of interconnected or related structures
- (psychoanalysis) a combination of emotions and impulses that have been rejected from awareness but still influence a person's behavior
verb
noun
- the analysis of complex things into simpler constituents
- a theory that all complex systems can be completely understood in terms of their components
- An approach to studying complex systems or ideas by reducing them to a set of simpler components.
- (philosophy) A philosophical position which holds that a complex system is nothing but the sum of its parts, and that an account of it can be reduced to accounts of individual constituents. In a reductionist framework, the phenomena that can be explained completely in terms of relations between other more fundamental phenomena are called "epiphenomena".
noun
- (topology, complex analysis) The complex numbers extended with the number ∞; the complex plane (representation of the complex numbers as a Euclidean plane) extended with a single idealised point at infinity and consequently homeomorphic to a sphere in 3-dimensional Euclidean space.
- (topology, complex analysis) The 2-sphere embedded in Euclidean three-dimensional space and often represented as a unit sphere, regarded as a homeomorphic representation of the extended complex plane and thus the extended complex numbers.
noun
- (complex analysis, broad sense) A number of the form a + bi, where a and b are real numbers and b is nonzero.
- (complex analysis, strict sense) A number of the form bi, where b is any real number and i denotes the imaginary unit.
- (mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1
noun
- a set of complex numbers that has a highly convoluted fractal boundary when plotted; the set of all points in the complex plane that are bounded under a certain mathematical iteration
- (mathematics) the set of complex numbers c for which the orbit of 0 under iteration of the complex quadratic polynomial zₙ₊₁ = zₙ² + c remains bounded. The boundary of this set is a fractal.
adj
- (complex analysis, of a complex function) Complex-differentiable on all of ℂ.
- (sometimes postpositive) Whole; complete.
- Internal; interior.
- (of a male animal) Not gelded.
- Morally whole; pure; sheer.
- (botany) Having a smooth margin without any indentation.
- (botany) Consisting of a single piece, as a corolla.
- (of leaves or petals) having a smooth edge; not broken up into teeth or lobes
- constituting the full quantity or extent; complete
- (used of domestic animals) sexually competent
- constituting the undiminished entirety; lacking nothing essential especially not damaged
noun
adj
- (complex analysis, of a family of continuous functions) Which is pre-compact.
- (topology, of a topology or topological space) In which disjoint closed sets can be separated by disjoint neighborhoods.
- (linear algebra, of a matrix) Which commutes with its conjugate transpose.
- (commutative algebra, of a domain) Integrally closed: equal its own integral closure in its field of fractions.
- (functional analysis, of a Hilbert space operator) Which commutes with its adjoint.
- (probability theory, statistics, of a distribution, random variable, etc.) Which has a very specific bell curve shape; that is or has the qualities of a normal distribution.
- (physics, of a mode in an oscillating system) In which all parts of an object vibrate at the same frequency (a normal mode).
- (rail transport, of points) In the default position, set for the most frequently used route.
- (chemistry) Of, relating to, or being a solution containing one equivalent weight of solute per litre of solution.
- (category theory, of a category) Which contains only normal morphisms.
- (organic chemistry) Describing a straight chain isomer of an aliphatic hydrocarbon, or an aliphatic compound in which a substituent is in the 1- position of such a hydrocarbon.
- (fandom slang, sarcastic, with “about”) Fervently interested in a subject; obsessed.
- (algebraic geometry, of a variety or scheme) Such that the local ring at every point is an integrally closed domain.
- (category theory, of a morphism) Which is the kernel or cokernel of some morphism, respectively.
- (number theory, of a real number) In whose representation in a given base b ≥ 2, for every positive integer n, the bⁿ possible strings of n digits follow a uniform distribution.
- Usual, healthy; not sick or ill or unlike oneself.
- (set theory, of a function from the ordinals to the ordinals) Which is strictly monotonically increasing and continuous with respect to the order topology.
- (algebra, of a field extension of a field K) Which is the splitting field of a family of polynomials in K.
- (algebra, of a subgroup) With cosets which form a group.
- (commutative algebra, of a ring) Such that all of its localizations at prime ideals are integrally closed domains.
- (education, of a school) Teaching teachers how to teach; teaching teachers the norms of education.
- According to norms or rules or to a regular pattern.
