Vocabularies I

investigate: carry out a systematic inquiry to discover the facts of an incident. examine: investigate thoroughly. scrutiny (n.): critical observation: the mayor’s spending came under public scrutiny. research: study carefully to discover information or knowledge about it. look into: explore the facts about something.

method: a particular form of procedure for accomplishing something. style: a way that is characteristic of particular period or person, etc.

religion: the belief and worship of superhuman powers or gods. religious: relating to religion.

convention: a way in which something is usually done. custom: a way of doing something that is specific to a particular society. tradition: a long-established custom that has been passed on from one generation to another. traditional: existing as a part of tradition.

society |səˈsaiət̬i|: the aggregate of people living together. civilization: advanced human society with organized communities and develop systems such as government, law, religion, and culture. folk |foʊk| (adj.): relating to the traditional art of a society.

campaign: organized actions carried out to achieve a particular goals. movement²: a campaign undertaken by a broad group of people working together to advance their social or political ideas.

typical: having the distinctive qualities of a particular type. typically: in a way that is characteristic of a particular type. hallmark: a distinctive feature of a particular type.

modest¹: unassuming in the estimation of one’s abilities or achievements. moderate: average in amount or intensity, etc. modest²: subjectively moderate; small.

remorse: deep regret for a wrong committed.

conflict¹: a protracted argument. conflict²: a condition in which a person experiences a clash of opposing wishes. conflict³: a prolonged armed struggle.

depart from: deviate from a traditional course. stray: wander away from a group or from the right course or place: I strayed a few blocks in the wrong direction | let us not stray from the main topic.

all the time: continuously. always: on every occasion. usual: frequently occurring or done. normal: conforming to a standard². standard¹: a level of quality. standard²: a required or agreed level of quality. standard³: a thing or idea used as a measure in comparative evaluations.

abnormal: deviating from what is normal. bizarre: very strange or unusual, so as to cause interest or amusement. unreasonable: not based on good sense. wildly: to an extreme degree; in an excessive and surprising way. absurd¹: wildly unreasonable and illogical. outrageous: extremely shocking, in a way that causes anger.

imply¹: intend to communicate something without saying it explicitly. suggest²: make someone think that something is possibly true. smack of: suggest² the presence or effect of something wrong. imply²: suggest² as a logical consequence.

reason¹ (n.): an explanation for why something happens or is true. reason² (n.): the power of the mind to think and form judgments by a process of logic. argument¹: a reason¹ given with the aim of persuading others that an idea is right or wrong.

argue²: exchange diverging views. debate²: argue² about, in a formal¹ manner. authority²: a person or organization having power. official: relating to an authority² or public body. formal¹: done in accordance with rules of conventions or etiquette. formal²: concerned with outward form or appearance, as distinct from content. distinct: recognizably different and clearly separate. resemble |rizembl|.

ascertain |esərˈtein|: make sure of: an attempt to ascertain the cause of the accident. determine²: ascertain exactly, as a result of research or calculation. confirm: establish correctness of something previously suspected.

moral: concerned with the principles of right and wrong of human. ethics: moral principles. just¹ (adj.): behaving according to what is morally right. justice: just behavior or treatment¹. treatment¹: the manner in which someone behaves toward someone or something.

integrity¹: the quality of being honest. integrity²: the state of being whole and undivided.

abominable: causing moral revulsion. revulsion: a sense of disgust. uprising (n.): an act of resistance.

established: having been in existence for a long time, and generally accepted. institution²: an established law or custom. repeal: put an end to a law. abolish: officially put an end to an institution². revoke: put an end to a permission or license.

practice²: the actual application of an idea. discipline |ˈdisəsplin|: the practice of training people to obey rules. enforce: compel² observance of a law or rule. compel¹: force someone to do something. compel²: bring about something by the use of force. bring about: cause something to happen.

restore: return to a former condition.

liberal¹: willing to respect opinion new and different from one’s own. liberal²: relating to a political and social philosophy that promotes individual right. conservative: favoring socially traditional ideas (contrasted with liberal¹).

