OpenLLM-France/wikimedia huggingface dataset:
# Number Theory

This book covers an elementary introduction to Number Theory, with an emphasis on presenting and proving a large number of theorems. No attempts will be made to derive number theory from set theory and no knowledge of Calculus will be assumed. It is important to convince yourself of the truth of each proof as you work through the book, and make sure you have a complete understanding. For those who wish to use this as a reference book, an index of theorems will be given.

## Front

* Cover
* Authors
* For Contributors

## Chapters

* Chapter 1: The Integers

## Appendix

* Appendix A: 32-Bit Linear Congruential Generator
* Appendix B: Powers modulo 11
* Appendix C: Powers modulo 19

## Back

* Bibliography

## See also

* Proofs in Number Theory

## External links

* A Computational Introduction to Number Theory and Algebra (Shoup)-retrieved Dec 21, 2009
# Number Theory/The Integers

Chapter 1: The Integers
← Chapter 0 · Chapter 2 →
Introduction

## Sections

* Notation and Introduction to Proof
* Axioms
* The Well-Ordering Property
* Elementary Divisibility
* Prime Numbers

## Extra

* Review
* Practice Problems
* Solutions to Practice Problems
* Glossary
# Geometry/Chapter 1/Exercises

A set of exercises related to concepts from Chapter 1.
This set contains 3 exercises (including the Conceptual Questions)

## Exercises
### Section 1.1

1.1 (Geometry in Real Life) Give the geometric term(s) that is best modeled by each.
1. The location of San Francisco, California 2. The surface of a chalkboard 3. The tip of a pencil 4. A piano chord 5. The edge of a desk 6. A knot in a rope 7. A telephone pole 8. Two connected walls 9. A partially opened folder
1.2 (Name the Line) Use the appropriate notation to name the following line in five different ways.
1.3 (Name the Plane) Use the appropriate notation to name the following plane in two different ways.
# Google Workspace/Getting Started
## Creating an account
### For work

* Click on Sign in button.
* Click "Create account" then click "For work or my business".
* Click "Try Google Workspace".
* Enter a business name, click on desired number of employees a business have, select a region.
* Enter your name and email address.
* You will be shown a prompt where you can use your email or setup a custom domain.
** If you choose to use your email, enter the 6-digit code to verify.
** If you choose to setup a custom domain, set up an existing domain or buy a new domain.
* Enter your password. The password should contain at least 8 characters.

### For personal use

* Click on Sign in button.
* Click "Create account" then click "For my personal use".
* Enter your name, date of birth and gender.
* Choose the email eddress from the list.
** Alternatively, you can enter a custom Gmail address or even a different one. For the latter, you will need to enter the 6-digit code to verfiy it's yours.
* Enter your password.
* Optionally, enter your recovery email address.
* Review your new account.
* Choose your privacy settings.
** For 1 step: Affects Web & App Activity, YouTube History and Personalized ads together.
** For 4 steps: Affects Web & App Activity, YouTube History, Personalized ads and privacy reminders individually.
* Review your privacy settings.
* Agree to the terms and conditions.
# Google Workspace

This is a wikibook about Google Workspace. It illustrates how to use these applications.

## Contents

* Getting Started
* Gmail
* Google Calendar
* Google Drive
* Google Docs
* Google Sheets
* Google Slides
* Google Meet
# Algebra/Chapter 22/Exercises

A set of exercises related to concepts from Chapter 22.
This set contains 2 exercises (including the Conceptual Questions)

## Exercises
### Section 22.1

22.1 (Continued Fraction Conversion) Convert the following fractions into finite simple continued fractions.
22.2 (p/q) Find p/q if:
# Algebra/Chapter 24/Graphs and Networks

| ------------------------ | Algebra Chapter 24: Graphs and Networks Section 1: Graphs and Networks | Euler Paths |
24.1: Graphs and Networks
* Caution!
* This chapter covers a topic which is infamous for using many different words which refer to the same thing, a result of many people from different cultures studying them in many different ways.
* For this reason, it is best to remember the concepts being described rather than the names we give them. We have also added alternative terminology alongside the ones that we will be using here.
# Google Workspace/Gmail

Gmail is the email service provided by Google. It provides a webmail interface, accessible through a web browser, and is also accessible through the official mobile application. Google also supports the use of third-party email clients via the POP and IMAP protocols. It is part of Google Workspace.

