OpenLLM-France/wikimedia huggingface dataset:
# Conworld/Examples

Here are some links to pages — mostly Wikipedia articles — on some famous conworlds:
* The World of Middle Earth by J.R.R Tolkien
* The Dune Universe
* The Star Trek Universe
* The Star Wars Universe
* The world of Westeros, Sothyros and the Free Cities by George R. R. Martin
* Mark Rosenfelder's Almea
* The Discworld of Terry Pratchett
# Convexity/The convex hull
## Definition

The convex hull, also known as the convex envelope, of a set X is the smallest convex set of which X is a subset. Formally,
Definition: The convex hull H(X) of a set X is the intersection of all convex sets of which X is a subset.
If X is convex, then obviously H(X) = X, since X is a subset of itself. Conversely, if H(X) = X, X is obviously convex.
Theorem: If X is closed and bounded, so is H(X).
Theorem: H(X) is the union of all straight lines joining all pairs of points in X (where the line includes the end-points).
Proof: Let A, B be any two points in X. They are also in any convex set Y containing X. The line joining them must also lie within Y hence it must lie within the intersection of all convex sets containing X, i.e. within H(X). Thus the union of all such straight lines is a subset of H(X).
# Convexity/The diameter of a set

If a distance measure between any two points, d(A,B), is defined on a space, and X is a set in this space, then the diameter D(X) is the supremum of d(A,B) over all points A, B in X.
Theorem: in Euclidean space, D(H(X)) = D(X).
# Conworld
## Creating Your Own World

Conworld is a shortened form of constructed world. Thus, "conworlding" is world constructing, (otherwise known as world building) the art of creating fictional worlds. The ideal conworld is one with depth, consistency, and beauty, which is why Tolkien's Middle-earth is often held as the best existing example of a conworld. But conworlds are usually as beautiful as they are difficult to make.
Conworlding is a many-faceted process, and can be divided into a large number of sub-fields, each of them with its own enthusiasts. For example, conlangers are people who like to make their own languages (known as conlangs, short for constructed languages). Conmappers like to draw maps of fantasy worlds. Consports enthusiasts dream up games that might be enjoyed in a fantasy world. In general, the prefix "con-" in front of any real-world field turns it into its conworlding counterpart: conmusic, conart, conpoetry, conhistory, consocieties, conreligions, conphilosophies... the list goes on. Name any area of study, and chances are that a conworlder has dabbled in it already!
Many people have had conworlding ideas before: a sketched map, a drawing of an outlandish race, or a simple secret language. At this point budding conworlders ask: "Now what?" So I have a map — How do I decide where the mountains go? How do I make the language sound cooler and less boring? How do I make up impressive mythologies? Can I create music that doesn't sound like any sort of music on earth?
It might seem that for really thorough answers to those questions — if you don't care how much time or effort it takes to get them — you would want to research the actual branches of science that deal with those things: geology, linguistics, anthropology, music theory, etc. Doing it that way could take an enormous amount of time and effort, though. These are all huge subjects, and the things about them that are of most interest for conworlding may not be the things that are of most interest to specialists in those fields. Details that would be of great value to you may be buried in a sea of details. High-level insights of the sort you need for conworlding may be entirely absent from the literature of the subject, because the sorts of alternative situations that matter to a conworlder may not be what experts in the subject spend their time on.
What you need is a guidebook, not to the whole subject, but to the things about the subject that especially matter for conworlding. That's where this series of books comes in. We'll tell you what you need to know for conworlding, skipping over the superficial tourist traps, and including the really interesting sights that aren't on the standard tour.
So pick an area that interests you, and start creating!
# Convexity/Helly's theorem

Helly's theorem is as follows:
Let R$^n$ be an n-dimensional real vector space and let N > n. Suppose you have N convex sets in R$^n$ such that, given any n+1 of them, they have at least one point in common. Then all N sets have at least one point in common.
Proof: Obviously, the theorem is true for N = n+1. Proceed by induction and assume it is true for N-1. Let the sets be X$_1$ to X$_N$. For each i, exclude set X$_i$. By the inductive hypothesis, there is at least one point x(i) belonging to all the sets except possibly X$_i$. Since N > n+1, the (n+1) equations
    $\displaystyle \sum _{i=1}^{N}\lambda _{i}x_{k}(i)=0$
       $\displaystyle (k=1,2,...n)$
    $\displaystyle \sum _{i=1}^{N}\lambda _{i}=0$
in the N unknowns λ$_1$ to λ$_N$ must have non-trivial solutions. For one such solution, denote by λ$_{j1}$ to λ$_{jk}$ those λ that are positive, and λ$_{h1}$ to λ$_{h(N-k)}$ those that are negative.
# Convexity/Convex functions

