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Interlinked Dictionary© based on 
Merriam-Webster's Collegiate® Dictionary (m-w.com)
and Star Dictionary
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not endowed with reason; marked by a lack of accord with reason or sound judgment
irrational thought, expression or behavior; irrationality; belief in feeling, instinct or other nonrational forces rather than.reason
the state or quality of being.irrational; an irrational idea, expression or act
irrational thought, expression or behavior; irrationality; belief in feeling, instinct or other non rational forces rather than reason

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

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

arrogantly.domineering or overbearing
synonyms.dictatorial, authoritarian, dogmatic, overbearing

emitting visible light as a result of being heated; shining brilliantly; very bright; characterized by ardent emotion, intensity or brilliance
the emission of visible light by a hot object such as aN incandescent light bulb; the light emitted by an incandescent object, such as the older yellow light bulbs we all used; a blaze (the incandescence of a beautiful outdoor warming fire)

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 snide remarks 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 response to the question); characterized by a lack of partiality; unbiased (a properly indifferent jury); undifferentiated
synonyms.unconcerned, incurious, detached, uninterested; nonchalant

the state or quality of being indifferent

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 light or the infrared part of the spectrum

if you talk about the irony of a situation, you mean that it is odd or amusing because it involves a contrast between apparent and intended.meaning; incongruity between what might be expected and what actually occurs (the irony is that many officials in governments agree in private that their policies are inconsistent); the use of words to express something different from and often opposite to their literal meaning; an expression or utterance.marked by a deliberatecontrast
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)
synonyms-sarcastic, caustic, satirical, sardonic

hostile or indifferent to religion; ungodly; an irreligious person does not accept the beliefs of any religion or opposes all religions

existing or remaining within; inherent (believing in God immanent in human beings); restricted entirely to the mind; subjective; maybe also compare imminent, eminent

incapable of erring; infallible; containing no errors

incapable of erring; incapable of failing; certain (an infallible Creator)

one who attacks and seeks to overthrow traditional or popular ideas or institutions

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

invective is rude and unpleasant things that people shout at people they hate or are angry with (racist books filled with invectives); denunciatory or abusive language; vituperation; denunciatory or abusive expression or discourse
of, relating to or characterized by denunciatory or abusive language

icosahedron.noun,.plural.icosahedrons or icosahedra
a polyhedron having 20 faces

not having the qualities.associated with connection to the invisible, intelligent energy field out of which everything emerges; not animate
Grammar:.belonging to the class of nouns that stand for nonliving things (the word car is inanimate; the word dog is animate)

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

firmly and long established; deep rooted (inveterate preferences and beliefs); persisting in an ingrained.habit; habitual (an inveterate liar); chronic

prone to outbursts of temper; easily angered; characterized by or resulting from anger

serving to indicate.(rainbows indicative of good weather); an insignia indicative of high rank; if one thing is indicative of another, it suggests or indicates what the other thing is likely to be
Grammar:.the indicative mood; a clause that is in the indicative or in the indicative mood, has a subject followed by a verb group, examples are (I'm hungry and she was followed); clauses of this kind are typically used to make statements

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
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 (the ancient Egyptian inscriptions; the inscriptions of the Assyrian king Sargon)

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

incapable of undergoing division (an indivisible union)
Mathematics:.incapable of being divided without a remainder (the number 15 is indivisible by 7)
indivisibleness or indivisibility.noun

devoid of or not subject to emotion; revealing no emotion; expressionless; incapable of physical sensation; motionless; still

idle, idler, idlest.adjective
inactive; if people who were working are idle, they have no jobs or work (employees have been idle almost a month because of shortages of supply); not employed or busy; if machines or factories are idle, they are not working or being used (now the machine is lying idle); if you say that someone is idle, you disapprove of them because they are not doing anything and you think they should be; not in use or operation (idle hands); lazy; lacking.substance, value or basis; idle is used to describe something that you do for no particular reason, often because you have nothing better to do (Brian kept up the idle chatter for another five minutes; we were not idly sitting around); not employed or busy (idle carpenters); inactive; to do nothing; not in use or operation (of all the tired kids he was the idlest of them all)
idle, idled, idling, idles.verbs
intransitive verb use.to pass time without working or while avoiding work; to run a motor vehicle or device at a slow speed or out of gear
transitive verb use.to pass time without working (relaxed and idled the afternoon away in the Sun); waste; to cause a motor, for example to idle (he forgot he left the engine running so the car idled for a long time)
idleness, idler.nouns

she sat idly by just soaking up the Sun
idyl.noun.also spelt.idyll
if you describe a situation as an idyll, you mean that it is idyllic (she finds that the sleepy town she moves to isn't the rural idyll she imagined); a short poem or prose piece depicting a rural or pastoral scene, usually in idealized.terms; a narrative poem treating an epic or romantic theme; a scene or an event of a simple and tranquil nature; a carefree episode or experience (a summer idyll on the coast of British Columbia); a romantic.interlude
of or having the nature of an idyl; simple and carefree (an idyllic vacation in a seashore cottage)

of, relating to or constituting an introduction; serving to introduce; preliminary
introduce, introduced, introducing, introduces.transitive verbs
to acquaint someone by name for the first time to others (if introducing someone to another that you have already been introduced to, you say 'may I present 'full name', such as Sally Jones, to you', as this lets the people know that you already know this person which is being introduced to them); to bring forward a plan, for example for consideration; to provide someone with a beginning knowledge or first experience of something (introduced me to yoga); to bring in and establish in a new place or environment (exotic plants that had been introduced from the jungle); to bring into use or practice; originate (introduced the new product in several test markets; introduced the tango into their circle of friends); to open or begin; preface (introduced the movie with an orienting talk)
the act or process of introducing or the state of being introduced; a means, such as a personal letter, of presenting one person to another; something recently introduced; an innovation; a preface, as to a book; in music, a short preliminary movement in a larger work; a basic introductory text or course of study

impossible to hear (an inaudible conversation); not audible