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noun
verb
adj
- (mathematics, mathematical analysis, of a function) Whose range is a subset of the complex numbers.
- (mathematics, algebra) Whose coefficients are complex numbers; defined over the field of 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
- (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.
- (mathematics) A complex number.
- 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
- (geometry) A subset of n-dimensional space that is congruent to a Euclidean space of lower dimension.
- (American football) The areas behind the line of scrimmage to either side of an offensive football formation.
- (rail transport) A flat spot on the wheel of a rail vehicle.
- (publishing) A flat, glossy children's book with few pages.
- An area of level ground (sometimes covered with shallow or tidal water).
- (technical, theatre, stagecraft) A rectangular wooden structure covered with masonite, lauan, or muslin, often produced in standard modules, that is used to build wall surfaces on stage. Flats can be painted and outfitted with doors and/or windows to depict a building or other part of a scene, and are a hard-surfaced alternative to a backcloth or backdrop.
- (entomology) Any of various hesperiid butterflies that spread their wings open when they land.
- A flat sheet for use on a bed.
- (horse racing, with 'the' or attributively, sometimes with capital) Level horse-racing ground, as contrasted with courses incorporating jumps, or the racing done on such ground.
- (postal) A large mail piece measuring at least 8 1/2 by 11 inches, such as catalogs, magazines, and unfolded paper enclosed in large envelopes.
- (music) A note played one chromatic semitone lower than a natural, denoted by the symbol ♭ placed after the letter representing the note (e.g., B♭) or in front of the note symbol (e.g. ♭♪).
- (in the plural) A type of ladies' shoe with a very low heel.
- (informal, automotive) A flat tyre/flat tire.
- (painting) A thin, broad brush used in oil and watercolour painting.
- (optics) A flat (i.e. plane) mirror
- Ellipsis of flat ride (“spinning amusement ride”).
- A wide, shallow container or pallet.
- (in the plural) A type of flat-soled running shoe without spikes.
- The most prominent flat part of something.
- A flat-bottomed boat, without keel, and of small draught.
- (swordfighting) The flat side of a blade, as opposed to the sharp edge.
- A straw hat, broad-brimmed and low-crowned.
- A platform on a wheel, upon which emblematic designs etc. are carried in processions.
- (Australia, horse racing, with 'the' or attributively, sometimes with capital) the area in the centre of a racecourse.
- (gambling, slang) A cheater's die with the edges shaved to make certain rolls more likely.
- (in the phrase 'the flat') Level ground in general.
- (historical) An early kind of toy soldier having a flat design.
- (US) Ellipsis of flat water (“nonfizzy drinking water”).
- (chiefly British, New England, South Africa, India, Australia, New Zealand, Singapore, archaic elsewhere) A complete domicile occupying only part of a building, especially one for rent
- (Canadian Prairies, British Columbia) A 24-case of beer.
- The palm of the hand, with the adjacent part of the fingers.
- (rail transport, US) A railroad car without a roof, and whose body is a platform without sides; a platform car or flatcar.
- (mining) A horizontal vein or ore deposit auxiliary to a main vein; also, any horizontal portion of a vein not elsewhere horizontal.
- a shallow box in which seedlings are started
- a deflated pneumatic tire
- scenery consisting of a wooden frame covered with painted canvas; part of a stage setting
- a level tract of land
- a musical notation indicating one half step lower than the note named
- a suite of rooms usually on one floor of an apartment house
- freight car without permanent sides or roof
adj
- (not comparable, commerce) Of fees, fares etc., fixed; unvarying.
- Smooth; having no protrusions, indentations or other surface irregularities, or relatively so.
- (golf, of a golf club) Having a head at a very obtuse angle to the shaft.
- At a consistently depressed level; consistently lacklustre.
- (of colours) Without variation in tone or hue (uniform), and dull (not glossy).
- (algebra, ring theory, of a ring homomorphism) Such that its target, regarded as a module over its source, is flat (as above).
- (music, note) Lowered by one semitone.
- In a horizontal line or plane; not sloping.
- (juggling, of a throw) Without spin; spinless.
- (algebraic geometry, scheme theory, of a morphism of schemes) Such that the induced map on every stalk is flat (as a map of rings).
- (authorship, figuratively, especially of a character) Lacking in depth, substance, or believability; underdeveloped; one-dimensional.
- (horticulture, of certain fruits) Flattening at the ends.
- (slang) Having small or invisible breasts and/or buttocks.
- (phonetics, of a vowel) Not diphthongal; without variation in height or backness.
- (of a tire or other inflated object) Deflated, especially because of a puncture.
- (homological algebra, of a module) Such that the tensor product preserves exact sequences. See Flat module on Wikipedia.Wikipedia.
- (of a battery) Unable to emit power; dead.
- (of measurements of time) Exact.
- Without variation in level, quantity, value, tone etc.
- Having no variations in height.
- (music) Of a note or voice, lower in pitch than it should be.
- (music, voice) Without variations in pitch.
- (figurative) Lacking liveliness or action; depressed; uninteresting; dull and boring.
- Absolute; downright; peremptory.
- (grammar) Not having an inflectional ending or sign, such as a noun used as an adjective, or an adjective as an adverb, without the addition of a formative suffix; or an infinitive without the sign "to".
- (wine) Lacking acidity without being sweet.
- (of coffee) Having little froth and little milk.
- (of a carbonated drink) With all or most of its carbon dioxide having come out of solution so that the drink no longer fizzes or contains any bubbles.