- (geometry) Perpendicular to a tangent of a curve or tangent plane of a surface.
- in accordance with scientific laws
- conforming with or constituting a norm or standard or level or type or social norm; not abnormal
- forming a right angle
- being approximately average or within certain limits in e.g. intelligence and development
noun
- (geometry, countable) A line or vector that is perpendicular to another line, surface, or plane.
- (medicine, countable) A person who is healthy, normal, as opposed to one who is morbid.
- (slang, countable) A person who is normal, who fits into mainstream society, as opposed to those who live alternative lifestyles.
- (countable, uncountable) The usual state.
- something regarded as a normative example
adj
- (mathematics, algebra) Whose coefficients are complex numbers; defined over the field of complex numbers.
- (mathematics, mathematical analysis, of a function) Whose range is a subset of the complex numbers.
- Made up of multiple parts; composite; not simple.
- (geometry) A curve, polygon or other figure that crosses or intersects itself.
- Not simple, easy, or straightforward; complicated.
- (mathematics, of a number) Having the form a + bi, where a and b are real numbers and i is (by definition) the imaginary square root of −1.
- difficult to analyze or understand
- complicated in structure; consisting of interconnected parts
noun
- (mathematics) A complex number.
- (psychology) A group of emotionally charged ideas or mental factors, unconsciously associated by the individual with a particular subject, arising from repressed instincts, fears, or desires and often resulting in mental abnormality.
- (taxonomy) A group of closely related species, often distinguished only with difficulty by traditional morphological methods.
- (linguistics) A multimorphemic word, one with several parts, one with affixes.
- A collection of buildings with a common purpose, such as a university or military base.
- An organized cluster of thunderstorms.
- (chemistry) A structure consisting of a central atom or molecule weakly connected to surrounding atoms or molecules, as for example coordination compounds in inorganic chemistry and protein complexes in biochemistry.
- A fixed mental tendency or obsession.
- A cluster of wildfires burning in the same vicinity.
- An assemblage of related things; a collection.
- A network of interconnected systems.
- a conceptual whole made up of complicated and related parts
- a compound described in terms of the central atom to which other atoms are bound or coordinated
- a whole structure (as a building) made up of interconnected or related structures
- (psychoanalysis) a combination of emotions and impulses that have been rejected from awareness but still influence a person's behavior
verb
adj
- (computing, complexity theory) Bounded above by a constant.
- Consistently recurring over time; persistent.
- Firm; solid; not fluid.
- Unchanged through time or space; permanent.
- Steady in purpose, action, feeling, etc.
- unvarying in nature
- uninterrupted in time and indefinitely long continuing
- steadfast in purpose or devotion or affection
noun
- That which is permanent or invariable.
- (sciences) Any property of an experiment, determined numerically, that does not change under given circumstances.
- (computing) An identifier that is bound to an invariant value; a fixed value given a name to aid in readability of source code.
- (algebra) A quantity that remains at a fixed value throughout a given discussion or operation.
- a quantity that does not vary
- a number representing a quantity assumed to have a fixed value in a specified mathematical context
adj
- (computing theory, of a problem) That is in a given complexity class and is such that every other problem in the class can be reduced to it (usually in polynomial time or logarithmic space).
- (algebra, of a lattice) In which every set with a lower bound has a greatest lower bound.
- With all parts included; with nothing missing; full.
- (logic, of a proof system of a formal system with respect to a given semantics) In which every semantically valid well-formed formula is provable.
- Generic intensifier.
- Finished; ended; concluded; completed.
- (ring theory, of a local ring) Complete as a topological group with respect to its m-adic topology, where m is its unique maximal idea.
- (mathematics, of a category) In which all small limits exist.
- (mathematical analysis, of a metric space or topological group) In which every Cauchy sequence converges to a point within the space.
- having every necessary or normal part or component or step
- highly skilled
- without qualification; used informally as (often pejorative) intensifiers
- having come or been brought to a conclusion
- perfect and complete in every respect; having all necessary qualities
noun
verb
- (transitive) To make whole or entire.
- (poker) To call from the small blind in an unraised pot.
- (ambitransitive) To finish; to make done; to reach the end.
- come or bring to a finish or an end
- write all the required information onto a form
- complete or carry out
- bring to a whole, with all the necessary parts or elements
- complete a pass