## Inbox

The inbox consists of a list of emails, separated into three categories by default: primary, promotions and social.
You can read an email by clicking on an email. You can select emails for archiving and deleting.
# Dutch Empire/Maps and Pictures of the Dutch Empire

Here are a list of maps, showing the rise and fall of the Dutch Empire. Currently, Aruba, Bonaire, Curaco, Saba and Sint Eustatius are part of the Kingdom of the Netherlands. They are all small islands in the Caribbean. I do not have a map between 1830-1938 because the only major event(s) that took place was the expansion in the East Indies, which can be seen by looking at Expansion in the East Indies section.

## Maps

* The Dutch Empire in 1630
* The Dutch Empire in 1650
* The Dutch Empire in 1674
* The Dutch Empire in 1700
* The Dutch Empire in 1750
* The Dutch Empire in 1795
* The Dutch Empire in 1830.
* The Dutch Empire prior to WWII.
* The Dutch Empire in 1960.
* The Dutch Empire in 1975.
* Dutch Islands in the Caribbean today.

## People

* William of Orange or William "the Silent", father of the Netherlands, age 47. c. 1580
* William the Silent at age 22.
* Statue of William the Silent in the Hague
* Maurice of Nassau son of William the Silent.
* Willam Barentsz, explorer.
* Willam Janszoon Blaeu, Dutch cartographer.
* Michiel de Ruyter Dutch Navy legend.
* Maarten Tromp, Dutch Navy legend.
* Piet Hein, Dutch Navy legend.
* Peter Stuyvesant, Director-General of New Netherland.
* Johan de Witt, Dutch politician.
* William V, last stadtholder of the Dutch Republic.
* Louis Bonaparte, King of Holland.
* King William I.
* King William II.
* King William III.
* Queen Wilhelmina, and future Queen Juliana.
* Queen Beatrix, current Queen of the Netherlands.

## Flags

* Flag of the Dutch Republic. 1581-1795
* Current Flag of the Netherlands. 1806–Present
* Flag of the VOC.1602-1800
* Flag of the Batavian Republic.1795-1806

## Legacy

* "New Amsterdam", present day New York City.
* Dutch Houses in Cape Town, South Africa.
* Fort Zeelandia in Suriname.
* Jakarta, formerly Batavia in Indonesia.
# Chess Opening Theory/1. Nf3/1...f5/2. g3
## 2. g3

This is a principled move similar to the King's Indian Attack that allows White to fianchetto a bishop next move. Black's most popular response is 2...Nf6 followed by 3...g6 3...d6, or 3...e6 to protect the f-pawn but Black could also prepare 3...e5 with 2...d6 to take the center.
When contributing to this Wikibook, please follow the Conventions for organization.
# Magar/Counting

* Zero = Wāng [वाङ]
* One = Kāt [काट]
* Two = Nhís [न्हीस]
* Three = Som [सोम]
* Four = Bulí [बुली]
* Five = Bāngä [बाङ्आ/बाङ्गा]
* Six = Tú [टू]
* Seven = Tūn [टून]
* Eight = Ké [के]
* Nine = Kú [कू]
* Ten = Chú [चू]
* Eleven = Chukat
* Twelve = Chunhis
* Thirteen = Chusom
* Fourteen = Chubuli
Decimal calculation In Magar Language[मगर भाषामा दशमलव/दशाङ्क गणना]
* Zero = Wāng [वाङ]
* One = Kāt [काट]
* Ten = Chú [चू]
* Hundred = Bhongga [भोङग]
* Thousand = Whānga [व्हाङ]
* Ten Thousand = Chu Whānga [चू व्हाङ]
* Lakh = Liwānga [लीवाङ]
* Ten Lakh = Chu Liwānga [चू लीवाङ]
* Crore = Kiwānga [कीवाङ]
* Ten Crore = Chu Kiwāng [चू कीवाङ]
# Colman Gambit
### 2...Ne7

