irrational.adjective
not endowed with reason; marked by a lack of accord with reason or sound judgment
irrationally.adverb
irrationalness.noun

irrational number.noun
any real number that cannot be expressed as an integer or as a ratio between two integers

imaginary number.noun
a complex number in which the real part is zero and the coefficient of the imaginary unit is not zero

irrationality.noun,.plural.irrationalities
the state or quality of being irrational; an irrational idea, expression, or act

irrationalism.noun
irrational thought, expression, or behavior; irrationality; belief in feeling, instinct, or other non rational forces rather than reason

imperious.adjective
arrogantly domineering or overbearing
imperiously.adverb
imperiousness.noun
synonyms-dictatorial, authoritarian, dogmatic, doctrinaire, overbearing

incandescent.adjective
emitting visible light as a result of being heated; shining brilliantly; very bright; characterized by ardent emotion, intensity, or brilliance
incandescently.adverb

indifferent.adjective
not mattering one way or the other; having no marked feeling for or against; not active or involved; having no particular interest in or concern for; apathetic (indifferent to the sufferings of others); being neither too much nor too little; moderate; being neither good nor bad; mediocre (an indifferent performance); being neither right nor wrong; neutral (an indifferent chemical in a reaction); characterized by a lack of partiality; unbiased (a properly indifferent jury); 
indifferently.adverb
synonyms-unconcerned, incurious, detached, uninterested

indifference.noun
the state or quality of being indifferent

infrared.adjective
of or relating to the range of invisible radiation wavelengths from about 750 nanometers, just longer than red in the visible spectrum, to 1 millimeter, on the border of the microwave region
infrared.noun
infrared light or the infrared part of the spectrum

irony.noun,.ironies.plural
the use of words to express something different from and often opposite to their literal meaning; an expression or utterance marked by a deliberate contrast between apparent and intended meanin; incongruity between what might be expected and what actually occurs: 
ironic, also ironical.adjective
characterized by or constituting irony; given to the use of irony; poignantly contrary to what was expected or intended: madness, an ironic fate for such a clear thinker
ironically.adverb
ironicalness.noun
synonyms-sarcastic, caustic, satirical, sardonic

irreligious.adjective
hostile or indifferent to religion; ungodly
irreligiously.adverb
irreligiousness.noun

immanent.adjective
existing or remaining within; inherent (believed in a God immanent in human beings); restricted entirely to the mind; subjective;  (compare imminent)
immanence-or-immanency.noun
immanently.adverb

inerrant.adjective
incapable of erring; infallible; containing no errors

infallible.adjective
incapable of erring; incapable of failing; certain (an infallible antidote)
infallibility.or.infallibleness.noun
infallibly.adverb

iconoclast.noun
one who attacks and seeks to overthrow traditional or popular ideas or institutions
iconoclastic.adjective
iconoclastically.adverb

ionosphere.noun
a region of the earth's atmosphere where ionization caused by incoming solar radiation affects the transmission of radio waves. It extends from a height of 50 kilometers (30 miles) to 400 kilometers (250 miles) above the surface
ionospheric.adjective

invective.noun
denunciatory or abusive language; vituperation; denunciatory or abusive expression or discourse
invective.adjective
of, relating to, or characterized by denunciatory or abusive language
invectively.adverb
invectiveness.noun

icosahedron.noun;.plural-icosahedrons or icosahedra
a polyhedron having 20 faces
icosahedral.adjective

inanimate.adjective
not having the qualities associated with active, living organisms; not animate; not animated or energetic; dull
Grammar.–.belonging to the class of nouns that stand for nonliving things (the word car is inanimate; the word dog is animate
inanimately.adverb
inanimateness.noun
synonym.dead

implore, implored, imploring, implores.transitive verbs
to appeal to in supplication; beseech.(implored the tribunal to have mercy; to beg for urgently; entreat
intransitive use.to make an earnest appeal
imploration, implorer.nouns
imploringly.adverb

inveterate.adjective
firmly and long established; deep rooted (inveterate preferences and beliefs); persisting in an ingrained habit; habitual (an inveterate liar); chronic
inveteracy.or.inveterateness.noun
inveterately.adverb

irascible.adjective
prone to outbursts of temper; easily angered; characterized by or resulting from anger
irascibility.or.irascibleness.noun
irascibly.adverb

indicative.(in dick a tiv).adjective
serving to indicate.(rainbows indicative of good weather); an insignia indicative of high rank
indicative.noun
indicatively.adverb
Grammar.-.the indicative mood

inscribe, inscribed, inscribing, inscribes.transitive verbs
to write, print, carve, or engrave (words or letters) on or in a surface; to mark or engrave (a surface) with words or letters; to enter (a name) on a list or in a register; to sign one's name or write a brief message in or on (a gift book or photograph, for example); to dedicate to someone
Mathematics.-.to draw (one figure) within another figure so that every vertex of the enclosed figure touches the outer figure
inscriber.noun

inscription.noun
the act or an instance of inscribing; something, such as the wording on a coin, medal, monument, or seal, that is inscribed; a short, signed message in a book or on a photograph given as a gift
inscriptional.or.inscriptive.adjective
inscriptively.adverb

impair, impaired, impairing, impairs.transitive verbs
to cause to diminish, as in strength, value, or quality (he bruised his arm imparing use of the hammer he used in his work; a severe storm impaired communications); injure
impairment.noun