- sounded or spoken in a tone unvarying in pitch
- not reflecting light; not glossy
- having lost effervescence
- lacking contrast or shading between tones
- horizontally level
- stretched out and lying at full length along the ground
- having a relatively broad surface in relation to depth or thickness
- lacking taste or flavor or tang
- flattened laterally along the whole length (e.g., certain leafstalks or flatfishes)
- not modified or restricted by reservations
- commercially inactive
- lacking stimulating characteristics; uninteresting
- having a surface without slope, tilt in which no part is higher or lower than another
- (of a musical note) lowered in pitch by one chromatic semitone
- lacking the expected range or depth; not designed to give an illusion or depth
adv
- Completely, firmly, or unequivocally.
- Directly; flatly.
- (with units of time, distance, etc) Used to emphasize the smallness of the measurement.
- (finance, slang) Without allowance for accrued interest.
- Completely.
- (of accurately measured timings) Exactly, precisely.
- So as to be flat.
- (of a sentence) Without parole.
- with flat sails
- in a forthright manner; candidly or frankly
verb
- (transitive) To dash or throw
- (poker slang) To make a flat call; to call without raising.
- (intransitive) To become flat or flattened; to sink or fall to an even surface.
- (intransitive, music, colloquial) To fall from the pitch.
- (intransitive) To dash, rush
- (transitive, music) To depress in tone, as a musical note; especially, to lower in pitch by half a tone.
noun
- (mathematics) calculation of the value of a function outside the range of known values
- (mathematics) A calculation of an estimate of the value of some function outside the range of known values.
- an inference about the future (or about some hypothetical situation) based on known facts and observations
- (music) The diametric opposite of interpolation.
- An inference about some hypothetical situation based on known facts.
noun
- The range or limit of any dimension in which one exists.
- The visible horizontal line (in all directions) where the sky appears to meet the earth in the distance.
- Any level line or surface.
- (computer chess) The point at which a computer chess algorithm stops searching for further moves.
- (figuratively) The range or limit of one's knowledge, experience or interest; a boundary or threshold.
- (archaeology, chiefly US) A cultural sub-period or level within a more encompassing time period.
- (geology) A specific layer of soil, or stratum
- a specific layer or stratum of soil or subsoil in a vertical cross section of land
- the line at which the sky and Earth appear to meet
- the great circle on the celestial sphere whose plane passes through the sensible horizon and the center of the Earth
- the range of interest or activity that can be anticipated
noun
- Ordinary n-dimensional space, characterized by an infinite extent along each dimension and a constant distance between any pair of parallel lines.
- (mathematics) Any real vector space on which a real-valued inner product (and, consequently, a metric) is defined.
- a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional
noun
- (mathematics) The value or range of values of a function for which a derivative does not exist.
- (physics) Ellipsis of gravitational singularity (“a point or region in spacetime in which gravitational forces cause matter to have an infinite density; associated with black holes”).
- Celibacy, singleness (as contrasted with marriage).
- A point where a measured variable reaches unmeasurable or infinite value.
- The state of being singular, distinct, peculiar, uncommon or unusual.
- (sometimes capitalized) Ellipsis of technological singularity (“a hypothetical turning point in the future, the culmination of ever-accelerating technological progress, when human history as we have known it ends, and a strange new era begins. For some writers, the catalyst is superhuman machine intelligence”).
- An unusual action or behaviour.
- A point where all parallel lines meet.
- strangeness by virtue of being remarkable or unusual
- the quality of being one of a kind
noun
- (mathematics) Any member of a (generalized) vector space.
- (computer graphics, attributive) A graphical representation using outlines; vector graphics.
- (history) Forces, developments, phenomena, processes, systems, etc. which influence the trajectory of history (e.g. imperialism)
- (aviation) A chosen course or direction for motion, as of an aircraft.
- (programming) A kind of dynamically resizable array.
- (psychology) A recurring psychosocial issue that stimulates growth and development in the personality.
- (sociology) A person or entity that passes along an urban legend or other meme.
- (mathematics, computing) An ordered tuple, originally one representing a directed quantity, but by extension any one-dimensional matrix.
- (mathematics, physics) A directed quantity, one with both magnitude and direction; the signed difference between two points.
- (molecular biology) A DNA molecule used to carry genetic information from one organism into another.
- (computing, operating systems) A memory address containing the address of a code entry point, usually one which is part of a table and often one that is dereferenced and jumped to during the execution of an interrupt.
- a straight line segment whose length is magnitude and whose orientation in space is direction
- (genetics) a virus or other agent that is used to deliver DNA to a cell
- any agent (person or animal or microorganism) that carries and transmits a disease
- a variable quantity that can be resolved into components
verb
adj
- (mathematics, of a category) In which all small limits exist.
- (algebra, of a lattice) In which every set with a lower bound has a greatest lower bound.
- (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).
- 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.
- (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
- (geometry) The set of all points in three-dimensional Euclidean space (or n-dimensional space, in topology) that are a fixed distance from a fixed point .
- (figuratively) The region in which something or someone is active; one's province, domain.
- The natural, normal, or proper place (of something).
- (historical, astronomy, mythology) Any of the concentric hollow transparent globes formerly believed to rotate around the Earth, and which carried the heavenly bodies; there were originally believed to be eight, and later nine and ten; friction between them was thought to cause a harmonious sound (the music of the spheres).
- (mythology) An area of activity for a planet; or by extension, an area of influence for a god, hero etc.
- (mathematics) A surface in three dimensions consisting of all points equidistant from a center. .
- An object which appears to be bounded by a sphere; a round object, a ball.