A convex function f(x) is a real-valued function defined over a convex set X in a vector space such that for any two points x, y in the set and for any λ with $\displaystyle 0\leq \lambda \leq 1,$
    $\displaystyle f(\lambda x+(1-\lambda )y)\leq \lambda f(x)+(1-\lambda )f(y).$
NB: Because X is convex, :$\displaystyle (\lambda x+(1-\lambda )y)$ must be in X.
If the function -f(x) is convex, f(x) is said to ba a concave function. It is easily seen that if a function is both convex and concave, it must be linear.
Theorem: A convex function on X is bounded above on any compact subset of X.
Theorem: A convex function on X is continuous at each point of the interior of X.
Theorem: If f(x) is convex in a set containing the origin O, and f(O) = 0, then $^{f(μx)}$⁄$_μ$ is an increasing function of μ for μ > 0.
# Convexity/Convex polytopes

Definition: A convex polytope is the convex hull of a finite number of points. Usually, there will be at least three non-collinear points.
Theorem: A set is a convex polytope if and only if:
   * It is not the empty set
   * It is bounded
   * It is the intersection of a finite number of closed half-spaces.
A simplex in an n-dimensional vector space is the convex hull of n+1 points that do not all lie on the same hyperplane. If n=2, a simplex is a triangle; if n=3, it is a tetrahedron.
# Convexity/Examples of convex sets
## Example 1

In a two-dimensional vector space, a parallelogram is a set such that in some suitably chosen basis x, y of the space, the set consists of the points ax + by with 0 < a < 1, 0 < b < 1.
All parallelograms are convex. For, given any two points A, B in the parallelogram, we have
    A = ax + by
    B = cx + dy
with all coefficients being between 0 and 1. An arbitrary point on the line AB is
    C = (λa+(1-λ)c)x + (λb+(1-λ)d)y
with 0 < λ < 1. These coefficients are also between 0 and 1, so C is also in the parallelogram.

## Example 2

In Euclidean space, a ball, centre O radius r is the set of points within distance r of O, i.e. it is the interior of a sphere or hypersphere. (In two dimensions, a ball is often called a disc.)
All balls are convex. For, given any two points A, B in the ball, we have their distances from O less than r. For an arbitrary point C on AB, C = λA+(1-λ)B so
    dist(O,C) < λdist(O,A) + (1-λ)dist(O,B) < r.
Hence C is also in the ball.
# Convexity/The intersection of convex sets is convex

Theorem: Given any collection of convex sets (finite, countable or uncountable), their intersection is itself a convex set.
Proof: If the intersection is empty, or consists of a single point, the theorem is true by definition.
Otherwise, take any two points A, B in the intersection. The line AB joining these points must also lie wholly within each set in the collection, hence must lie wholly within their intersection.
# Convexity/What is a convex set?

A convex set is a set of points such that, given any two points A, B in that set, the line AB joining them lies entirely within that set.
Intuitively, this means that the set is connected (so that you can pass between any two points without leaving the set) and has no dents in its perimeter. Sections of the perimeter may be straight lines.

## Notes

* It is assumed that the concept of a line joining two points is defined. In a vector space over the reals, it is the set {λA+(1-λ)B}, 0 < λ < 1}. It will be assumed that we are dealing with vector spaces over the reals unless the contrary is stated explicitly.
* By convention, the empty set and all sets consisting of a single point are regarded as convex. Since we cannot find two distinct points in such sets, we cannot say that the line joining two such points isn't contained in the set.