The Colman Gambit is an unorthodox and rare response to White's 2. Nf3. While it is seldom seen at high levels of play, the gambit seeks to confuse the opponent and create dynamic, unbalanced positions. Black's idea is to support a later ...f5 pawn push or prepare unexpected central play. White has several responses to take advantage of Black's unusual move:
   * 3. Nxe5 is a critical response, directly challenging Black's setup. After 3...d6, White can retreat with 4. Nf3, where Black must play carefully to justify the unorthodox knight placement.
   * 3. d4 is the Classical Variation, striking in the center and exploiting Black's delayed development. Black typically responds with 3...exd4, leading to an open game where White has a central advantage.
   * 3. Bc4 develops another piece actively, aiming at Black's weak f7 square. This often forces Black to play defensively with moves like 3...d6 or transpose into a reversed King's Gambit setup with 3...Ng6 followed by ...f5.
   * 3. c3 prepares to establish a strong pawn center with d4. Black may reply with 3...d6, maintaining flexibility, or even 3...f5, leading to sharp play.
   * 3. Nc3 develops a piece and prepares to control the center. Black can transpose into standard openings or continue with ...Ng6 or ...d6, aiming for later counterplay.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation.
1. e4 e5 2. Nf3 Ne7
| | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| Classical Variation | d4 exd4 | Nxd4 d5 | exd5 Qxd5 | Be3 Nbc6 | Nb5 Qd8 | Bf4 Nd5 | Qxd5 Qxd5 | Nxc7+ Kd8 | Nxa8 Bf5 | c3 Kc8 | 0-0-0 Be7 | Balanced |
| 3. Nxe5 | Nxe5 d6 | Nf3 f5 | exf5 Bxf5 | Bc4 Qd7 | 0-0 O-O-O | d4 Ng6 | Be3 Kb8 | Balanced |
| Reversed King's Gambit | Bc4 Ng6 | Balanced |
How to read the theory table: The rows of the table represent different variations of the Colman Gambit. The columns show the sequential moves in each variation, with Black's responses listed below White's moves. The final column provides an evaluation of the resulting position, such as "Balanced," indicating an equal game. Chess notations are written in algebraic notation.
When contributing to this Wikibook, please follow the Conventions for organization.

## Example Games

The Colman Gambit has been used in a few notable games. Below are some examples with full game details:
* Jadanowski, Lukasz vs. Toczek, Grzegorz
* Keskin, Ilkin Zeynep vs. Halpert, Alexandra
* Balog, Marton vs. Foldi, Martin

## References

* Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.
# Chess Opening Theory/1. b4/1...e6
## 1...e6

Black pushes the e-pawn so they can gain control over the center. This move also allows the pawn to move without getting attacked by a bishop on b2. Secondly, this move attacks the pawn on b4. However, White can play 2. Bb2 anyways, as Black cannot capture with 2...Bxb4??, as it hangs a rook with 3. Bxg7!.
When contributing to this Wikibook, please follow the Conventions for organization.
# Bahasa Indonesia
## Table of Contents

* Phonology and Alphabet
* Affixation

## See also

* Indonesian
* Indonesian Reader
* Wikijunior:Languages/Indonesian
# Muggles' Guide to Harry Potter/Magic/Obscuro

Obscuro is a spell used to put a blindfold on the caster, that cannot be taken off without magical means. Hermione uses it on Phineas Nigellus Black's portrait in Harry Potter and the Deathly Hallows. Hermione does this because she knows that Professor Snape has access to his portrait, so she wants to get him to slip information about Hogwarts without revealing their location. This event suggests that spells can be used on portraits.
Because Obscuro is a basic spell, it can likely be lifted by Finite Incantatem.
# Algebra/Chapter 3/Inverses

| What are Equations? | Algebra Chapter 3: Solving Equations Section 2: Inverses of Numbers | Properties of Equality |
Numbers have two inverses: additive inverses, or opposites, and multiplicative inverses, or reciprocals. All real numbers besides 0 have both of these inverses.