primarily |praiˈmerəli|: as the chief or central thing rather than a secondary one. mostly: to a great extent. largely: mostly, but not completely.

division²: each of the parts into which something is divided. class¹: a division² in a system of classification: this drug belongs to a class of antibiotics called macrolides. class²: a social division² based on social or economic status.

type¹: a kind of person or thing that has a recognizable set of characteristics: this type of heather grows better in a drier habitat. type²: a person or thing considered as a representative of a type¹: I’m an adventurous type.

pick out (v.): choose someone or something from a number of alternatives. alternative |əlˈtər.nə.t̬iv|. get rid of: take action so as to be free of a troublesome or unwanted person or thing.

so as (to-infinitival clause): in order (to-infinitival clause). according to (p.): as stated by or in. with respect to: concerning. in terms of: from the point of view of a particular aspect. by means of: with the help of. in accordance with: in a manner complying with. apart from: except for. in hopes of (p.): with the aim of.

more or less (adv.): almost or roughly, with small differences. measurement²: the amount of something, as established by measuring. approximately: nearly, but not exactly; used to give an estimated number or measurement². approximation¹: a value or quantity that is nearly but not exactly correct. approximation²: a thing that is similar to something else, but is not exactly the same.

leading: top-ranked in a particular situation. overriding: more important than anything else. imperative: extremely important and needing immediate attention. crucial: decisive in the success or failure of something.

preliminary |prɪˈlimineri| (adj.): denoting an event preceding for something more important.

foreground (v.): make something the most important feature.

emerge²: become apparent or important.

only (adv.): merely (implying that more was expected).

have¹: own. have²: possesses something as a feature.

fall²: pass into a specified state or position.

climate²: the prevailing trend in something of particular era.

reflection¹: an image seen in a mirror or shiny surface. reflection²: serious thought, especially deep retrospective one. consideration: serious thought over a period of time, especially in order to make a decision.

intelligent: having intelligence, especially of a high level. clever: having quick ingenuity. brilliant²: extremely intelligent; talented.

habitat: the natural home or environment of an animal, plant, or other organism. house: a building for people to live in. home: the place where one lives permanently, especially as a member of a family. residence: a place where someone lives, especially in a legal or official sense.

compromise |ˈkɑmprəmaiz|: an agreement reached by mutual concession. settlement: an agreement that brings a dispute to an end.

equal: being the same in quantity or degree. fair: treating people without giving an unfair advantage to one side.

advantage¹ |ədˈvent̬idʒ|: a condition that makes someone or something more successful or effective than others: she had an advantage over her mother’s generation. advantage²: the opportunity to gain something. pro: a consideration supporting one choice. benefit: an actually good effect of gain from something. merit: a feature of something that gives it genuine worth or value.

anticipate |enˈtisipeit|: think about something before it happens. look forward to: anticipate with pleasure.

forecast: predict future conditions or developments, especially by analyzing data.

item: an individual unit¹ that is a part of a list or collection. verify: make sure that something is true, accurate, or justified. justified: marked by a good or legitimate reason. unit²: a quantity chosen as a standard³ in terms of which other quantities may be expressed.

memo: a written message within a business or organization.

hire: engage someone for work. employ: make use of a person or thing for a particular purpose. workplace: a place where people work. workspace: the area in which a person works.

secondary: not primary, but lower in importance. incidental: accompanying in connection with something major. mention: speak or write about someone or something briefly, especially in a incidental way. allude to: mention without discussing at length. refer to¹: direct attention to someone or something in relation to what is being said or written: the reports of the commission are often referred to in the media. refer to²: describe or denote: mathematical propositions do not refer to physical reality. refer to³: use a source of information in order to ascertain something: I always refer to a dictionary when I come across a new word.

turn out²: happen in a particular way. work out: have² a good result.

corrupt: having a willingness to act dishonestly in return for money or personal gain.

flaw: an imperfection or weakness in something or someone. defect (n.): an abnormality or fault that impairs quality or function.

senior (adj.): of older people in a social sense, especially when used of people as a group. elderly: being well past middle age and approaching old age.