- the geographical area in which one nation is very influential
- a solid figure bounded by a spherical surface (including the space it encloses)
- the apparent surface of the imaginary sphere on which celestial bodies appear to be projected
- any spherically shaped artifact
- a three-dimensional closed surface such that every point on the surface is equidistant from the center
- a particular environment or walk of life
- a particular aspect of life or activity
verb
noun
adj
- (mathematics) Characterised by a rate of change that is proportional to the value of the varying quantity, or, equivalently, by a doubling or halving over successive fixed intervals of time or other parameter, described as exponential growth or exponential decay.
- Relating to an exponent.
- (loosely) Characterised by a very rapid rate of change, especially increase, or merely a very large amount or degree.
- (mathematics) Expressed in terms of an exponent (power of a base), the base often being 10 or e.
- of or involving exponents
noun
- (mathematics) An infinitesimal interval of a quantity, a differential.
- One of the simplest or essential parts or principles of which anything consists, or upon which the constitution or fundamental powers of anything are based.
- A factor, one of the conditions contributing to a result.
- (chemistry) A chemical substance made entirely of one such type of atom; any one of the simplest chemical substances that cannot be decomposed in a chemical reaction or by any chemical means and made up of atoms all having the same number of protons.
- (usually in the plural) A basic, simple substance out of which something is made, raw material.
- A place or state of being that a person or object is best suited to.
- (chemistry) Any one of the types of atom distinguished by having a certain number of protons in its nucleus.
- (set theory) One of the objects in a set.
- (in the plural only, with "the") Atmospheric forces such as strong winds and rains.
- A group of people within a larger group having a particular common characteristic.
- A small but present amount of a quality, a hint.
- (law) A required aspect or component of a cause of action. A deed is regarded as a violation of law only if each element can be proved.
- A component in electrical equipment, often in the form of a coil, having a high resistance, thereby generating heat when a current is passed through it.
- (astronomy) An orbital element; one of the parameters needed to uniquely specify a particular orbit.
- (computing) One of the conceptual objects in a markup language, usually represented in text by tags.
- One of the four basic building blocks of matter in theories of ancient philosophers and alchemists: water, earth, fire, and air.
- (mathematics) One of the entries of a matrix.
- (Christianity, usually in the plural) The bread and wine taken at Holy Communion.
- Any of the teeth of a zip fastener.
- A small part of the whole.
- (in the plural only) The basic principles of a field of knowledge, basics, fundamentals, rudiments.
- an abstract part of something
- one of four substances thought in ancient and medieval cosmology to constitute the physical universe
- a straight line that generates a cylinder or cone
- any of the more than 100 known substances (of which 92 occur naturally) that cannot be separated into simpler substances and that singly or in combination constitute all matter
- the situation in which you are happiest and most effective
- the most favorable environment for a plant or animal
- an artifact that is one of the individual parts of which a composite entity is made up; especially a part that can be separated from or attached to a system
noun
- (algebraic topology, geometry) A generalization of a triangle or tetrahedron to an arbitrary dimension, the generalization being the simplest possible convex polytope for a given dimension; more accurately, the convex hull of n+1 affinely independent points in n-dimensional space.
- A word which is not compound and contains no derivational affixes (inflectional affixes are usually disregarded); a monomorphemic word.
- (originally and chiefly US) An apartment (or, sometimes, another type of property) having only one floor or storey; a single-storey property.
adj
- (linguistics) Of a word: having no (derivational) affixes; simple, monomorphemic, uncompounded.
- (computing, telecommunications) Of a circuit or device: involving signals which travel in one direction at a time; unidirectional.
- Of a polyploid organism: having one dominant allele at a given locus on all homologous chromosomes.
- (anatomy, historical) Of an eye: (supposedly) having pigment on only the posterior surface of the iris and not the anterior surface, and thus appearing blue; this was later found to be inaccurate, as eye colour is due to the amount of pigment in the anterior surface of the iris; also, of eye pigmentation: present only on the posterior surface of the iris; and of a person: having eyes with this form of pigmentation.
- (originally and chiefly US) Of an apartment (or, sometimes, another type of property): having only one floor or storey; single-storey.
- allowing communication in only one direction at a time, or in telegraphy allowing only one message over a line at a time
- having only one part or element
noun
verb
- (design, ambitransitive) To repeat an activity, making incremental changes each time.
- (computing, mathematics) To perform or repeat an action on the results of each such prior action.
- (computing) To perform or repeat an action on each item in a set.
- run or be performed again
- to say, state, or perform again
noun
- (geometry) A geometric figure in four or more dimensions, which is analogous to a cube in three dimensions. Specifically, the n-dimensional equivalent of a cube for any non-negative integer n.
- (geometry) Such a figure in four dimensions; a tesseract.
- (computing) A computer architecture in which each processor is connected to n others, by analogy with a hypercube of n dimensions.
- (computing) A data cube with more than three dimensions.
noun
- (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.
- 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
adj
- (mathematics, of a function) having an infinite number of derivatives at a point (otherwise it is monogenic)
- (genetics) controlled by the interaction of more than one gene
- of or relating to an inheritable character that is controlled by several genes at once; of or related to or determined by polygenes
noun
- the branch of mathematics that is concerned with limits and with the differentiation and integration of functions
- a hard lump produced by the concretion of mineral salts; found in hollow organs or ducts of the body
- an incrustation that forms on the teeth and gums
- (countable, mathematics) Any formal system in which symbolic expressions are manipulated according to fixed rules.
- (countable, medicine) A stony concretion that forms in a bodily organ.
- (uncountable, dentistry) Deposits of calcium phosphate salts on teeth.
- (uncountable, often definite, the calculus) Differential calculus and integral calculus considered as a single subject.
