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Glossary of Math Terms
beginning with letter I
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icosahedron Tweet Definition of icosahedron Like Definition of icosahedron on Facebook
noun ( icosahedr, a , pl2=icosahedrons)
  1. (geometry) a polyhedron with twenty faces; the regular icosahedron has regular triangles as faces and is one of the Platonic solids.
ideal Tweet Definition of ideal Like Definition of ideal on Facebook
noun
  1. a perfect standard of beauty, intellect, etc., or a standard of excellence.
  2. (algebra) A subring closed under multiplication by its containing ring.
  3. (mathematics) In order theory, a special subset of a partially ordered set.
  4. an unattainable state/process in a given time/space but endlessly approachable.
adjective
  1. being optimal or relating to the best option for something.
  2. being perfect, having no flaws or defects.
  3. 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 Tweet Definition of idempotent Like Definition of idempotent on Facebook
adjective
  1. (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 Tweet Definition of identity element Like Definition of identity element on Facebook
noun
  1. (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 Tweet Definition of identity matrix Like Definition of identity matrix on Facebook
    noun (pluralidentity matrices)
    1. (linearalg) A diagonal matrix all of the diagonal elements of which are equal to 1.
    IFF Tweet Definition of IFF Like Definition of IFF on Facebook
    initialism
    1. Interchange File Format, a file format standard developed for Amiga computers.
    2. identification friend or foe
    image Tweet Definition of image Like Definition of image on Facebook
    noun
    1. An optical or other representation of a real object; a graphic; a picture.
    2. A mental picture of something not real or not present.
    3. (computing) A copy of all or part of a disk drive retained for backup or replication purposes.
    4. A characteristic of a person, group or company etc., style, manner of dress, how one is, or wishes to be, perceived by others.
    5. (mathematics) Something mapped to by a function.
    5 is the of 3 under f.
    1. (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)
    1. (context, computing) To convert an idea to an image.
    2. (context, computing) To create a complete backup copy of a filesystem.
    imaginary Tweet Definition of imaginary Like Definition of imaginary on Facebook
    adjective
    1. that exists only in the imagination
    1. (mathematics) of, or being the imaginary part of a complex number
    imaginary axis Tweet Definition of imaginary axis Like Definition of imaginary axis on Facebook
    noun
    1. (mathematics) The vertical line in the complex plane, every point on which corresponds to a complex number having zero real component
    imaginary number Tweet Definition of imaginary number Like Definition of imaginary number on Facebook
    noun (pluralimaginary numbers)
    1. (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 Tweet Definition of imaginary part Like Definition of imaginary part on Facebook
    noun (pluralimaginary parts)
    1. (complex) Of a complex number a + bi, the value b.
    implicit Tweet Definition of implicit Like Definition of implicit on Facebook
    adjective
    1. 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.
        1. contained, Contained in the essential nature of something but not openly shown
        2. 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.
        1. (obsolete) entangled, twisted together.
    improper fraction Tweet Definition of improper fraction Like Definition of improper fraction on Facebook
    noun (pluralimproper fractions)
    1. (arithmetic) A vulgar fraction of which the numerator has a greater magnitude than the denominator, such as 3/2.
    incircle Tweet Definition of incircle Like Definition of incircle on Facebook
    noun (wikipedia, Incircle and excircles of a triangle)
    1. The circle within a triangle that is tangent to all three sides. The incentre is the center of this circle.
    increasing Tweet Definition of increasing Like Definition of increasing on Facebook
    verb
    1. (present participle of, increase)
    indefinite integral Tweet Definition of indefinite integral Like Definition of indefinite integral on Facebook
    noun
    1. (mathematics) A function whose derivative is a given function; an antiderivative
    independent Tweet Definition of independent Like Definition of independent on Facebook
    noun
    1. A candidate or voter not affiliated with any political party, a free thinker, free of a party platform.
    2. A neutral or uncommitted person.
    adjective
    1. not dependent; not contingent or depending on something else; free
    independent variable Tweet Definition of independent variable Like Definition of independent variable on Facebook
    noun (pluralindependent variables)
    1. (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.
    1. (science) The variable that is changed in an experiment.
    indeterminate Tweet Definition of indeterminate Like Definition of indeterminate on Facebook
    adjective
    1. not accurately determined or determinable
    2. imprecise or vague
    induction Tweet Definition of induction Like Definition of induction on Facebook
    noun
    1. the act of inducting
    2. a formal ceremony in which a person is inducted into an office or into military service
    3. (physics) the generation of an electric current by a varying magnetic field
    4. (logic) the derivation of general principles from specific instances
    5. (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
    6. the act of inducing childbirth
    7. 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.
    8. (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.
