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Glossary of Math Terms beginning with letter I
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icosahedron noun ( icosahedr, a , pl2=icosahedrons) (geometry) a polyhedron with twenty faces; the regular icosahedron has regular triangles as faces and is one of the Platonic solids. ideal noun a perfect standard of beauty, intellect, etc., or a standard of excellence. (algebra) A subring closed under multiplication by its containing ring. (mathematics) In order theory, a special subset of a partially ordered set. an unattainable state/process in a given time/space but endlessly approachable. adjective being optimal or relating to the best option for something. being perfect, having no flaws or defects. being something that exists only in the mind; CONCEPTUAL, ideational, IDEATIONAL, Life and death appeared to me ideal bounds :" Wikipedia:Mary W. Shelley, Mary W. Shelley idempotent adjective (computing) Describing an action which, when performed multiple times, has no further effect on its subject after the first time it is performed. identity element noun (algebra) A member of a structure which, when applied to any other element via a binary operation induces an identity mapping; more specifically, given an operation , an element I is a left identity if I x = x for any x in the structure a right identity, x I = x for any x in the structure simply an identity element if both are true identity matrix noun (plural identity matrices) (linearalg) A diagonal matrix all of the diagonal elements of which are equal to 1. IFF initialism Interchange File Format, a file format standard developed for Amiga computers. identification friend or foe image noun An optical or other representation of a real object; a graphic; a picture. A mental picture of something not real or not present. (computing) A copy of all or part of a disk drive retained for backup or replication purposes. A characteristic of a person, group or company etc., style, manner of dress, how one is, or wishes to be, perceived by others. (mathematics) Something mapped to by a function. 5 is the of 3 under f. (mathematics) The subset of a codomain comprising those elements that are images of something. The of this step function is the set of integers. verb (imag, ing) (context, computing) To convert an idea to an image. (context, computing) To create a complete backup copy of a filesystem. imaginary adjective that exists only in the imagination (mathematics) of, or being the imaginary part of a complex number imaginary axis noun (mathematics) The vertical line in the complex plane, every point on which corresponds to a complex number having zero real component imaginary number noun (plural imaginary numbers) (complex) A number of the form ai, where a is a real number and i² = −1; a complex number whose real part is zero. imaginary part noun (plural imaginary parts) (complex) Of a complex number a + bi, the value b. implicit adjective implied, Implied indirectly, without being directly expressed 1983, w:Ronald Reagan, Ronald Reagan, s:Proclamation 5018, Proclamation 5018 :The Bible and its teachings helped form the basis for the Founding Fathers' abiding belief in the inalienable rights of the individual, rights which they found in the Bible's teachings of the inherent worth and dignity of each individual. contained, Contained in the essential nature of something but not openly shown Having no reservations or doubts; unquestioning or unconditional; usually said of faith or trust. 1765, Anonymous, s:Considerations on Behalf of the Colonists, Considerations on Behalf of the Colonists :He is not only a zealous advocate for pusilanimous and passive obedience, but for the most faith in the dictatorial mandates of power. (obsolete) entangled, twisted together. improper fraction $Tweet Definition of improper fraction$ $Like Definition of improper fraction on Facebook$ noun (plural improper fractions) (arithmetic) A vulgar fraction of which the numerator has a greater magnitude than the denominator, such as 3/2. incircle noun (wikipedia, Incircle and excircles of a triangle) The circle within a triangle that is tangent to all three sides. The incentre is the center of this circle. increasing verb (present participle of, increase) indefinite integral noun (mathematics) A function whose derivative is a given function; an antiderivative independent noun A candidate or voter not affiliated with any political party, a free thinker, free of a party platform. A neutral or uncommitted person. adjective not dependent; not contingent or depending on something else; free independent variable noun (plural independent variables) (algebra) In an equation, any variable whose value is not dependent on any other in the equation. In the equation z = x² + y, x and y are the independent variables. (science) The variable that is changed in an experiment. indeterminate adjective not accurately determined or determinable imprecise or vague induction noun the act of inducting a formal ceremony in which a person is inducted into an office or into military service (physics) the generation of an electric current by a varying magnetic field (logic) the derivation of general principles from specific instances (mathematics) a general proof of a theorem by first proving it for a specific integer (for