vania-janet/multiturn-rag-retrieval-data huggingface dataset:
List of mathematical symbols
Symbol in HTML Symbol in TeX Name Explanation Examples Read as Category < > < ( \ displaystyle < ) > ( \ displaystyle > ) strict inequality is less than , is greater than order theory x < y ( \ displaystyle x < y ) means x is less than y . x > y ( \ displaystyle x > y ) means x is greater than y . 3 < 4 ( \ displaystyle 3 < 4 ) 5 > 4 ( \ displaystyle 5 > 4 ) proper subgroup is a proper subgroup of group theory H < G ( \ displaystyle H < G ) means H is a proper subgroup of G . 5 Z < Z ( \ displaystyle 5 \ mathrm ( Z ) < \ mathrm ( Z ) ) A 3 < S 3 ( \ displaystyle \ mathrm ( A ) _ ( 3 ) < \ mathrm ( S ) _ ( 3 ) ) ≪ ≫ ≪ ( \ displaystyle \ ll ) ≫ ( \ displaystyle \ gg ) \ ll \ gg significant ( strict ) inequality is much less than , is much greater than order theory x ≪ y means x is much less than y . x ≫ y means x is much greater than y . 0.003 ≪ 1000000 asymptotic comparison is of smaller order than , is of greater order than analytic number theory f ≪ g means the growth of f is asymptotically bounded by g . ( This is I.M. Vinogradov 's notation . Another notation is the Big O notation , which looks like f = O ( g ) . ) x ≪ e absolute continuity is absolutely continuous with respect to measure theory μ ≪ ν ( \ displaystyle \ mu \ ll \ nu ) means that μ ( \ displaystyle \ mu ) is absolutely continuous with respect to ν ( \ displaystyle \ nu ) , i.e. , whenever ν ( A ) = 0 ( \ displaystyle \ nu ( A ) = 0 ) , we have μ ( A ) = 0 ( \ displaystyle \ mu ( A ) = 0 ) . If c ( \ displaystyle c ) is the counting measure on ( 0 , 1 ) ( \ displaystyle ( 0 , 1 ) ) and μ ( \ displaystyle \ mu ) is the Lebesgue measure , then μ ≪ c ( \ displaystyle \ mu \ ll c ) .
Negative number
That is , the negation of a positive number is the additive inverse of the number .
Oil drop experiment
Why did n't they discover the new number was higher right away ? It 's a thing that scientists are ashamed of -- this history -- because it 's apparent that people did things like this : When they got a number that was too high above Millikan 's , they thought something must be wrong -- and they would look for and find a reason why something might be wrong . When they got a number close to Millikan 's value they did n't look so hard . And so they eliminated the numbers that were too far off , and did other things like that ...
Income inequality in the United States
Related to income inequality is the topic of wealth inequality , which refers to the distribution of net worth ( i.e. , what is owned minus what is owed ) as opposed to annual income . Net worth is affected by movements in the prices of assets , such as stocks , bonds , and real estate , which can fluctuate significantly over the short - term . Income inequality also has a significant effect over long - term shifts in wealth inequality , as income is accumulated . Wealth inequality is also highly concentrated and increasing :
Potentiality and actuality
Entelecheia , as can be seen by its derivation , is a kind of completeness , whereas `` the end and completion of any genuine being is its being - at - work '' ( energeia ) . The entelecheia is a continuous being - at - work ( energeia ) when something is doing its complete `` work '' . For this reason , the meanings of the two words converge , and they both depend upon the idea that every thing 's `` thinghood '' is a kind of work , or in other words a specific way of being in motion . All things that exist now , and not just potentially , are beings - at - work , and all of them have a tendency towards being - at - work in a particular way that would be their proper and `` complete '' way .
Glory (religion)
In another way vainglory may be contrary to charity , on the part of the one who glories , in that he refers his intention to glory as his last end : so that he directs even virtuous deeds thereto , and , in order to obtain it , forbears not from doing even that which is against God . On this way it is a mortal sin . Wherefore Augustine says ( De Civ . Dei v , 14 ) that `` this vice , '' namely the love of human praise , `` is so hostile to a godly faith , if the heart desires glory more than it fears or loves God , that our Lord said ( John 5 : 44 ) : How can you believe , who receive glory one from another , and the glory which is from God alone , you do not seek ? ''
Potentiality and actuality
We speak of an entity being a `` seeing '' thing whether it is currently seeing or just able to see . We speak of someone having understanding , whether they are using that understanding or not . We speak of corn existing in a field even when it is not yet ripe . People sometimes speak of a figure being already present in a rock which could be sculpted to represent that figure .