## Theorem

If X is a convex set and x$_1$ ... x$_k$ are any points in it, then
$\displaystyle x=\sum _{i=1}^{k}\lambda _{i}x_{i}$ where all $\displaystyle \lambda _{i}>0$ and $\displaystyle \sum _{i=1}^{k}\lambda _{i}=1$
is also in X.
Proof: If $k=2$, the theorem is true by the definition of a convex set.
Now we proceed by induction. Assume the theorem is true for $k=m$. If $k=m+1$, we can formulate the definition of $x$ as a linear combination of two points, one of which is itself a linear combination of the first $m$ points and the other is the $(m+1)$th point:
$\displaystyle x=L\sum _{i=1}^{m}(\lambda _{i}/L)\,x_{i}+(1-L)\,x_{m+1}$ where $\displaystyle L=\sum _{i=1}^{m}\lambda _{i}$.
By the induction hypothesis, the first point must be in $X$; therefore, from the definition, $x\in X$.
# Bulgarian/Common Phrases
## Bulgarian (Slavic)

| Translation | Phrase | Pronunciation | Pronunciation | Remarks |
| hi | здравей | /zdraˈvɛj/ | zdra-ˈvey | informal |
| hi | здрасти | /ˈzdrasti/ | ˈzdra-sti | informal |
| good morning | Добро утро | /dɔˈbrɔ ˈutrɔ/ | do-'broh 'oo-tro |
| good day | Добър ден | /ˈdɔbər dɛn/ | 'do-buhr den |
| good evening | Добър вечер | /ˈdɔbər ˈvɛtʃer/ | 'do-buhr 'veh-cher |
| good night | Лека нощ | /ˈlɛka nɔʃt/ | 'leka nosht |
| goodbye | Довиждане | /dɔˈviʒdanɛ/ | do-'vizh-da-ne |
| how are you? | Как си? | /ˈkak si/ | kak see | informal |
| how are you? | Как сте? | /ˈkak stɛ/ | kak steh | formal or plural |
| I’m fine | Добре съм | /dɔˈbrɛ səm/ | do-'bre suhm |
| Where is the toilet? | Къде е тоалетната? | /kəˈdɛ ɛ tɔaˈlɛtnata/ | kuh-'de e toa -'let-na-tah |
| all the best | Всичко най-хубаво | /vˈsitʃkɔ naj-ˈxubavɔ/ | 'vsich-ko nay 'hoo- bavo |
| regards | Поздрави | /ˈpɔzdravi/ | 'poz-dra-vi |
| thank you | Благодаря | /blagɔdaˈrʲə/ | bla-go-da-'ryuh |
| happy birthday | Честит рожден ден! | /tʃɛˈstit rɔʒdˈɛn dɛn/ | chestit rozh'den den |
| Bulgarian language | Български език | /ˈbəlgarski ɛˈzik/ | 'buhl-gar-ski e -'zik |
| Do you speak Bulgarian? | Говорите ли български? | /goˈvoritɛ li ˈbəlgarski/ | Go-'vo-ree-teh lee 'buhl-gar-ski? |
| yes | да | /da/ | da |
| no | не | /nɛ/ | ne |
| of course | разбира се | /razˈbira sɛ/ | razbira se |
| Please, enter! | Влезте, моля! | /ˈvlɛstɛ ˈmɔʎa/ | 'vleste 'molya | formal (2nd p. plural) |
| Enter! | Влез! | /vlɛs/ | vles | informal (2nd p. singular) |
# Bulgarian/Expressions
## Common expressions