example) and showing that, if it is true for one integer then it must be true for the next the act of inducing childbirth In theatre, induction is the use of rumors to twist and complicate the plot of a play or to narrate in a way that does not have to state truth nor fact within the play. (biology) In developmental biology, the development of a feature from part of a formerly homogenous field of cells in response to a morphogen whose source determines the feature's position and extent. (obsolete) an introduction inequality noun (inequalit, ies) An unfair, not equal, state. The in living standards lead to a civil war as the have nots rebelled. (mathematics) A statement that of two quantities one is specifically less than (or greater than) another. The x is less than y, together with that y<z, allows us to deduce the x<z. (context, mathematics, more, _, generally) A statement that of two quantities one is specifically less than (or greater than, or not less than, or not greater than) another. infimum noun (infima) (mathematics) (of a subset) the greatest element of the containing set that is smaller or equal to all elements of the subset. The infimum may or may not be a member of the subset. infinite adjective boundless, Boundless, endless, without end or limits, uncountable, innumerable. (mathematics) A number which is larger than any given number. (figuratively) Very large. infinitesimal noun (mathematics) A non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number). adjective Too small to measure (mathematics) Of or pertaining to values that approach zero as a limit infinitesimal calculus noun (uncountable) (calculus) differential calculus, Differential calculus and integral calculus considered together as a single subject. inflection noun (grammar) a change in the form of a word that reflects a change in grammatical function. a change in pitch or tone of voice. (context, math) a change in curvature from concave to convex or from convex to concave. a turning away from a straight course. inflection point noun (mathematics) a point of inflection injection noun The act of injecting, or something that is injected. (context, specifically, medicine) Something injected subcutaneously, intravenously, or intramuscularly by use of a syringe and a needle. (math) A function of "one-to-many" mapping relationship; more formally, f: X → Y is an injection if and only if, for every x in the function domain, domain X, there is at least one y in the function codomain, codomain Y with f(x) = y. inradius noun (mathematics) the radius of the largest circle that will fit inside any given geometric shape, especially inside a regular polygon (mathematics) the radus of the largest sphere that will fit inside any given polyhedron inscribe verb (inscrib, ing) (transitive) To write or cut words onto something, especially a hard surface; to engrave. (geometry) To draw a circle, sphere, etc. inside a polygon, polyhedron, etc. and tangent to all its sides. integer noun (arithmetic) An element of the infinite and numerable set ...,-3,-2,-1,0,1,2,3,.... adjective (arithmetic) Of a number, whole. integrable adjective (calculus) Able to be integrated integral noun (mathematics) A numerical measure computed by a limiting process in which the domain of a function is divided into small subintervals and the value of the function at a point in each subinterval is multiplied by the measurement of that subinterval, all these products then being summed. (mathematics) the result of summation of the product of a function and an infinitesimal. adjective constitute, Constituting a whole together with other parts or factors; not omittable or removable (mathematics) Of or relating to an integer. integral calculus noun (uncountable) (calculus) The calculus that generalizes summation to find areas, masses, volumes, sums, and totals of quantities described by continuously varying functions. integral equation noun (mathematics) An equation involving a function <math>f(x)</math> and integrals of that function to be solved for <math>f(x)</math> integral function noun (mathematics) An entire function integrand noun (calculus) The function that is to be integrated integrate verb (integrates, integrating, integrated) To form into one whole; to make entire; to complete; to renew; to restore; to perfect. To indicate the whole of; to give the sum or total of; as, an integrating anemometer, one that indicates or registers the entire action of the wind in a given time. (mathematics) To subject to the operation of integration; to find the integral of. To desegregate, as a school or neighborhood. integration noun The act or process of making whole or entire. (calculus) The operation of finding the integral of a function. In evolution, the process by which the manifold is compacted into the relatively simple and permanent; supposed to alternate with differentiation as an agent in development. intercept noun (rfc-level, Noun at L4+ not in L3 POS section) An interception of a radio broadcast or a telephone call. An interception of a missile. (alggeom) The coordinate of the point at which a curve intersects an axis. verb (transitive) To stop, deflect or divert (something in progress or motion). (context, transitive, sports) To gain possession of (the ball) in a ball game. interior noun The inside of a building, container, cavern, or