Negative number
In mathematics , a negative number is a real number that is less than zero . Negative numbers represent opposites . If positive represents a movement to the right , negative represents a movement to the left . If positive represents above sea level , then negative represents below sea level . If positive represents a deposit , negative represents a withdrawal . They are often used to represent the magnitude of a loss or deficiency . A debt that is owed may be thought of as a negative asset , a decrease in some quantity may be thought of as a negative increase . If a quantity may have either of two opposite senses , then one may choose to distinguish between those senses -- perhaps arbitrarily -- as positive and negative . In the medical context of fighting a tumor , an expansion could be thought of as a negative shrinkage . Negative numbers are used to describe values on a scale that goes below zero , such as the Celsius and Fahrenheit scales for temperature . The laws of arithmetic for negative numbers ensure that the common sense idea of an opposite is reflected in arithmetic . For example , − ( − 3 ) = 3 because the opposite of an opposite is the original thing .
Cross of Gold speech
I would be presumptuous , indeed , to present myself against the distinguished gentlemen to whom you have listened if this were a mere measuring of abilities ; but this is not a contest between persons . The humblest citizen in all the land , when clad in the armor of a righteous cause , is stronger than all the hosts of error . I come to speak to you in defense of a cause as holy as the cause of liberty -- the cause of humanity .
Working capital
An increase in net working capital indicates that the business has either increased current assets ( that it has increased its receivables or other current assets ) or has decreased current liabilities -- for example has paid off some short - term creditors , or a combination of both .
Something New (How I Met Your Mother)
This article 's lead section does not adequately summarize key points of its contents . Please consider expanding the lead to provide an accessible overview of all important aspects of the article . Please discuss this issue on the article 's talk page . ( December 2015 )
Time dilation
This constancy of the speed of light means that , counter to intuition , speeds of material objects and light are not additive . It is not possible to make the speed of light appear greater by moving towards or away from the light source .
Necessity is the mother of invention
`` Necessity is the mother of invention '' is an English - language proverb . It means , roughly , that the primary driving force for most new inventions is a need .
Mental calculation
The + / - superscript after the error represents if the actual number value is higher or lower than the approximation ; for example the approximation of ln ( 400 ) is less than 6 . The + / - symbols after errors may also be used to make the approximations more accurate by compensation , for example ;
Apple of my eye
The phrase apple of my eye refers to something or someone that one cherishes above all others .
Utilitarianism
Hooker describes two aspects to the problem : act utilitarianism requires huge sacrifices from those who are relatively better off and also requires sacrifice of your own good even when the aggregate good will be only slightly increased . Another way of highlighting the complaint is to say that in utilitarianism , `` there is no such thing as morally permissible self - sacrifice that goes above and beyond the call of duty . '' Mill was quite clear about this , `` A sacrifice which does not increase , or tend to increase , the sum total of happiness , it considers as wasted . ''
Cogito, ergo sum
A further expansion , dubito , ergo cogito , ergo sum -- res cogitans ( `` ... -- a thinking thing '' ) extends the cogito with Descartes 's statement in the subsequent Meditation , `` Ego sum res cogitans , id est dubitans , affirmans , negans , pauca intelligens , multa ignorans , volens , nolens , imaginans etiam et sentiens ... '' , or , in English , `` I am a thinking ( conscious ) thing , that is , a being who doubts , affirms , denies , knows a few objects , and is ignorant of many ... '' . This has been referred to as `` the expanded cogito '' .