- (countable) A decision-making method, especially one appropriate for a specialised realm.
adj
- (mathematics, of a function) Having derivatives of all finite orders at all points within the function’s domain.
- (of muscles, medicine) Involuntary and non-striated.
- (of an action) Natural; unconstrained.
- Bland; glib.
- (mathematics, of a number) That factors completely into small prime numbers.
- Having a texture that lacks friction. Not rough.
- (of a motion) Unbroken.
- (linguistics, classical studies, of a vowel) Lacking marked aspiration.
- (of food or drink) Not grainy; having an even texture.
- (of an edge) Lacking projections or indentations; not serrated.
- Without difficulty, problems, or unexpected consequences or incidents.
- (of a beverage) Having a pleasantly rounded flavor; neither rough nor astringent.
- Flowing or uttered without check, obstruction, or hesitation; not harsh; fluent.
- Suave; sophisticated.
- (chiefly of water) Placid, calm.
- smooth and unconstrained in movement
- of the margin of a leaf shape; not broken up into teeth
- smoothly agreeable and courteous with a degree of sophistication
- lacking obstructions or difficulties
- (of a body of water) free from disturbance by heavy waves
- having a surface free from roughness or bumps or ridges or irregularities
- of motion that runs or flows or proceeds without jolts or turbulence
- (music) without breaks between notes; smooth and connected
adv
noun
verb
- (transitive) To make straightforward or easy.
- (transitive) To make smooth or even.
- (West Country) To stroke; especially to stroke an animal's fur.
- (transitive) To calm or palliate.
- (transitive) To reduce to a particular shape or form by pressure; to press, to flatten.
- (statistics, image processing, digital audio) To capture important patterns in the data, while leaving out noise.
- free from obstructions
- make smooth or smoother, as if by rubbing
- make (a surface) shine
noun
- (calculus) The operator which maps a function F=(F₁, ... Fₙ) from a n-dimensional vector space to itself to the function ∑ᵢ₌₁ⁿ(∂F_i)/(∂x_i).
- The process in which two or more populations accumulate genetic changes (mutations) through time.
- The state or degree of being divergent: of diverging.
- a difference between conflicting facts or claims or opinions
- an infinite series that has no limit
- a variation that deviates from the standard or norm
- the act of moving away in different direction from a common point
adj
- (of an algebra over a commutative ring) Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.
- (Lie theory, of an element x of a Lie algebra L) Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
- (Lie theory, of a Lie algebra) Such that the lower central series terminates.
- (ring theory, of an ideal I) Such that there exists a natural number k with Iᵏ = 0.
- (semigroup theory, of a semigroup with zero) Containing only nilpotent elements.
- (mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0.
- (group theory, of a group) Admitting a central series of finite length.
- equal to zero when raised to a certain power
noun
noun
adj
noun
- A range; a continuous, infinite, one-dimensional set, possibly bounded by extremes.
- (psychology, education, usually with the) The autism spectrum.
- Specifically, a range of colours representing light (electromagnetic radiation) of contiguous frequencies; hence electromagnetic spectrum, visible spectrum, ultraviolet spectrum, etc.
- (mathematics, linear algebra) The set of eigenvalues of a matrix.
- (mathematics, functional analysis) Of a bounded linear operator A, the set of scalar values λ such that the operator A—λI, where I denotes the identity operator, does not have a bounded inverse; intended as a generalisation of the linear algebra sense.
- The image of something seen that persists after the eyes are closed.
- (chemistry) The pattern of absorption or emission of radiation produced by a substance when subjected to energy (radiation, heat, electricity, etc.).
- (commutative algebra, algebraic geometry) An abstract object in mathematics created from a commutative ring R and denoted operatorname Spec(R) or operatorname SpecR and said to be the spectrum of R; useful in the study of such rings for providing a geometric object which encodes many of the properties R, and in modern geometry for generalizing the notion of an algebraic variety to that of an affine scheme. Formally, the set of all prime ideals R equipped with the Zariski topology and augmented with a sheaf of rings called the structure sheaf, generated by the B-sheaf on the distinguished open sets D_f which assigns the localization of R at f to each set D_f, regarded as a ring of functions on D_f. See Spectrum of a ring on Wikipedia.Wikipedia
- an ordered array of the components of an emission or wave
- a broad range of related objects or values or qualities or ideas or activities
noun
- (mathematics) Any of several abstractions of this concept of limit.
- The final, utmost, or furthest point; the border or edge.
- (colloquial, as "the limit") A person who is exasperating, intolerable, astounding, etc.
- (logic, metaphysics) A determining feature; a distinguishing characteristic.
- (cycling) The first group of riders to depart in a handicap race.
- A restriction; a bound beyond which one may not go.
- (music) Ellipsis of harmonic limit.
- (category theory) The cone of a diagram through which any other cone of that same diagram can factor uniquely.
- (mathematics) A value to which a sequence converges. Equivalently, the common value of the upper limit and the lower limit of a sequence: if the upper and lower limits are different, then the sequence has no limit (i.e., does not converge).
- (poker) Fixed limit.
- the boundary of a specific area
- the greatest possible degree of something
- final or latest limiting point
- the greatest amount of something that is possible or allowed
- as far as something can go
- the mathematical value toward which a function goes as the independent variable approaches infinity
adj
verb
adj
- (mathematics) Of a function: that is always nonincreasing or nondecreasing on an interval.
- (of speech or a sound) Having a single unvaried pitch.
- (printing) Synonym of monochrome.
- sounded or spoken in a tone unvarying in pitch
- of a sequence or function; consistently increasing and never decreasing or consistently decreasing and never increasing in value
noun
verb
noun
verb
noun
- (geometry) A subset of n-dimensional space that is congruent to a Euclidean space of lower dimension.