contend: state a position while implying¹ opposition. assert: state something firmly and forcefully. affirm: state that something previous is correct. claim: state that something is true, especially when it not yet be proven. argue¹: give reason in support of a position. assure: tell someone something confidently to dispel any doubts they may have.

mix: mix things together so that they form an uniform whole.

fail¹: be unsuccessful in achieving one’s goal. fail²: judge not to have passed. fail³: neglect to do something.

director¹: a person who supervise staff for a movie or program, etc. director²: a person who is in charge of a department or activity. director³: a member of the board of people that oversees the affairs of a business. direct |diˈrekt|.

damage: harm caused to something; one that causes specific and noticeable impairment on its function or value.

intrude: put oneself deliberately into a place or situation where one is unwelcome or uninvited: I did not want to intrude into their conversation. break in: force entry to (a building). invade: (of an armed force) enter a region so as to subjugate it.

property¹: a quality belongs to something. hallmark: a distinctive quality by which someone or something is easily recognized. feature: a noticeable property¹. characteristic: a typical quality of a type¹. trait: a distinguishing quality belongs to a person. nature²: |in singular| the inherent features of something: I realized the nature of the problems.

property²: something that is owned by a person or group. asset: a useful or valuable thing or person. fortune²: a large amount of money that is owned by a person.

define: state or describe exactly the nature² or meaning of

soft: easy to mold. smooth: having an even surface.

remark¹ (v.): regard with attention. remark² (n.): something said, usually briefly. comment (n.): something said or written that expresses an opinion or explanation about a particular subject.

passage¹ |pesidʒ|: the act or process of moving through, under, or over something on the way from one place to another. passage²: a short extract from a book or other printed material.

abate |əˈbeit|: become less intense.

abet |əˈbet|: encourage or assist someone, in particular, to commit crime. abettor.

hate: dislike very strongly. abhor |ebˈhɔl| (v.): hate something because it’s unacceptable.

abundant |əˈbəndənt|: existing in large quantities. bountiful |ˈbaʊntifl|: giving generously.

handy: useful in a convenient, practical, or easy-to-use way.

essay: a short piece of writing on a particular subject.

severely: to a great or intense degree. seriously: in a way that is important.

treat¹ (v.): behave toward in a particular way. treat² (n.): an event that is out of the ordinary and gives great pleasure. deal with¹: take action to handle a problem, situation, or person. deal with²: take as a subject²: the novel deals with several different topics.

interest¹ (n.): the state of wanting to know about something. interest² (n.): a subject about which one is concerned or enthusiastic.

center: the exact point that is equidistant from every point on the circumference. middle: the position between two ends or sides.

take care of¹: take responsibility for handling a problem. take care of²: keep someone or something safe. care for: provide care for someone, especially they are sick, old, or young.

vocation: a strong feeling of suitability for a particular career or occupation. calling (n.): a strong inner feeling that a particular life purpose is what one is meant to do. mission²: an important task or purpose that someone feels a strong sense of duty to carry out.

conclusion²: the summing-up of a text. closing: the end of an event or activity.

careful: giving close attention to behavior. cautious: paying close attention to assessing risk. prudent: making sensible and well-judged decisions.

appoint: officially place someone in a role. assign: give someone specific task or duty.

document: a piece of written or printed material that contains information. paperwork: routine documents involved in an administrative process. text¹: written or printed words considered as language content. text²: the main body of a piece of writing, as distinct from other material such as illustrations.

count¹ (v.): determine the total number of. count² (v.): recite numbers in ascending order. count³ (v.): be significant². significant² |siɡˈnifikənt|: having a particular meaning. count (on-PP): regard someone or something as certain for what is expected. rely (on-PP): depend on someone or something for support.

freedom: the right or power to act or think as one wants. autonomy |ɑˈtənəmi|: the right of self-government (of a particular resource). independence: the state of not relying on another person or group.

psychological |sai.kəˈlɑː.dʒi.kəl|: affecting or arising in the mind.

attribute: regard something as being caused by someone or something.