other enclosed structure. The inside regions of a country, distanced from from the borders or coasts. ''Sir Richard Burton explored far into the African . adjective having to do with the inner part of something having to do with the inland parts of a country far from the coasts interior angle noun (geometry) The inner angle between two sides of a polygon. interpolate verb (interpolat, ing) To estimate the value of a function between two points between which it is tabulated. (Computing) During the course of processing some data, and in response to a directive in that data, to fetch data from a different source and process it in-line along with the original data. intersect verb to cross each other; to cut each other Parallel lines don't intersect. (mathematics) two sets if and only if they have at least one common element INTO initialism The Irish national teacher's organisation invariant adjective never changing inverse function noun (mathematics) The function having as independent variable the dependent variable of another inversely adverb In an inverse order or manner; by inversion. inversion noun (music) The move of one pitch in an interval or chord up or down an octave (music) The reversal of an interval (music) The reversal of the pitch contour (music) The reversal of a pitch class succesion such as a melody or counterpoint, contrapuntal line (music) Subtraction of pitch classes in a set from twelve which maps intervals onto their complements with respect to 0 and preserves interval classes, symbolized IX where X is the transposition which is inverted (DeLone? et. al. (Eds.), 1975, chap. 6). (genetics) a segment of DNA in the context of a chromosome that is reversed in orientation relative to a reference karyotype or genome (Weather). An increase of air temperature with increase in altitude (the ground being colder than the surrounding air). When an inversion exists, there are no convection currents and wind speeds are below 5 knots. The atmosphere is stable and normally is considered the most favorable state for ground release of chemical agents. (grammar) deviation, Deviation from standard word order by putting the predicate before the subject. It takes place in questions with auxiliary verbs and in normal, affirmative clauses beginning with a negative particle, for the purpose of emphasis. (with an auxiliary verb) Inversion takes place in the sentence 'Is she here?' — 'is', the predicate, is before 'she', the subject. (for the purpose of emphasis) Inversion takes place in the sentence 'Never have I done that.' — 'have', the predicate, is before 'I', the subject, due to 'never' being the first word of the sentence. involute noun (mathematics) A curve that cuts all tangents of another curve at right angles; traced by a point on a string that unwinds from a curved object. adjective difficult to understand, or complicated (context, botany, of a leaf or petal) having the edges rolled inwards (context, biology, of some shells) having a complex pattern of coils involution noun entanglement; a spiralling inwards; intricacy 1968: "Gomez," said the mortician, "is an expert only on the involutions of his own rectum." " Anthony Burgess, Enderby Outside (mathematics) An endofunction whose square is equal to the identity function; a function equal to its inverse. irrational adjective ((compar) more irrational, (superl) most irrational) Not rational; unfounded or nonsensical. an irrational decision (mathematics) (no comparative or superlative) Of a real number, that cannot be written as the ratio of two integers. The number π is irrational. irrational number noun (plural irrational numbers) (mathematics) Any real number that cannot be expressed as a ratio of two integers. isogon noun A line of equal or constant wind direction on a graph or chart, such as a weather map. isometric noun A line connecting isometric points. adjective Of, or exhibiting equality in dimensions Of, or being a geometric system of three equal axes lying at right angles to each other (especially in crystallography). (physiology) Of or involving muscular contraction against resistance in which the length of the muscle remains the same (physics) (of a thermodynamic process) taking place at constant volume because of being confined by rigid boundaries isometry noun (isometries) (mathematics) A function between metric spaces (or on a single metric space) having the property that the distance between two images is equal to the distance between their pre-images. isomorphic adjective (biology) having a similar structure to something that is not related genetically (mathematics) related by an isomorphism isomorphism noun (biology) the similarity in form of organisms of different ancestry (mathematics) a one-to-one correspondence between all the elements of two sets such that any operation returns the same result on either set; a function that maps one of these sets to the other (chemistry) the similarity in the crystal structures of similar chemical compounds (sociology) the similarity in the structure or processes of different organizations (computer science) a one-to-one correspondence between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets isosceles adjective (geometry) having two sides of equal length, used especially of an isosceles triangle.

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