- (American football) The areas behind the line of scrimmage to either side of an offensive football formation.
- (rail transport) A flat spot on the wheel of a rail vehicle.
- (publishing) A flat, glossy children's book with few pages.
- An area of level ground (sometimes covered with shallow or tidal water).
- (technical, theatre, stagecraft) A rectangular wooden structure covered with masonite, lauan, or muslin, often produced in standard modules, that is used to build wall surfaces on stage. Flats can be painted and outfitted with doors and/or windows to depict a building or other part of a scene, and are a hard-surfaced alternative to a backcloth or backdrop.
- (entomology) Any of various hesperiid butterflies that spread their wings open when they land.
- A flat sheet for use on a bed.
- (horse racing, with 'the' or attributively, sometimes with capital) Level horse-racing ground, as contrasted with courses incorporating jumps, or the racing done on such ground.
- (postal) A large mail piece measuring at least 8 1/2 by 11 inches, such as catalogs, magazines, and unfolded paper enclosed in large envelopes.
- (music) A note played one chromatic semitone lower than a natural, denoted by the symbol ♭ placed after the letter representing the note (e.g., B♭) or in front of the note symbol (e.g. ♭♪).
- (in the plural) A type of ladies' shoe with a very low heel.
- (informal, automotive) A flat tyre/flat tire.
- (painting) A thin, broad brush used in oil and watercolour painting.
- (optics) A flat (i.e. plane) mirror
- Ellipsis of flat ride (“spinning amusement ride”).
- A wide, shallow container or pallet.
- (in the plural) A type of flat-soled running shoe without spikes.
- The most prominent flat part of something.
- A flat-bottomed boat, without keel, and of small draught.
- (swordfighting) The flat side of a blade, as opposed to the sharp edge.
- A straw hat, broad-brimmed and low-crowned.
- A platform on a wheel, upon which emblematic designs etc. are carried in processions.
- (Australia, horse racing, with 'the' or attributively, sometimes with capital) the area in the centre of a racecourse.
- (gambling, slang) A cheater's die with the edges shaved to make certain rolls more likely.
- (in the phrase 'the flat') Level ground in general.
- (historical) An early kind of toy soldier having a flat design.
- (US) Ellipsis of flat water (“nonfizzy drinking water”).
- (chiefly British, New England, South Africa, India, Australia, New Zealand, Singapore, archaic elsewhere) A complete domicile occupying only part of a building, especially one for rent
- (Canadian Prairies, British Columbia) A 24-case of beer.
- The palm of the hand, with the adjacent part of the fingers.
- (rail transport, US) A railroad car without a roof, and whose body is a platform without sides; a platform car or flatcar.
- (mining) A horizontal vein or ore deposit auxiliary to a main vein; also, any horizontal portion of a vein not elsewhere horizontal.
- a shallow box in which seedlings are started
- a deflated pneumatic tire
- scenery consisting of a wooden frame covered with painted canvas; part of a stage setting
- a level tract of land
- a musical notation indicating one half step lower than the note named
- a suite of rooms usually on one floor of an apartment house
- freight car without permanent sides or roof
adj
- (not comparable, commerce) Of fees, fares etc., fixed; unvarying.
- Smooth; having no protrusions, indentations or other surface irregularities, or relatively so.
- (golf, of a golf club) Having a head at a very obtuse angle to the shaft.
- At a consistently depressed level; consistently lacklustre.
- (of colours) Without variation in tone or hue (uniform), and dull (not glossy).
- (algebra, ring theory, of a ring homomorphism) Such that its target, regarded as a module over its source, is flat (as above).
- (music, note) Lowered by one semitone.
- In a horizontal line or plane; not sloping.
- (juggling, of a throw) Without spin; spinless.
- (algebraic geometry, scheme theory, of a morphism of schemes) Such that the induced map on every stalk is flat (as a map of rings).
- (authorship, figuratively, especially of a character) Lacking in depth, substance, or believability; underdeveloped; one-dimensional.
- (horticulture, of certain fruits) Flattening at the ends.
- (slang) Having small or invisible breasts and/or buttocks.
- (phonetics, of a vowel) Not diphthongal; without variation in height or backness.
- (of a tire or other inflated object) Deflated, especially because of a puncture.
- (homological algebra, of a module) Such that the tensor product preserves exact sequences. See Flat module on Wikipedia.Wikipedia.
- (of a battery) Unable to emit power; dead.
- (of measurements of time) Exact.
- Without variation in level, quantity, value, tone etc.
- Having no variations in height.
- (music) Of a note or voice, lower in pitch than it should be.
- (music, voice) Without variations in pitch.
- (figurative) Lacking liveliness or action; depressed; uninteresting; dull and boring.
- Absolute; downright; peremptory.
- (grammar) Not having an inflectional ending or sign, such as a noun used as an adjective, or an adjective as an adverb, without the addition of a formative suffix; or an infinitive without the sign "to".
- (wine) Lacking acidity without being sweet.
- (of coffee) Having little froth and little milk.
- (of a carbonated drink) With all or most of its carbon dioxide having come out of solution so that the drink no longer fizzes or contains any bubbles.
- sounded or spoken in a tone unvarying in pitch
- not reflecting light; not glossy
- having lost effervescence
- lacking contrast or shading between tones
- horizontally level
- stretched out and lying at full length along the ground
- having a relatively broad surface in relation to depth or thickness
- lacking taste or flavor or tang
- flattened laterally along the whole length (e.g., certain leafstalks or flatfishes)
- not modified or restricted by reservations
- commercially inactive
- lacking stimulating characteristics; uninteresting
- having a surface without slope, tilt in which no part is higher or lower than another
- (of a musical note) lowered in pitch by one chromatic semitone
- lacking the expected range or depth; not designed to give an illusion or depth
adv
- Completely, firmly, or unequivocally.