Limiting magnitude
In reality a telescope allows one to see much fainter stars because at higher powers the background is darkened and contrast increased . A typical 10 - inch scope at high power ( 250 × or more ) will easily reach magnitude 15 . A formula including a correction for improved contrast is
It ain't over till the fat lady sings
It ai n't over till ( or until ) the fat lady sings is a colloquialism which is often used as a proverb . It means that one should not presume to know the outcome of an event which is still in progress . More specifically , the phrase is used when a situation is ( or appears to be ) nearing its conclusion . It cautions against assuming that the current state of an event is irreversible and clearly determines how or when the event will end . The phrase is most commonly used in association with organized competitions , particularly sports .
Speed of light
There are situations in which it may seem that matter , energy , or information travels at speeds greater than c , but they do not . For example , as is discussed in the propagation of light in a medium section below , many wave velocities can exceed c . For example , the phase velocity of X-rays through most glasses can routinely exceed c , but phase velocity does not determine the velocity at which waves convey information .
You're either with us, or against us
Some see the statement as a way of persuading others to choose sides in a conflict which does not afford the luxury of neutrality . Only when there are no alternatives like a middle ground does the phrase hold validity as a logical conclusion . The phrases are a form of argumentation .
Negative number
( Because , for example , if you have £ - 8 , a debt of £ 8 , you would have less after adding , say £ 10 , to it than if you have £ - 5 . ) It follows that any negative number is less than any positive number , so
You're either with us, or against us
The statement generally is a descriptive statement identifying the beliefs of the speaker ( s ) , and thus state a basic assumption , not a logical conclusion . It may also be interpreted as a speech act . Sometimes but not always interpreted as a splitting or a false dilemma , which is an informal fallacy .
Limiting magnitude
Even higher limiting magnitudes can be achieved for telescopes above the Earth 's atmosphere , such as the Hubble Space Telescope , where the sky brightness due to the atmosphere is not relevant . For orbital telescopes , the background sky brightness is set by the zodiacal light . The Hubble telescope can detect objects as faint as 31st magnitude , and the James Webb Space Telescope ( operating in the infrared spectrum ) is expected to have a magnitude limit of 34th magnitude .
Limiting magnitude
In astronomy , limiting magnitude is the faintest apparent magnitude of a celestial body that is detectable or detected by a given instrument .
Vaishnavism
The charity or gift is the armour in the world , All beings live on the gift of the other , Through gifts strangers become friends , Through gifts , they ward off difficulties , On gifts and giving , everything rests , That is why charity is the highest . --
Native Son
Mrs. Thomas : Bigger 's mother . She struggles to keep her family alive on the meager wages earned by taking in other people 's laundry . She is a religious woman who believes she will be rewarded in an `` afterlife '' , but as a black woman accepts that nothing can be done to improve her people 's situation . Additionally , she knows Bigger will end up hanging from the `` gallows '' for his crime , but this is just another fact of life .
Aggregate demand
According to the aggregate demand - aggregate supply model , when aggregate demand increases , there is movement up along the aggregate supply curve , giving a higher level of prices .
Said the actress to the bishop
The phrase `` Said the actress to the bishop '' is a colloquial and vulgar British exclamation , offering humour by serving as a punch line that exposes an unintended double entendre . An equivalent phrase in North America is `` that 's what she said '' . Each phrase is an example of a Wellerism , exposing a second meaning of what precedes it . The versatility of such phrases , and their popularity , lead some to consider them clichéd .
Negative number
On the other hand , subtracting a negative number yields the same result as the addition a positive number of equal magnitude . ( The idea is that losing a debt is the same thing as gaining a credit . ) Thus
List of mathematical symbols
Z ≤ Z A ≤ S reduction is reducible to computational complexity theory A ≤ B means the problem A can be reduced to the problem B. Subscripts can be added to the ≤ to indicate what kind of reduction . If ∃ f ∈ F . ∀ x ∈ N . x ∈ A ⇔ f ( x ) ∈ B ( \ displaystyle \ exists f \ in F ( \ mbox ( . ) ) \ forall x \ in \ mathbb ( N ) ( \ mbox ( . ) ) x \ in A \ Leftrightarrow f ( x ) \ in B ) then A ≤ F B ( \ displaystyle A \ leq _ ( F ) B ) ≦ ≧ ≦ ( \ displaystyle \ leqq ) ≧ ( \ displaystyle \ geqq ) \ leqq \ geqq congruence relation ... is less than ... is greater than ... modular arithmetic 10a ≡ 5 ( mod 5 ) for 1 ≦ a ≦ 10 vector inequality ... is less than or equal ... is greater than or equal ... order theory x ≦ y means that each component of vector x is less than or equal to each corresponding component of vector y . x ≧ y means that each component of vector x is greater than or equal to each corresponding component of vector y . It is important to note that x ≦ y remains true if every element is equal . However , if the operator is changed , x ≤ y is true if and only if x ≠ y is also true . ≺ ≻ ≺ ( \ displaystyle \ prec ) ≻ ( \ displaystyle \ succ ) \ prec \ succ Karp reduction is Karp reducible to ; is polynomial - time many - one reducible to computational complexity theory L ≺ L means that the problem L is Karp reducible to L . If L ≺ L and L ∈ P , then L ∈ P . Nondominated order is nondominated by Multi-objective optimization P ≺ Q means that the element P is nondominated by element Q .