    See Common Phrases
* Здравей (zdravéy) — Hello
* Здрасти (zdrásti) — Hi
* Добро утро (dobró útro) — Good morning
* Добър ден (dóbər dén) — Good day
* Добър вечер (dóbər vécher) — Good evening
* Лека нощ (léka nósht) — Good night
* Довиждане (dovízhdane) — Good-bye
* Доскоро (doskóro) — See you soon
* Чао (cháo) (informal) - Bye
* Как си? (kák si) (informal) — How are you?
* Как сте? (kák ste) (formal, and also plural form) - How are you?
* Да (da) - Yes
* Не (ne) - No
* Може би (mózhe bi) - Maybe
* Не знам (neznám) - I don't know
* Какво правиш? (kakvó právish) (informal) — What are you doing?
* Какво правите? (kakvó právite) (formal, and also plural form) - What are you doing?
* Добре съм (dobré səm) — I’m fine
* Всичко най-хубаво (vsíchko nay-húbavo) — All the best
* Поздрави (pózdravi) — Regards
* Благодаря (blagodaryə́ ) (formal and informal) — Thank you
* Мерси (mersí) (informal) - Thank you
* Моля (mólya) — Please or You are welcome
* Извинете! (izvinéte) (formal) — Excuse me!
* Извинявай! (izvinyávay) (informal) — Sorry!
* Колко е часът? (kólko e chasə́t) — What time is it?
* Говорите ли ...? (govórite li...) — Do you speak ...?
    ...английски (anglíyski) — English
    ...български (bə́lgarski) — Bulgarian
    ...китайски (kitáyski) — Chinese
    ...френски (frénski) — French
    ...немски (némski) — German
    ...гръцки (grə́tski) — Greek
    ...италиански (italyánski) — Italian
    ...японски (yapónski) — Japanese
    ...корейски (koréyski) — Korean
    ...латински (latínski) — Latin
    ...испански (ispánski) — Spanish
* Ще се видим скоро (shte se vídim skóro) - See you soon
* Ще се видим утре (shte se vídim útre) - See you tomorrow

## Expressions for showing affection

* Обичаш ли ме? (Obíchash li me?) - Do you love me?
* Обичам те! (Obícham te!) - I love you!
* Харесваш ли ме? (Harésvash li me?) - Do you like me?
* Харесвам те (Harésvam te) - I like you
* Много ми липсваш/липсват (Mnógo mi lípsvash/lípsvat) - I miss you/them very much
* Много си хубав/хубава (Mnógo si húbaf/húbava) ) - You're very pretty (ending in "a" is said to females)

## Expressions for activities/hobbies/leisure time

* Караш ли... (Kárash li?) (informal) - Do you ride/drive...?
    ...кола? (kolá) - a car?
    ...мотор? (motór) - a motorcycle?
      * Да, карам. (Da, káram.) - Yes, I do.
* Искаш ли да ходим на...? (Ískash li da hódim na...) - Do you want to go to...?
    ...кино (kíno) - the movies
    ...театър (teátar) - the theater
    ...ресторант (restoránt) - a restaurant
    ...кафе - (kafé) - a cáfe
# Bulgarian/Post Office
## Post Office Vocabulary

* Поща (poshta) = Post office
* Картичка (kártichka) = Postcard
* Плик (plik) = Envelope
* Марка (márka) = Stamp
* Марки (márki) = Stamps
# Bulgarian/Directions
## Directions/outside

* Къде е...? (Kadé e...?) = Where is ...?
* ляв (lyav) = Left
* На ляво (na lyávo) = To the left
* десен (dásen) = Right
* На дясно (na dyásno) = To the right
* Право/Направо (právo/naprávo) = Straight
* Давай/карай направо (Dàvay/káray naprávo) = Keep going/driving straight
* Горе/нагоре (góre/nagóre) = Up
* Долу/надолу (dólu/nadólu) = Down
* Далеч, далече ( daléch, daléche ) = Far
* Близо, близко ( blízo, blísko ) = Near
* Дълго (də́lgo) = Long
* Късо (kə́so) = Short
* (Туристическа) карта ( (turistícheska) kárta) = (tourist) Map
* Туриситическа информация (Turistícheska informátsia) = Tourist Information
* Музей (muzey) = Museum
* Улица (ulitsa) = Street
* Булевард (bulevart) = Boulevard
* Площад (ploshtat) = Square
* (Авто)магистрала ( (afto)magistrála ) = Highway, Freeway
# Bulgarian/Places
## Institutions/buildings/places

* Банка (bánka) = Bank
* Полиция (Polítsia) = Police
* Полицейско управление (politséysko upravlenie) = Police station
* Болница (bólnitsa) = Hospital
* Аптека (aptéka) = Pharmacy, Chemists
* Магазин (magazín) = Store, Shop
* Ресторант (restoránt) = Restaurant
* Училище (uchílishte) = School
* Църква (tsə́rkva) = Church
* Поща (póshta) = Post office
* Улица (úlitsa) = Street
* Булевард (bulevárt) = Boulevard
* Площад (ploshtát) = Square
* Планина (planiná) = Mountain
* Хълм (halm) = Hill
* Долина (doliná) = Valley
* Океан (okeán) = Ocean
* Езеро (ézero) = Lake
* Река (reká) = River
* Басейн (baseyn) = Swimming pool
* Кула (kúla) = Tower
* Мост (most) = Bridge
# Bulgarian/Emergencies
## Emergency action words