thought (n.): something that passes through the mind as a mental event. idea: a thought concerning a possible course of action. course of action: a procedure adopted to deal with a situation. self-image: the opinion one has of one’s ability, appearance, and personality.

allow²: give the opportunity for.

anxiety: a feeling of worry. insecurity: anxiety about oneself; lack of confidence. distress: extreme anxiety or sorrow. suffering (n.): the state of undergoing pain or distress. hardship: severe suffering or privation.

integrate: combine one thing with another so that they become a whole. incorporate: include something as part of a whole.

sense (of-PP): someone’s awareness or sensitivity to the importance of something. awareness: knowledge or perception² of something. perception¹: the ability to become aware of something. perception²: the state of being aware of something. sensitive: quick to detect or respond to slight changes or signals. sensitivity: the quality² of being sensitive. quality²: the degree of excellence of something.

collaborate with: work jointly on an activity, especially to produce something. cooperate in: work jointly toward the same end. cooperate with: assist someone or comply with their requests.

suddenly: unexpectedly and quickly. dramatically: to a strikingly large extent. sharply: with a sudden and dramatical change.

tip: a small but useful piece of advice. secret: a valid but not commonly known method.

modern: relating to the present as opposed to the past (implying relative comparison). contemporary: occurring in the present (implying periodization).

better² (adv.): to a greater degree.

relationship: the way in which people or things are connected: romantic relationship, working relationship. connection: a link between two people or things: connection between stress and sleep problems. relevance: the quality of being closely connected or appropriate: its relevance to the topic. involvement: the fact of being involved with something: his involvement in the crime.

setting: the place, situation, and atmosphere in which something happens: the movie’s setting feels very romantic. venue: a place where an event is held: the wedding venue. site: a place where something exists or happens. area¹ |ˈeriə|: a part of a place, space, or surface. area²: a place allocated for a specific purpose. region: a part of a country or the world having definable characteristic.

subject¹: a branch of knowledge. subject²: the area or matter that something is about. topic: a specific matter dealt with in a text, discourse, or conversation.

utility¹ (n.): the state of being beneficial. utility² (adj.): being able to perform several functions.

landscape: all the visible features of an area of land: a desert landscape | the urban landscape. scenery: the natural features of a landscape considered in terms of their appearance, especially when picturesque.

shortage: a situation in which something is not supplied sufficiently for a demand. scarcity: the state of being rare, often as a structural condition. famine |ˈfemin|: extreme scarcity of food, causing widespread starvation. privation: a state in which things that are essential for human well-being such as warmth and food are scarce.

refill: fill a specific container again. replenish: restore a depleted resource.

estimate: roughly calculate. assess: examine the state or degree of something. evaluate: judge whether something is effective, successful, or valuable, often according to particular standards.

unique: unlike anything else. unique to: belonging or connected to one particular place or person.

bad²: failing to conform to standards of moral virtue or acceptable conduct. virtue: a quality considered morally good. conduct (n.): the manner in which a person behaves.

extensive: affecting a large area. widespread: found over a large area or number of people.

learning (n.): the acquisition of knowledge. study (n.): the devotion of time and attention to acquiring knowledge. studies: study as pursued by one person.

account for: provide or serve as a reason¹ for something. illustrate²: explain something by using pictures or examples. demonstrate: clearly show the existence or truth of something by giving proof or evidence. elaborate: explain something more fully by adding details.

express: make a thought, feeling, or quality noticeable. describe: give an account in words of someone or something. depict |diˈpikt|: represent by drawing or painting.

depiction: the concrete result of depicting something, especially in art: the painting’s horrific depiction of war. portrayal: the representation of someone or something in a particular way or as being of a certain nature: the media portrayal of immigration. profile |proʊfail|: a short outline of the main facts or features of a person or thing.

instruction: information that tells someone how to do. direction: guidance or command about what to do or where to go.

the sun²: the light or warmth received from the earth’s sun.