    9. (obsolete) an introduction
    inequality Tweet Definition of inequality Like Definition of inequality on Facebook
    noun (inequalit, ies)
    1. An unfair, not equal, state.
    The in living standards lead to a civil war as the have nots rebelled.
    1. (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.
    1. (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 Tweet Definition of infimum Like Definition of infimum on Facebook
    noun (infima)
    1. (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 Tweet Definition of infinite Like Definition of infinite on Facebook
    adjective
    1. boundless, Boundless, endless, without end or limits, uncountable, innumerable.
    2. (mathematics) A number which is larger than any given number.
    3. (figuratively) Very large.
    infinitesimal Tweet Definition of infinitesimal Like Definition of infinitesimal on Facebook
    noun
    1. (mathematics) A non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number).
    adjective
    1. Too small to measure
    1. (mathematics) Of or pertaining to values that approach zero as a limit
    infinitesimal calculus Tweet Definition of infinitesimal calculus Like Definition of infinitesimal calculus on Facebook
    noun (uncountable)
    1. (calculus) differential calculus, Differential calculus and integral calculus considered together as a single subject.
    inflection Tweet Definition of inflection Like Definition of inflection on Facebook
    noun
    1. (grammar) a change in the form of a word that reflects a change in grammatical function.
    2. a change in pitch or tone of voice.
    3. (context, math) a change in curvature from concave to convex or from convex to concave.
    4. a turning away from a straight course.
    inflection point Tweet Definition of inflection point Like Definition of inflection point on Facebook
    noun
    1. (mathematics) a point of inflection
    injection Tweet Definition of injection Like Definition of injection on Facebook
    noun
    1. The act of injecting, or something that is injected.
    2. (context, specifically, medicine) Something injected subcutaneously, intravenously, or intramuscularly by use of a syringe and a needle.
    3. (math) A function of "one-to-many" mapping relationship; more formally, f:&nbsp;X&nbsp;&rarr;&nbsp;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)&nbsp;=&nbsp;y.
    inradius Tweet Definition of inradius Like Definition of inradius on Facebook
    noun
    1. (mathematics) the radius of the largest circle that will fit inside any given geometric shape, especially inside a regular polygon
    2. (mathematics) the radus of the largest sphere that will fit inside any given polyhedron
    inscribe Tweet Definition of inscribe Like Definition of inscribe on Facebook
    verb (inscrib, ing)
    1. (transitive) To write or cut words onto something, especially a hard surface; to engrave.
    2. (geometry) To draw a circle, sphere, etc. inside a polygon, polyhedron, etc. and tangent to all its sides.
    integer Tweet Definition of integer Like Definition of integer on Facebook
    noun
    1. (arithmetic) An element of the infinite and numerable set ...,-3,-2,-1,0,1,2,3,....
    adjective
    1. (arithmetic) Of a number, whole.
    integrable Tweet Definition of integrable Like Definition of integrable on Facebook
    adjective
    1. (calculus) Able to be integrated
    integral Tweet Definition of integral Like Definition of integral on Facebook
    noun
    1. (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.
    2. (mathematics) the result of summation of the product of a function and an infinitesimal.
    adjective
    1. constitute, Constituting a whole together with other parts or factors; not omittable or removable
    2. (mathematics) Of or relating to an integer.
    integral calculus Tweet Definition of integral calculus Like Definition of integral calculus on Facebook
    noun (uncountable)
    1. (calculus) The calculus that generalizes summation to find areas, masses, volumes, sums, and totals of quantities described by continuously varying functions.
    integral equation Tweet Definition of integral equation Like Definition of integral equation on Facebook
    noun
    1. (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 Tweet Definition of integral function Like Definition of integral function on Facebook
    noun
    1. (mathematics) An entire function
    integrand Tweet Definition of integrand Like Definition of integrand on Facebook
    noun
    1. (calculus) The function that is to be integrated
    integrate Tweet Definition of integrate Like Definition of integrate on Facebook
    verb (integrates, integrating, integrated)
    1. To form into one whole; to make entire; to complete; to renew; to restore; to perfect.
    2. 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.
    3. (mathematics) To subject to the operation of integration; to find the integral of.
    4. To desegregate, as a school or neighborhood.
    integration Tweet Definition of integration Like Definition of integration on Facebook
    noun
    1. The act or process of making whole or entire.
    2. (calculus) The operation of finding the integral of a function.
    3. 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 Tweet Definition of intercept Like Definition of intercept on Facebook
    noun (rfc-level, Noun at L4+ not in L3 POS section)
    1. An interception of a radio broadcast or a telephone call.
    2. An interception of a missile.
    3. (alggeom) The coordinate of the point at which a curve intersects an axis.
    verb
    1. (transitive) To stop, deflect or divert (something in progress or motion).