## Additive Inverses

The 'additive inverse of a number is such that a number added to its additive inverse is zero. It is also called an opposite. To find a number's additive inverse, find if the number is positive, negative, or neither. If a number n is positive, then its additive inverse is -n. Likewise, the additive inverse of -n is n. 0 is the additive inverse of itself.

## Multiplicative Inverses

The multiplicative inverse of a number is such that a number multiplied by its multiplicative inverse is 1; that is, unity. It is also called a reciprocal. The multiplicative inverse of a number n is 1/n. To find a number's multiplicative inverse you may also write it as a fraction and reverse its numerator and denominator; recall that any number divided by 1 is itself. 0 has no multiplicative inverse; it would be 1/0, but numbers can not be divided by zero.
# Salute, Jonathan!/Grammar (nouns)
### No single obligatory ending for nouns

Occidental does not have a single obligatory ending for nouns, as is often the case in constructed languages.
Examples: castelle (castle), benedition (blessing/benediction), nebul (cloud).

### The common -e ending

The -e neutral final vowel is extremely common and used for many reasons, such as:
* To show that the word is a noun, and not another type of word such as an adjective. Examples: scrit (written) vs. scrite (something written), vocal (vocal) vs. vocale (vowel), mortal (mortal), mortale (a mortal).

### No grammatical gender

There is no grammatical gender, in the same way as in English. Nouns are masculine, feminine, or neuter according to their meaning.
The gender can be indicated in names for entities: -o for masculine, and -a for feminine:
* Maritos e maritas deve sempre dir li veritá, ne ver? - Husbands and wives should always tell the truth, right?
The -o ending is often used in a neutral sense, especially when adding an -e would change the pronunciation of the preceding consonant:
* Veni, amicos, noi have coses a far. - Come, friends, we have things to do.
However, the -s plural can be added without an -e- in between if one wants to use a plural form that can only be interpreted as neuter.
* It ne es un surprise que mi amics volet que yo intra li asil. - It is no surprise that my friends wanted me to enter the asylum.

### Deriving adjectives from nouns

For the most part, the final vowel in a noun is not part of the root itself, and when the ending is not obligatory, it and disappears when adding endings to form adjectives.
* angel (angel): angelic
* metall/e (metal): metallic
* córpor/e (body): corporal
* témpor/e (time): temporal
In many cases, the derived adjectives are more familiar to English speakers than the original nouns themselves, as is the case with the words corporal and temporal.

### Nouns ending in -u and -a

Most nouns ending in -u and a few ending in -a do not lose this vowel when adjectives are formed using them. The -a nouns in this case are almost entirely from Greek, and end in -ma.
* usu (use): usual
* spíritu (spirit): spiritual
* sistema (system): sistematic
* aqua (water): aquatic
# Colors-צבעים

In Hebrew, colors are a common form of adjective. Refer to the page on Hebrew adjectives for more information on the grammar, usage, and agreement of adjectives.

## Vocab list

| English | Hebrew | transliteration |
| black | שחור | shakhor |
| blue | כחול | kahol |
| green | ירוק | yarok |
| brown | חום | khoom |
| red | אדום | adom |
| white | לבן | lavan |
| yellow | צהוב | tsahov |
| pink | ורוד | varod |
| purple | סגול | sagol |
| orange | כתום | katom |
| color | צבע | tseva |

# Exercises-תרגילים

* _____השמיים בצבע
* The sky is [colored]
* _____השלג בצבע
* The snow is [colored]
* ______תפוז בצבע
* Orange colored

# Answers-תשובות

* השמיים בצבע כחול
* Hashamaim batzeba kahol
* השלג בצבע לבן
* hasheleg batzeba lavan
* תפוז בצבע כתום
* tapuz batzeva katom
# Hebrew/Elementary/Lesson 1

Welcome to lesson 1 of the Hebrew Language Course. In this lesson, we will learn some basic words.