assist: help as a secondary supporter. encourage: motivate someone to do something. foster: help the development of something over time by creating the right conditions for it. promote: further the progress of something. development: the process of developing. advance |ədˈvens| (n.): a forward movement. growth: the process of increasing in physical size such as amount, number, etc.

in spite of that (adv.): nevertheless.

representative¹ |ˌrepriˈzent̬et̬iv|: a person chosen or appointed to act or speak for others. delegate: a person sent to represent others. ambassador¹ |emˈbeset̬ər|: an accredited diplomat sent by a country as its official representative to a foreign country. ambassador²: a person who acts as a representative or promoter of a particular body or activity. representative²: an example of a class².

concise: giving the necessary information clearly and in a few worlds. brief: of short duration.

settle for: accept or agree to something that one considers to be less than satisfactory.

if² (p.): whenever. when (p.): temporal background. how² (relative pron.): the fact that. what¹ (interrogative pron.). what² (relative pron.): the thing that.

walk (n.): an act of traveling.

desire: a feeling of wanting something. intention: a plan or purpose that someone has in mind before acting. volition: a faculty of acting or deciding something by your own will, especially despite inner resistance or psychological obstacles. faculty: an inherent mental power: her critical faculty.

recognize |rekəgnaiz|: identify someone or something as already known. perceive: become aware of something through the senses. find²: perceive by chance.

general: applying to most situations, people, or things, but not necessarily every single one. universal |juniˈvəlsl|: applying to everyone or everything, without exception.

arrange: put things in a particular order. align: arrange in a straight line.

help (to-infinitival clause) (v.): play a part in causing something to happen.

rewarding (adj.): providing satisfaction.

leave of absence (n.): time when one has permission to be absent from work or from duty. ask (object) (for-PP) (v.): request (someone) to give something: I asked him for a leave of absence.

fancy¹: expensive in a way that is intended to impress. fancy²: elaborate in decoration. elaborate (adj.): involving many carefully arranged details.

sophisticated² (adj.): having a great deal of worldly experience and knowledge. sophistication: the quality of being sophisticated.

humankind (n.): all human beings.

admire: feel respect for someone or something. honor (v.): show great respect for someone or something, often through actions or words. celebrate²: honor publicly.

extend: make something longer. expand: make something larger or broader.

uneasy: slightly uncomfortable (vague sense that something is wrong). anxious: experiencing worry about an imminent event.

era: a distinctive period of history defined by major events: the Obama era. age: a broad period defined by a particular way of life: the Stone Age | the digital age.

function (v.): operate in a proper way. function as (v.): fulfill the purpose of a specified thing.

gender: identities concerning social differences rather than biological ones.

passion: a deep emotional drive, especially the one that runs through one’s life. enthusiasm |inˈθuziæzm|: intense and eager interest or enjoyment, especially the one lasting in a short period.

compulsory: required by a law or rule, with no choice to refuse. mandatory: officially required by a law or rule. obligatory: required by a moral rule or social expectation.

electronic¹: (of a device) having many small components, especially microchips and transistors. electronic²: relating to electrons. mobile |ˈmoʊbl|.

more (det.): a greater or additional amount of. only too (det.): an extreme degree of (often carrying negative nuance): her words were only too fast.

nothing but (adv.): only: it is nothing but a game. none but (adv.): only: none but the brave deserve the fair. anything but (adv.): definitely not: the test was anything but hard.

take the place of: replace. keep on: continue to do something.

privacy: the state or condition of being free from being observed or disturbed by other people.

upset (v.): make someone unhappy or disappointed.

invent²: make up a story, especially so as to deceive someone.

reputation (for-PP) |re-|. secret (to-PP). succeed (in-PP) (v.).

devote (object) (to-PP): give a large part of one’s time or resources to something.

present (v.): bring something to the attention of someone for consideration. illustrate:. treatment²: a systematic discussion of a subject¹: the modern treatment of abstract algebra. systematic |sisteˈmet̬ik|: done or acting according to a fixed plan. throughout (adv.): from beginning to an end of an event or period of time. as well as: and also.

then² (adv.): after that.