    2. (context, transitive, sports) To gain possession of (the ball) in a ball game.
    interior Tweet Definition of interior Like Definition of interior on Facebook
    noun
    1. The inside of a building, container, cavern, or other enclosed structure.
    2. The inside regions of a country, distanced from from the borders or coasts.
    ''Sir Richard Burton explored far into the African .
    adjective
    1. having to do with the inner part of something
    2. having to do with the inland parts of a country far from the coasts
    interior angle Tweet Definition of interior angle Like Definition of interior angle on Facebook
    noun
    1. (geometry) The inner angle between two sides of a polygon.
    interpolate Tweet Definition of interpolate Like Definition of interpolate on Facebook
    verb (interpolat, ing)
    1. To estimate the value of a function between two points between which it is tabulated.
    2. (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 Tweet Definition of intersect Like Definition of intersect on Facebook
    verb
    1. to cross each other; to cut each other
    Parallel lines don't intersect.
    1. (mathematics) two sets if and only if they have at least one common element
    INTO Tweet Definition of INTO Like Definition of INTO on Facebook
    initialism
    1. The Irish national teacher's organisation
    invariant Tweet Definition of invariant Like Definition of invariant on Facebook
    adjective
    1. never changing
    inverse function Tweet Definition of inverse function Like Definition of inverse function on Facebook
    noun
    1. (mathematics) The function having as independent variable the dependent variable of another
    inversely Tweet Definition of inversely Like Definition of inversely on Facebook
    adverb
    1. In an inverse order or manner; by inversion.
    inversion Tweet Definition of inversion Like Definition of inversion on Facebook
    noun
    1. (music) The move of one pitch in an interval or chord up or down an octave
    2. (music) The reversal of an interval
    3. (music) The reversal of the pitch contour
    4. (music) The reversal of a pitch class succesion such as a melody or counterpoint, contrapuntal line
    5. (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).
    6. (genetics) a segment of DNA in the context of a chromosome that is reversed in orientation relative to a reference karyotype or genome
    7. (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.
    8. (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?' &mdash; 'is', the predicate, is before 'she', the subject.
    (for the purpose of emphasis) Inversion takes place in the sentence 'Never have I done that.' &mdash; 'have', the predicate, is before 'I', the subject, due to 'never' being the first word of the sentence.
    involute Tweet Definition of involute Like Definition of involute on Facebook
    noun
    1. (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
    1. difficult to understand, or complicated
    2. (context, botany, of a leaf or petal) having the edges rolled inwards
    3. (context, biology, of some shells) having a complex pattern of coils
    involution Tweet Definition of involution Like Definition of involution on Facebook
    noun
    1. 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
      1. (mathematics) An endofunction whose square is equal to the identity function; a function equal to its inverse.
    irrational Tweet Definition of irrational Like Definition of irrational on Facebook
    adjective ((compar) more irrational, (superl) most irrational)
    1. Not rational; unfounded or nonsensical.
    an irrational decision
    1. (mathematics) (no comparative or superlative) Of a real number, that cannot be written as the ratio of two integers.
    The number &pi; is irrational.
    irrational number Tweet Definition of irrational number Like Definition of irrational number on Facebook
    noun (pluralirrational numbers)
    1. (mathematics) Any real number that cannot be expressed as a ratio of two integers.
    isogon Tweet Definition of isogon Like Definition of isogon on Facebook
    noun
    1. A line of equal or constant wind direction on a graph or chart, such as a weather map.
    isometric Tweet Definition of isometric Like Definition of isometric on Facebook
    noun
    1. A line connecting isometric points.
    adjective
    1. Of, or exhibiting equality in dimensions
    2. Of, or being a geometric system of three equal axes lying at right angles to each other (especially in crystallography).
    3. (physiology) Of or involving muscular contraction against resistance in which the length of the muscle remains the same
    4. (physics) (of a thermodynamic process) taking place at constant volume because of being confined by rigid boundaries
    isometry Tweet Definition of isometry Like Definition of isometry on Facebook
    noun (isometries)
    1. (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 Tweet Definition of isomorphic Like Definition of isomorphic on Facebook
    adjective
    1. (biology) having a similar structure to something that is not related genetically
    2. (mathematics) related by an isomorphism
    isomorphism Tweet Definition of isomorphism Like Definition of isomorphism on Facebook
    noun
    1. (biology) the similarity in form of organisms of different ancestry
    2. (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
    3. (chemistry) the similarity in the crystal structures of similar chemical compounds
    4. (sociology) the similarity in the structure or processes of different organizations
    5. (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 Tweet Definition of isosceles Like Definition of isosceles on Facebook
    adjective
    1. (geometry) having two sides of equal length, used especially of an isosceles triangle.

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