Native Son
Bigger Thomas is mentioned in one of the lyrical hooks of `` The Ritual '' in Saul Williams ' The Inevitable Rise and Liberation of NiggyTardust ! ( 2007 ) .
Send In the Clowns
The word `` next '' is important : `` Maybe next year '' as opposed to `` this year '' . ( Desirée means , ) `` All right , I 've screwed it up this year . Maybe next year I 'll do something right in my life . '' So ( it 's ) `` well , maybe next year '' even though it is n't accented in the music . This is a place where the lyric and the music are n't as apposite as they might be , because the important word is `` next '' , and yet the accented word is `` year '' . That 's my fault , but ( something the performer must ) overcome .
It (novel)
The narrative changes and `` It '' informs the reader that it existed originally in a void between our universe and others in a dimension known as the Macroverse , boasting of It 's superiority to anything on Earth . It also explains that it chooses to prey on children because their fears are easier to interpret in a physical form .
Andrew Carnegie
To spend the first third of one 's life getting all the education one can . To spend the next third making all the money one can . To spend the last third giving it all away for worthwhile causes .
Negative number
The absolute value of a number is the non-negative number with the same magnitude . For example , the absolute value of − 3 and the absolute value of 3 are both equal to 3 , and the absolute value of 0 is 0 .
Necessity is the mother of invention
In the Oxford Dictionary , the proverb has been defined as : `` when the need for something becomes imperative , you are forced to find ways of getting or achieving it . '' According to the Cambridge Dictionary , this is `` an expression that means that if you really need to do something , you will think of a way of doing it . '' Longman dictionary has defined the proverb as : `` if someone really needs to do something , they will find a way of doing it . ''
Glory (religion)
The theologian C.S. Lewis , in his essay The Weight of Glory , writes `` Glory suggests two ideas to me , of which one seems wicked and the other ridiculous . Either glory means to me fame , or it means luminosity . '' He concludes that glory should be understood in the former sense , but states that one should not desire fame before men ( human glory ) , but fame before God ( divine glory ) .
Gatekeeping (communication)
Proximity is the fourth element . People prefer news that is local , close in proximity . People pay close attention to local news more than they do to international or national affairs . Local media outlets do well because they focus most of their stories on local events , about seventy - five percent . There is a strong preference for local news over international and national news .
Limiting magnitude
In amateur astronomy , limiting magnitude refers to the faintest objects that can be viewed with a telescope . A two - inch telescope , for example , will gather about 16 times more light than a typical eye , and will allow stars to be seen to about 10th magnitude ; a ten - inch ( 25 cm ) telescope will gather about 400 times as much light as the typical eye , and will see stars down to roughly 14th magnitude , although these magnitudes are very dependent on the observer and the seeing conditions .
Acronym
In formal writing for a broad audience , the expansion is typically given at the first occurrence of the acronym within a given text , for the benefit of those readers who do not know what it stands for . The capitalization of the original term is independent of it being acronymized , being lowercase for a common noun such as frequently asked questions ( FAQ ) but uppercase for a proper noun such as the United Nations ( UN ) ( as explained at Case > Casing of expansions ) .