- Directly; flatly.
- (with units of time, distance, etc) Used to emphasize the smallness of the measurement.
- (finance, slang) Without allowance for accrued interest.
- Completely.
- (of accurately measured timings) Exactly, precisely.
- So as to be flat.
- (of a sentence) Without parole.
- with flat sails
- in a forthright manner; candidly or frankly
verb
- (transitive) To dash or throw
- (poker slang) To make a flat call; to call without raising.
- (intransitive) To become flat or flattened; to sink or fall to an even surface.
- (intransitive, music, colloquial) To fall from the pitch.
- (intransitive) To dash, rush
- (transitive, music) To depress in tone, as a musical note; especially, to lower in pitch by half a tone.
noun
- (mathematics) calculation of the value of a function outside the range of known values
- (mathematics) A calculation of an estimate of the value of some function outside the range of known values.
- an inference about the future (or about some hypothetical situation) based on known facts and observations
- (music) The diametric opposite of interpolation.
- An inference about some hypothetical situation based on known facts.
noun
- The range or limit of any dimension in which one exists.
- The visible horizontal line (in all directions) where the sky appears to meet the earth in the distance.
- Any level line or surface.
- (computer chess) The point at which a computer chess algorithm stops searching for further moves.
- (figuratively) The range or limit of one's knowledge, experience or interest; a boundary or threshold.
- (archaeology, chiefly US) A cultural sub-period or level within a more encompassing time period.
- (geology) A specific layer of soil, or stratum
- a specific layer or stratum of soil or subsoil in a vertical cross section of land
- the line at which the sky and Earth appear to meet
- the great circle on the celestial sphere whose plane passes through the sensible horizon and the center of the Earth
- the range of interest or activity that can be anticipated
noun
- Ordinary n-dimensional space, characterized by an infinite extent along each dimension and a constant distance between any pair of parallel lines.
- (mathematics) Any real vector space on which a real-valued inner product (and, consequently, a metric) is defined.
- a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional
noun
- (mathematics) The value or range of values of a function for which a derivative does not exist.
- (physics) Ellipsis of gravitational singularity (“a point or region in spacetime in which gravitational forces cause matter to have an infinite density; associated with black holes”).
- Celibacy, singleness (as contrasted with marriage).
- A point where a measured variable reaches unmeasurable or infinite value.
- The state of being singular, distinct, peculiar, uncommon or unusual.
- (sometimes capitalized) Ellipsis of technological singularity (“a hypothetical turning point in the future, the culmination of ever-accelerating technological progress, when human history as we have known it ends, and a strange new era begins. For some writers, the catalyst is superhuman machine intelligence”).
- An unusual action or behaviour.
- A point where all parallel lines meet.
- strangeness by virtue of being remarkable or unusual
- the quality of being one of a kind
noun
- (mathematics) Any member of a (generalized) vector space.
- (computer graphics, attributive) A graphical representation using outlines; vector graphics.
- (history) Forces, developments, phenomena, processes, systems, etc. which influence the trajectory of history (e.g. imperialism)
- (aviation) A chosen course or direction for motion, as of an aircraft.
- (programming) A kind of dynamically resizable array.
- (psychology) A recurring psychosocial issue that stimulates growth and development in the personality.
- (sociology) A person or entity that passes along an urban legend or other meme.
- (mathematics, computing) An ordered tuple, originally one representing a directed quantity, but by extension any one-dimensional matrix.
- (mathematics, physics) A directed quantity, one with both magnitude and direction; the signed difference between two points.
- (molecular biology) A DNA molecule used to carry genetic information from one organism into another.
- (computing, operating systems) A memory address containing the address of a code entry point, usually one which is part of a table and often one that is dereferenced and jumped to during the execution of an interrupt.
- a straight line segment whose length is magnitude and whose orientation in space is direction
- (genetics) a virus or other agent that is used to deliver DNA to a cell
- any agent (person or animal or microorganism) that carries and transmits a disease
- a variable quantity that can be resolved into components
verb
noun
- (geometry) The set of all points in three-dimensional Euclidean space (or n-dimensional space, in topology) that are a fixed distance from a fixed point .
- (figuratively) The region in which something or someone is active; one's province, domain.
- The natural, normal, or proper place (of something).
- (historical, astronomy, mythology) Any of the concentric hollow transparent globes formerly believed to rotate around the Earth, and which carried the heavenly bodies; there were originally believed to be eight, and later nine and ten; friction between them was thought to cause a harmonious sound (the music of the spheres).
- (mythology) An area of activity for a planet; or by extension, an area of influence for a god, hero etc.
- (mathematics) A surface in three dimensions consisting of all points equidistant from a center. .
- An object which appears to be bounded by a sphere; a round object, a ball.
- the geographical area in which one nation is very influential
- a solid figure bounded by a spherical surface (including the space it encloses)
- the apparent surface of the imaginary sphere on which celestial bodies appear to be projected
- any spherically shaped artifact
- a three-dimensional closed surface such that every point on the surface is equidistant from the center
- a particular environment or walk of life
- a particular aspect of life or activity
verb
noun
adj
- (mathematics) Characterised by a rate of change that is proportional to the value of the varying quantity, or, equivalently, by a doubling or halving over successive fixed intervals of time or other parameter, described as exponential growth or exponential decay.
- Relating to an exponent.
- (loosely) Characterised by a very rapid rate of change, especially increase, or merely a very large amount or degree.