## Basic words (מילים בסיסיות)

| English | Hebrew | Transliterated | IPA |
| Hello | שָׁלוֹם | shalom | /ʃaˈlom/ |
| Yes | כֵּן | ken | /ken/ |
| No | לֹא | lo | /lo/ |
| OK | בְּסֵדֶר | beseder | /bˈse.ðɛr/ |
| Goodbye | לְהִתְרָאוֹת | lehitraot | /le(h)itʁaˈ(ʔ)ot/ |
| Thanks | תּוֹדָה | toda | /toda/ |
| Good Morning | בֹּקֶר טוֹב | boker tov | /ˈbo.keʁ tov/ |
| Good evening | עֶרֶב טוֹב | erev tov | /ˈeʁev tov/ |
| Sorry | סְלִיחָה | slikha | /'sliχa/ |
| Please | בְּבַקָּשָׁה | bevakasha | /be.va.kaˈʃa/ |
| Where | אֵיפׂה | eyfo | /eˈfo/ |

### Notes:

* When people thank you, it is customary to answer "עַל לֹא דָּבָר" ("Al lo davar" or "אֵין בְּעֳד מָה" ("Eyn be'ad ma"), both meaning "for nothing". Alternatively, you can say "בְּבַקָשָׁה" ("Bevakashah"), which means both "please" and "you're welcome".
* When "בֹּקֶר טוֹב" is spelled without vowels, it is generally spelled with a ו, as in "בוקר טוב".
* When speaking informally, "אֵיפׂה" is generally pronounced with an accent on the first syllable rather than the second.

## Pronouns (מילות גוף)

| English | Hebrew | Transliterated | IPA |
| I | אני | Ani | /(ʔ)aˈni/ |
| We | אנחנו | Anakhnu | /(ʔ)aˈnaχ.nu/ |
| You (male) | אתה | Ata | /(ʔ)aˈta/ |
| You (female) | את | At | /(ʔ)at/ |
| You (plural, male) | אתם | Atem | /(ʔ)aˈtem/ |
| You (plural, female) | אתן | Aten | /(ʔ)aˈten/ |
| He | הוא | Hoo | /(h)u/ |
| She | היא | Hee | /(h)i/ |
| It | זה | Ze | /zɛ/ |
| Them (male) | הם | Hem | /(h)em/ |
| Them (female) | הן | Hen | /(h)en/ |

### Notes:

* In biblical Hebrew, "אנחנו" is sometimes used interchangeably with "אנו". In modern Hebrew, "אנו" tends to be used less often, and is generally more formal.
# Hebrew/Aims

| Development | Aims and Objectives |
| > Next | Aims and Objectives |
| Contents | |

## Vision

This book aims to be able to be a resource for those trying to teach themselves Hebrew by having succinct lessons on vocabulary, grammar, in addition to practice sheets and work to help improve at the language.
# Hebrew/Introduction

Lessons · Vocabulary · Grammar · Appendices · Texts

## Contenidos
### Studying Hebrew · ללמוד עברית

    ¿Por qué estudiar hebreo? · ¿Cómo estudiar hebreo?

### The Hebrew World · עולם העברית

    Culture · History of Hebrew · The Jewish State

### Alphabet · אלפבית

    Letters · Consonants · Gereshes · Vowels · Vowel Reduction · Shva · Semi-consonants also Acting as Vowels · Final Letters · Dagesh · Cursive
    Vocabulary · Punctuation · Numerals

### Pronunciation & Spelling · ההגייה והאיות

    Phonology · Sounds & Syllables · Spelling

### Greetings · ברכות

    Vocabulary · Introductions · Hello · Goodbye · How are you?