accountable: (of a person, organization, or institution) required or expected to justify actions or decisions: parents are accountable for their children’s actions. accountability: the fact or condition of being accountable: their lack of accountability has corroded public respect. responsible¹: having the duty to take care of a task, person, or thing: she is responsible for the marketing team. responsibility: the fact or state of having duty to do something.

at last: after much delay. eventual: occurring at the end of or as a result.

feeling (for-PP) (n.): an intuitive understanding of something. grasp |ɡresp|: understand the main idea of something; get metal hold of something. comprehend: understand something fully. appreciate¹: recognize the full implications, value, or importance of something. appreciate²: be grateful for something.

definitely: without any doubt (used for emphasis). precisely |preˈsaisli|: in an exact and specific way, without vagueness. accurately: in a way that is correct.

release¹: let someone or something go free. liberate: set someone free from a situation in which their liberty is severely restricted.

reveal: make something known. release²: make information available to the public. disclose: make secret known. uncover: discover something previously secret.

dominate: have controlling power or the strongest influence over someone, something, or a situation. occupy: take up a space or time. seize: take hold of something suddenly and forcibly.

reveal²: cause or allow¹ something to be seen.

serendipity |serənˈdipit̬i|: the occurrence of finding something valuable, pleasant, or useful by chance.

instant: coming with little waiting. instantaneous |instənˈteiniəs|: occurring or done in an instant. immediate: happening right after something else: the book’s success was immediate. prompt: (of a response) done quickly and without unnecessary delay.

design² (n.): the way something is intentionally planned, structured, or made for a particular purpose. initiative (n.): a new action or strategy intended to solve a problem or improve a situation: the city launched a new initiative to reduce food waste.

favorable¹: expressing approval. favorable²: to the advantage of someone or something: a settlement favorable to the unions. beneficial: having a good or helpful effect on someone or something. profitable: yielding financial gain.

persistent¹: continuing obstinately in a course of action in spite of difficulty or opposition. persistent²: continuing to exist over a prolonged period. endless: having or seeming to have no end.

while: at the same time as.

utilitarian |jutiləˈteriən|: designed to be useful rather than attractive. practical: likely to succeed or be effective in real circumstances. pragmatic: dealing with things in a way that is based on practical rather than theoretical considerations.

compilation: a thing that is put together by assembling previously separate items. digest |ˈdaidʒest| (n.): a summary of collected materials.

for the sake of: for the purpose of.

concise: giving the necessary information clearly and in a few words. brevity: concise use of words in writing or speech: for the sake of brevity, we generally suppress information like this.

exertion: the use of physical and mental energy. strenuous |ˈstren.ju.əs|: requiring great exertion. arduous |ˈɑːr.dʒu.əs|: involving strenuous exertion; difficult and tiring. quest: a long and arduous search for something.

effort |ˈefərt|: an attempt to accomplish something. hard work (n.): a great deal of effort: it takes hard work to be successful in business. strive (v.): make great effort to achieve something. endeavor |inˈdev.ər| (n.): an attempt to achieve something.

millennium (plural millennia): a period of a thousand years.

conform: behave according to socially acceptable conventions: he never felt the need to conform to other people’s expectations. comply: act in accordance with a command or request: the company agreed to comply with the new safety regulations.

configuration: the way parts are set up to form a working system. configure¹: put together in a particular configuration. configure²: Computing set up the options or settings of a system so that it works in a particular way.

specialist (in-PP): a person who concentrates primarily on a particular subject. adept (at -PP) (adj.): very skilled or proficient at something. skill (n.): the ability to execute specific procedures, apply structured frameworks, or utilize specialized tools: her technical skill allowed her to execute complex code without errors. art²: a way of doing something well, especially one that requires judgement or ingenuity: he has mastered the art of negotiation. rhetoric |ˈret̬ərik| (n.): the art of persuasive speaking or writing.

available: able to be used or obtained.

imagine²: suppose or assume: after Ned died, everyone imagined that Mabel would move away.

dawn: the beginning of a phenomenon or period of time, especially one considered positive: the dawn of humanity.

