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.
  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

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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
1. (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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