* Помощ! (pómosht) = Help!
* Полиция! (polítsia) = Police!
* Пожар! (pozhár) = Fire!
* Bнимавай! (vnimávai) = Be careful!
* Спри! or Стой! (spri) or (stój) = Stop!/Freeze!
# Bulgarian/Numbers
## The numbers

Число (čislo) = Number

## Cardinal numbers
### 1 to 10

Different forms of the words for the numbers 1 and 2 are used for masculine, feminine and neuter gender.
* едно (ednó) = one (neuter)
** един (edin) = one (masculine)
** една (edna) = one (feminine)
* две (dve) = two (neuter and feminine)
** два (dva) = two (masculine)
* три (tri) = three
* четири (čétiri) = four
* пет (pet) = five
* шест (šest) = six
* седем (sédem) = seven
* осем (ósem) = eight
* девет (dévet) = nine
* десет (déset) = ten
When referring to men or groups of men and women, often different forms are used: двама, трима, четирима, петима, шестима, (седмина, осмина, деветима).

### 11 to 20

Informally the final "т" is not pronounced. These are the shortened versions of the numbers. The long (and very formal) versions end in -десет instead of -йсет.
* единайсет (edinájset) = 11
* дванайсет (dvanajset) = 12
* тринайсет (trinájset) = 13
* четиринайсет (četirinájset) = 14
* петнайсет (petnájset) = 15
* шестнайсет (šestnájset) = 16
* седемнайсет (sedemnájset) = 17
* осемнайсет (osemnájset) = 18
* деветнайсет (devetnájset) = 19
* двайсет (dvájset) = 20

## Ordinal numbers

masc./fem./neuter
* първи = first
* втори = second
* трети = third
* четвърти = fourth
* пети = fifth
* шести = sixth
* седми = seventh
* осми = eighth
* девети = ninth
* десети = tenth
# Bulgarian/Colors

Цвят (Tsvyát) = Color
Below are the neuter forms of the colors. When referring to masculine nouns, remove the final -о, when referring to feminine nouns, remove the final -о and add -а. Example: бяло = white, бял цвят (цвят is masculine) = color white, бяла котка (котка is feminine) = white cat.

## Colors

* Бяло (byálo) = White
* Зелено (zeléno) = Green
* Червено (chervéno) = Red
* Синьо (sínyo) = Blue (masc. син - sin, fem. синя - sínya)
* Черно (chérno) = Black
* Жълто (zhə́lto) = Yellow
* Оранжево (oránževo) = Orange
* Кафяво (kafyávo) = Brown
* Сиво (sívo) = Grey
* Розово (rózovo) = Pink
* Лилаво (lilávo) = Violet

## Shades

* Светло (svétlo) = Light (masc. светъл - svétal, fem. светла - svétla)
* Тъмно (tə́mno) = Dark (masc. тъмен - tə́men, fem. тъмна - tə́mna)
# Bulgarian/Market
## Market Vocabulary

* Колко струва? (Kólko strúva?) = How much does it cost?
* Какво е това? (Kakvó e tová?) = What is this?
* Ще го купя. (Shte go kúpya.) = I'll buy it.
* Дайте ми онова. (Dáyte mi onová.) = Give me that one.
* Искам да купя... (Ískam da kúpya...) = I would like to buy ...
* Имате ли... (Ímate li...) = Do you have ...
* Отворено (Otvóreno) = Open
* Затворено (Zatvóreno) = Closed
* Намаление до ...% (Namalénie do ...%) = Sale, Discount to ... %
* Кеш (kesh), В брой (V broy) = Cash
* Банкомат (Bankomát) = ATM
# Economic Sophisms/Chapter 16