- (mathematics) Expressed in terms of an exponent (power of a base), the base often being 10 or e.
- of or involving exponents
noun
- (mathematics) An infinitesimal interval of a quantity, a differential.
- One of the simplest or essential parts or principles of which anything consists, or upon which the constitution or fundamental powers of anything are based.
- A factor, one of the conditions contributing to a result.
- (chemistry) A chemical substance made entirely of one such type of atom; any one of the simplest chemical substances that cannot be decomposed in a chemical reaction or by any chemical means and made up of atoms all having the same number of protons.
- (usually in the plural) A basic, simple substance out of which something is made, raw material.
- A place or state of being that a person or object is best suited to.
- (chemistry) Any one of the types of atom distinguished by having a certain number of protons in its nucleus.
- (set theory) One of the objects in a set.
- (in the plural only, with "the") Atmospheric forces such as strong winds and rains.
- A group of people within a larger group having a particular common characteristic.
- A small but present amount of a quality, a hint.
- (law) A required aspect or component of a cause of action. A deed is regarded as a violation of law only if each element can be proved.
- A component in electrical equipment, often in the form of a coil, having a high resistance, thereby generating heat when a current is passed through it.
- (astronomy) An orbital element; one of the parameters needed to uniquely specify a particular orbit.
- (computing) One of the conceptual objects in a markup language, usually represented in text by tags.
- One of the four basic building blocks of matter in theories of ancient philosophers and alchemists: water, earth, fire, and air.
- (mathematics) One of the entries of a matrix.
- (Christianity, usually in the plural) The bread and wine taken at Holy Communion.
- Any of the teeth of a zip fastener.
- A small part of the whole.
- (in the plural only) The basic principles of a field of knowledge, basics, fundamentals, rudiments.
- an abstract part of something
- one of four substances thought in ancient and medieval cosmology to constitute the physical universe
- a straight line that generates a cylinder or cone
- any of the more than 100 known substances (of which 92 occur naturally) that cannot be separated into simpler substances and that singly or in combination constitute all matter
- the situation in which you are happiest and most effective
- the most favorable environment for a plant or animal
- an artifact that is one of the individual parts of which a composite entity is made up; especially a part that can be separated from or attached to a system
noun
- (algebraic topology, geometry) A generalization of a triangle or tetrahedron to an arbitrary dimension, the generalization being the simplest possible convex polytope for a given dimension; more accurately, the convex hull of n+1 affinely independent points in n-dimensional space.
- A word which is not compound and contains no derivational affixes (inflectional affixes are usually disregarded); a monomorphemic word.
- (originally and chiefly US) An apartment (or, sometimes, another type of property) having only one floor or storey; a single-storey property.
adj
- (linguistics) Of a word: having no (derivational) affixes; simple, monomorphemic, uncompounded.
- (computing, telecommunications) Of a circuit or device: involving signals which travel in one direction at a time; unidirectional.
- Of a polyploid organism: having one dominant allele at a given locus on all homologous chromosomes.
- (anatomy, historical) Of an eye: (supposedly) having pigment on only the posterior surface of the iris and not the anterior surface, and thus appearing blue; this was later found to be inaccurate, as eye colour is due to the amount of pigment in the anterior surface of the iris; also, of eye pigmentation: present only on the posterior surface of the iris; and of a person: having eyes with this form of pigmentation.
- (originally and chiefly US) Of an apartment (or, sometimes, another type of property): having only one floor or storey; single-storey.
- allowing communication in only one direction at a time, or in telegraphy allowing only one message over a line at a time
- having only one part or element
noun
verb
- (design, ambitransitive) To repeat an activity, making incremental changes each time.
- (computing, mathematics) To perform or repeat an action on the results of each such prior action.
- (computing) To perform or repeat an action on each item in a set.
- run or be performed again
- to say, state, or perform again
noun
- (geometry) A geometric figure in four or more dimensions, which is analogous to a cube in three dimensions. Specifically, the n-dimensional equivalent of a cube for any non-negative integer n.
- (geometry) Such a figure in four dimensions; a tesseract.
- (computing) A computer architecture in which each processor is connected to n others, by analogy with a hypercube of n dimensions.
- (computing) A data cube with more than three dimensions.
noun
- (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.
- 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
noun
- the branch of mathematics that is concerned with limits and with the differentiation and integration of functions
- a hard lump produced by the concretion of mineral salts; found in hollow organs or ducts of the body
- an incrustation that forms on the teeth and gums
- (countable, mathematics) Any formal system in which symbolic expressions are manipulated according to fixed rules.
- (countable, medicine) A stony concretion that forms in a bodily organ.
- (uncountable, dentistry) Deposits of calcium phosphate salts on teeth.
- (uncountable, often definite, the calculus) Differential calculus and integral calculus considered as a single subject.
- (countable) A decision-making method, especially one appropriate for a specialised realm.
noun
- (calculus) The operator which maps a function F=(F₁, ... Fₙ) from a n-dimensional vector space to itself to the function ∑ᵢ₌₁ⁿ(∂F_i)/(∂x_i).
- The process in which two or more populations accumulate genetic changes (mutations) through time.
- The state or degree of being divergent: of diverging.
- a difference between conflicting facts or claims or opinions
- an infinite series that has no limit
- a variation that deviates from the standard or norm
- the act of moving away in different direction from a common point
noun
adj
noun
- A range; a continuous, infinite, one-dimensional set, possibly bounded by extremes.
- (psychology, education, usually with the) The autism spectrum.
- Specifically, a range of colours representing light (electromagnetic radiation) of contiguous frequencies; hence electromagnetic spectrum, visible spectrum, ultraviolet spectrum, etc.