### Numbers · מספרים

    Vocabulary · Feminine Numerals · Masculine Numerals · Ordinal Numbers · Mathematics · How much?

### Dates · תאריכים

    Vocabulary · Days · Months · Years · Seasons · Jewish Calendar · Holidays · Birthdays

### Telling Time · ?מה השעה

    Vocabulary · Time · Time of Day
# 3. King's Gambit Accepted: Tumbleweed Variation

This allows 3...Qh4+! 4.g3 fxg3+ 5.Kg2 Qxe4+ 6.Nf3 gxf2 7.Rxh4. It seems that White has given up three pawns and destroyed their kingside for nothing, but Black must proceed cautiously, or White can use the many open lines with surprising effectiveness.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1.e4 e5 2.f4 exf4 3. Kf2?
| | 3 | 4 | 5 |
| King's Own Gambit | ... Qh4+! | g3 fxg3+ | Kg2 Qxe4+ | -/+ |
When contributing to this Wikibook, please follow the Conventions for organization.

## References

* Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.

## External links

* 365Chess. 1. e4 e5 2. f4
* chessgames. 1. e4 e5 2. f4
* Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.
# Algebra/Chapter 17/The Pythagorean Theorem

| ------------------------ | Algebra Chapter 17: Conic Sections Section 1: The Distance Formula | Loci of Points |
17.1: The Distance Formula

## The Distance Formula

Let's say that there are two dots on a coordinate plane. How would you find the distance between the two without a ruler? Hint: draw a right triangle. Let's see if you can figure this out yourself before peeking!
Suppose you have two points, (x$_1$, y$_1$) and (x$_2$, y$_2$), and suppose that the length of the straight line between them is d. You can derive the distance formula by noticing that you can follow the following path between any two points to obtain a right triangle: start at point 1, change x (keep y constant) until you're directly above or below point 2, and then alter y and keep x constant until you're at point 2.
If you follow this path, the length of the first segment that you draw is $|x_{2}-x_{1}|$ and the length of the second is $|y_{2}-y_{1}|$. Also, since these two line segments form a right triangle, the Pythagorean Theorem applies and we can write $(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}=d^{2}\,$ or, solving for d,
$d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}$
This formula is called the distance formula.
Another Formula is (and more simplified):
$a^{2}+b^{2}=c^{2}$
# Algebra/Chapter 14

Chapter 14: Trigonometry
← Chapter 13 · Chapter 15 →
Introduction

## Sections

* Pythagoras' Theorem
* Right Triangle Trigonometry
* The Law of Sines
* The Law of Cosines
* Angles and their Measure
* The Unit Circle
* Trigonometric Identities
* Sum and Difference Identities
* Double Angle, Half Angle, and Reduction Formulas
* Sum-to-Product and Product-to-Sum Formulas
* Graphs of Trigonometric Functions
* Inverse Trigonometric Functions
* Solving Trigonometric Equations

## Extra

* Review
* Practice Problems
* Solutions to Practice Problems
* Glossary
# Nimzo-Indian Defence, Leningrad Variation
### 4. Bg5

White decides to match Black pin for pin, and the e4 square is once more a no man's land. More subtle is the fact that Black's knight no longer controls d5 either. For that reason, van der Sterren calls the d5 advance "the point but also the necessary consequence of 4. Bg5." Either 4...h6 5. Bh4 c5 6. d5 or 4...c5 5. d5 h6 6. Bh4 is almost always played.
4. Bg5 is a fairly uncommon move against the Nimzo-Indian, being only played by 2% of Masters on the lichess opening database. With no black pawn on d5 white isn't threatening to win it like he often is against the Ragozin or Queen's Gambit Declined.
When contributing to this Wikibook, please follow the Conventions for organization.

## References

* ↑ van der Sterren, Paul (2009). Fundamental Chess Openings. Bracknell: Gambit Publications Ltd. p. 72. ISBN 978-1-906454-13-5.