| ←Reciprocity again | Economic Sophisms by Author:Frédéric Bastiat Chapter 16 Obstructed Navigation pleading for the Prohibitionists | A Negative Railway→ |
what he sends into the market of the world is purchased by a fellow-countryman or by a foreigner; whether the drafts or orders he receives come from a Frenchman or an Englishman; whether the commodities for which he afterwards exchanges these drafts or orders are produced on this or on the other side of the Ehine or the Pyrenees. There is always in each individual case an exact balance between what is contributed and what is received, between what is poured into and what is drawn out of the great common reservoir; and if this is true of each individual, it is true of the nation at large.
The only difference between the two cases is, that in the last each has to face a more extended market both as regards sales and purchases, and has consequently more chances of transacting both advantageously.
This objection may perhaps be urged: If everybody enters into a league not to take from the general mass the commodities of a certain individual, that individual cannot, in his turn, obtain from the mass what he is in want of. It is the same of nations.
The reply to this is, that if a nation cannot obtain what it has need of in the general market, it will no longer contribute anything to that market. It will work for itself. It will be forced in that case to submit to what you want to impose on it beforehand—isolation.
And this will realize the ideal of the prohibitive régime.
Is it not amusing to think that you inflict upon the nation, now and beforehand, this very régime, from a fear that it might otherwise run the risk of arriving at it independently of your exertions?
# Economic Sophisms/Chapter 17

| ←Obstructed Navigation pleading for the Prohibitionists | Economic Sophisms by Author:Frédéric Bastiat Chapter 17 A Negative Railway | There are No Absolute Principles→ |
I HAVE said that when, unfortunately, one has regard to the interest of the producer, and not to that of the consumer, it is impossible to avoid running counter to the general interest, because the demand of the producer, as such, is only for efforts, wants, and obstacles.
I find a remarkable illustration of this in a Bordeaux newspaper.
M. Simiot proposes this question:—
Should the proposed railway from Paris to Madrid offer a solution of continuity at Bordeaux?
He answers the question in the affirmative, and gives a multiplicity of reasons, which I shall not stop to examine, except this one:
The railway from Paris to Bayonne should have a break at Bordeaux, for if goods and passengers are forced to stop at that town, profits will accrue to bargemen, pedlars, commissionaires, hotel-keepers, etc.
Here we have clearly the interest of labour put before the interest of consumers.
But if Bordeaux has a right to profit by a gap in the line of railway, and if such profit is consistent with the public interest, then Angoulème, Poitiers, Tours, Orleans, nay, more, all the intermediate places, Kuffec, Châtellerault, etc., should also demand gaps, as being for the general interest, and, of course, for the interest of national industry; for the more these breaks in the line are multiplied, the greater will be the increase of consignments, commissions, transhipments, etc., along the whole extent of the railway. In this way, we shall succeed in having a line of railway composed of successive gaps, and which may be denominated a Negative Railway.
Let the protectionists say what they will, it is not the less certain that the principle of restriction is the very same as the principle of gaps; the sacrifice of the consumer's interest to that of the producer,—in other words, the sacrifice of the end to the means.
# Entry Level PHP Web Application Development/Our First Programs: Hello, World!/HelloUserWorld-Answer

<?php
# Entry Level PHP Web Application Development/Our First Programs: Hello, World!/DQS-Answer

A double-quoted string (also known as a double-quoted string literal) has the purpose of including a string into a program, with variable substitution. For example, the string "$foo on you" will appear as on you if $foo is not defined; if $foo contains the value 'Poo', then the resulting string will appear as Poo on you when output to the user’s web browser.
# Entry Level PHP Web Application Development/Table of Contents

* What is Programming? Why Write for the Web?
* PHP Web Application Development Environments
* Our First Programs: Hello, World!
* HTML and CSS: Presentation to the User
* PHP: Performing (Relatively) Simple IO (Input-Output)
# Entry Level PHP Web Application Development/Our First Programs: Hello, World!/SQS-Answer

A single-quoted string (also known as a single quoted string literal, because it is a value that means exactly what it looks like) has the purpose of including a string verbatim into a program. Single-quoted strings are not inspected by the PHP interpreter for variables to perform substitution in; for example, the string '$foo on you' will appear as $foo on you when output to the user’s web browser.