- (mathematics, linear algebra) The set of eigenvalues of a matrix.
- (mathematics, functional analysis) Of a bounded linear operator A, the set of scalar values λ such that the operator A—λI, where I denotes the identity operator, does not have a bounded inverse; intended as a generalisation of the linear algebra sense.
- The image of something seen that persists after the eyes are closed.
- (chemistry) The pattern of absorption or emission of radiation produced by a substance when subjected to energy (radiation, heat, electricity, etc.).
- (commutative algebra, algebraic geometry) An abstract object in mathematics created from a commutative ring R and denoted operatorname Spec(R) or operatorname SpecR and said to be the spectrum of R; useful in the study of such rings for providing a geometric object which encodes many of the properties R, and in modern geometry for generalizing the notion of an algebraic variety to that of an affine scheme. Formally, the set of all prime ideals R equipped with the Zariski topology and augmented with a sheaf of rings called the structure sheaf, generated by the B-sheaf on the distinguished open sets D_f which assigns the localization of R at f to each set D_f, regarded as a ring of functions on D_f. See Spectrum of a ring on Wikipedia.Wikipedia
- an ordered array of the components of an emission or wave
- a broad range of related objects or values or qualities or ideas or activities
noun
- (mathematics) Any of several abstractions of this concept of limit.
- The final, utmost, or furthest point; the border or edge.
- (colloquial, as "the limit") A person who is exasperating, intolerable, astounding, etc.
- (logic, metaphysics) A determining feature; a distinguishing characteristic.
- (cycling) The first group of riders to depart in a handicap race.
- A restriction; a bound beyond which one may not go.
- (music) Ellipsis of harmonic limit.
- (category theory) The cone of a diagram through which any other cone of that same diagram can factor uniquely.
- (mathematics) A value to which a sequence converges. Equivalently, the common value of the upper limit and the lower limit of a sequence: if the upper and lower limits are different, then the sequence has no limit (i.e., does not converge).
- (poker) Fixed limit.
- the boundary of a specific area
- the greatest possible degree of something
- final or latest limiting point
- the greatest amount of something that is possible or allowed
- as far as something can go
- the mathematical value toward which a function goes as the independent variable approaches infinity
adj
verb
Nessuna parola corrispondente trovata. Prova una descrizione più ampia.
Nessuna parola corrispondente trovata. Prova una descrizione più ampia.
adj
- (mathematics, mathematical analysis, of a function) Whose range is a subset of the complex numbers.
- (mathematics, algebra) Whose coefficients are complex numbers; defined over the field of 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
- (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.
- (mathematics) A complex number.
- 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
- (mathematics, of a category) In which all small limits exist.
- (algebra, of a lattice) In which every set with a lower bound has a greatest lower bound.
- (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).
- 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.
- (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
adj
- (mathematics, of a function) having an infinite number of derivatives at a point (otherwise it is monogenic)
- (genetics) controlled by the interaction of more than one gene
- of or relating to an inheritable character that is controlled by several genes at once; of or related to or determined by polygenes
adj
- (mathematics, of a function) Having derivatives of all finite orders at all points within the function’s domain.
- (of muscles, medicine) Involuntary and non-striated.
- (of an action) Natural; unconstrained.
- Bland; glib.
- (mathematics, of a number) That factors completely into small prime numbers.
- Having a texture that lacks friction. Not rough.
- (of a motion) Unbroken.
- (linguistics, classical studies, of a vowel) Lacking marked aspiration.
- (of food or drink) Not grainy; having an even texture.
- (of an edge) Lacking projections or indentations; not serrated.
- Without difficulty, problems, or unexpected consequences or incidents.
- (of a beverage) Having a pleasantly rounded flavor; neither rough nor astringent.
- Flowing or uttered without check, obstruction, or hesitation; not harsh; fluent.
- Suave; sophisticated.
- (chiefly of water) Placid, calm.
- smooth and unconstrained in movement
- of the margin of a leaf shape; not broken up into teeth
- smoothly agreeable and courteous with a degree of sophistication
- lacking obstructions or difficulties
- (of a body of water) free from disturbance by heavy waves
- having a surface free from roughness or bumps or ridges or irregularities
- of motion that runs or flows or proceeds without jolts or turbulence
- (music) without breaks between notes; smooth and connected
adv
noun
verb
- (transitive) To make straightforward or easy.
- (transitive) To make smooth or even.
- (West Country) To stroke; especially to stroke an animal's fur.
- (transitive) To calm or palliate.
- (transitive) To reduce to a particular shape or form by pressure; to press, to flatten.
- (statistics, image processing, digital audio) To capture important patterns in the data, while leaving out noise.
- free from obstructions
- make smooth or smoother, as if by rubbing
- make (a surface) shine
adj
- (of an algebra over a commutative ring) Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.
- (Lie theory, of an element x of a Lie algebra L) Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
- (Lie theory, of a Lie algebra) Such that the lower central series terminates.
- (ring theory, of an ideal I) Such that there exists a natural number k with Iᵏ = 0.
- (semigroup theory, of a semigroup with zero) Containing only nilpotent elements.
- (mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0.
- (group theory, of a group) Admitting a central series of finite length.
- equal to zero when raised to a certain power
noun
adj
- (mathematics) Of a function: that is always nonincreasing or nondecreasing on an interval.
- (of speech or a sound) Having a single unvaried pitch.
- (printing) Synonym of monochrome.
- sounded or spoken in a tone unvarying in pitch
- of a sequence or function; consistently increasing and never decreasing or consistently decreasing and never increasing in value