determination: firmness of purpose. ambition: a strong desire to do or to achieve something, typically requiring determination and hard work. revenge (n.): the desire to inflict retribution: it was difficult not to be overwhelmed with feelings of hate and revenge.

course: the way in which something progresses or develops: the course of natural events. guide² (v.): have an influence on or direct the course of action of someone or something: it will help us guide the world’s actions to our advantage.

originally: in the beginning; at first: potatoes originally came from South America.

in turn: in succession; one after the other. alternation: the repeated occurrence of two things in turn: the alternation of day and night.

incessant: (of something regarded as unpleasant) continuing without pause or interruption: the incessant barking kept me awake all night. relentless: incessant with the same force or pressure without weakening: the team faced relentless pressure in the second half. indefinite: lasting for an unlimited period of time.

attendant (adj.): occurring as a result of: the regular change of the seasons and the attendant influence on the weather.

control (n.): the power to influence the course of events: the situations slipping out of her control. controlled¹: not showing emotion: his every word seemed to be calm and controlled. controlled²: under the control of someone or something: the controlled apparent motion of the Moon.

connotation: a feeling or idea that a word invokes in addition to its literal meaning.

disentangle (v.): free (someone or something) from a thing that they are entangled with: “I must go,” she said, disentangling her fingers from Gabriel’s.

astrology: the study of the movements and relative positions of celestial bodies interpreted as having an influence on all of human affairs: let’s see what astrology can reveal about their romance. constellation: a group of stars forming a recognizable pattern.

redundant: not or no longer needed or useful.

unassailable: unable to be attacked or questioned: with mathematical proof, it was possible to make significant assertions of an unassailable nature.

instinctively: in a way that happens naturally and immediately, without deliberate thought or reasoning: I instinctively knew something was wrong. unconsciously: without being aware of one’s action: she unconsciously started tapping her foot under the table.

natural²: (of a skill) coming instinctively to a person. artistic¹: having or revealing natural² creative skill. artistic²: relating to art.

literature¹: written works considered of having artistic² merit. literature² (on-PP): books and writings published on a particular subject.

idealized: regarded as more ideal than in reality.

robustness: the ability to withstand adverse conditions or rigorous testing: we find a great robustness in mathematics.

unfounded: having no foundation or basis in fact.

compatible: (of two things) able to exist or occur together without conflict: this makes the usual polynomial notation completely compatible with the underlying set-theoretic definition.

refine²: improve something by making small adjustments that increase its precision. revise: re-examine and make alterations to (written or printed matter).

present¹ |priˈzent| (v.): give or award formally: a top executive will present an award to him. present² (v.): show (something) for others to consider. present³ (v.): represent (someone or something) to others in a particular way: he presented himself as a hardworking man. put forward: present² a proposal or theory for consideration: scientists will put forward models of the world.

provide (someone) (with-PP): give someone something that is needed or useful for a particular purpose.

blueprint (n.): a detailed guide or plan for building or organizing something: the blueprint for modern science.

question² (n.): a matter forming the basis of a problem requiring resolution: the question of the internal consistency of a scientific model.

dual (adj.): consisting of two parts or elements: the dual structure of reality and ideal.

lead up to: immediately precede something.

manifest (adj.): clear or obvious to the eye or mind.

nonliteral: not using or taking words in their usual or most basic sense.

retain: continue to have (something): if a set is closed, then all limiting points are retained.

exploit (v.): make full use of and derive benefit from (a resource).

fundamental: forming a deep basis for something: the fundamental problem. foundational: providing the base on which something else is built or developed. essential: absolutely necessary. basic: relating to the simplest or most elementary level of something.

prototype: a first or preliminary model of something, from which other forms are developed: the prototype of an $$n$-$ dimensional manifold is an $$n$-$ dimensional Euclidean space.

juxtaposition |dʒʌkstəpəˈziʃən|: the fact of two things being seen or placed close together. collocation: Linguistics the habitual juxtaposition of a particular word with another word.

characterize: describe the distinctive nature of someone or something: Heine–Borel theorem characterize compact subsets of Euclidean space.