Las Meninas
What is a life ? A frenzy . What is life ? A shadow , an illusion , and a sham . The greatest good is small ; all life , it seems Is just a dream , and even dreams are dreams . Detail
Native Son
Bigger has a similar experience . He muses , `` He had done this . He had brought all this about . In all of his life these two murders were the most meaningful things that had ever happened to him . He was living , truly and deeply , no matter what others might think , looking at him with their blind eyes . Never had he had the chance to live out the consequences of his actions : never had his will been so free as in this night and day of fear and murder and flight '' . It is the first time in the novel where Bigger does not throw the blame on others but instead asserts that he was responsible for his actions . Through that , he finally experiences free will and finds freedom .
Grip (job)
Beef -- Refers to the power of a light , such as `` beef it up . ''
Hawaii
Jump up ^ `` Other '' refers to religions other than Christianity , Buddhism , or Judaism ; this group includes Bahá'í Faith , Confucianism , Daoism , the Hawaiian religion , Hinduism , Islam , Sikhism , Shintoism , Zoroastrianism , and other religions . Jump up ^ `` Unaffiliated '' refers to people who do not belong to a congregation ; this group includes agnostics , atheists , humanists , deists and the irreligious .
Major and minor
With regard to intervals , the words major and minor just mean large and small , so a major third is a wider interval , and a minor third a relatively narrow one . The intervals of the second , third , sixth , and seventh ( and compound intervals based on them ) may be major or minor .
Ellipsis
In news reporting , often associated with brackets , it is used to indicate that a quotation has been condensed for space , brevity or relevance .
Natural logarithm
The natural logarithm of x is the power to which e would have to be raised to equal x . For example , ln ( 7.5 ) is 2.0149 ... , because e = 7.5 . The natural log of e itself , ln ( e ) , is 1 , because e = e , while the natural logarithm of 1 , ln ( 1 ) , is 0 , since e = 1 .
Income inequality in the United States
The ability to move from one income group into another ( income mobility ) is a means of measuring economic opportunity . A higher probability of upward income mobility theoretically would help mitigate higher income inequality , as each generation has a better chance of achieving higher income groups . Conservatives and libertarians such as economist Thomas Sowell , and Congressman Paul Ryan ( R. , Wisc . ) argue that more important than the level of equality of results is America 's equality of opportunity , especially relative to other developed countries such as western Europe .
Income inequality in the United States
On the other side of the issue are those who have claimed that the increase is not significant , that it does n't matter because America 's economic growth and / or equality of opportunity are what 's important , that it is a global phenomenon which would be foolish to try to change through US domestic policy , that it `` has many economic benefits and is the result of ... a well - functioning economy '' , and has or may become an excuse for `` class - warfare rhetoric '' , and may lead to policies that `` reduce the well - being of wealthier individuals '' .
Potentiality and actuality
The genus of which motion is a species is being - at - work - staying - itself ( entelecheia ) , of which the only other species is thinghood . The being - at - work - staying - itself of a potency ( dunamis ) , as material , is thinghood . The being - at - work - staying - the - same of a potency as a potency is motion .
Lexicographical order
For example , for ordering the increasing sequences ( or the sets ) of two natural integers , the lexicographical order begins by
Lexicographical order
The degree reverse lexicographical order consists also in comparing first the total degrees , and , in case of equality of the total degrees , using the reverse of the colexicographical order . That is , given two exponent vectors , one has
Shoplifting
Shoplifting ( also known as boosting and five - finger discount ) , is the unnoticed theft of goods from an open retail establishment . Shoplifting typically involves a person concealing a store item on their person , in pockets or under clothes ( or in a bag , baby stroller , etc . ) and leaving the store without paying for it . With clothing , shoplifters may put on items from the store and leave the store wearing the clothes . The terms `` shoplifting '' and `` shoplifter '' are not usually defined in law . The crime of shoplifting generally falls under the legal classification of larceny . Shoplifting is distinct from burglary ( theft by breaking into a closed store ) , robbery ( stealing by threatening or engaging in violent behavior ) or armed robbery ( stealing by using a weapon ) . In the retail industry , the word shrinkage or shrink , can be used to refer to merchandise lost by shoplifting , but the word also includes loss by other means , such as waste , uninsured damage to products , and theft by store employees .
Themistocles
`` My boy , you will be nothing insignificant , but definitely something great , either for good or evil . ''