OpenLLM-France/wikimedia huggingface dataset:
# Mizar Commentary on Walter Rudin's Principles of Mathematical Analysis/Preface

The Mizar system consists of three parts: a formal language to write mathematical proofs in, a programm to check these proofs for correctness automatically and the Mizar Mathematical Library (MML). The MML has gotten quite large since its founding in 1989 and therein lies a small problem:
This book is an attempt to overcome this problem. We've selected the well known classic analysis book Principles of Mathematical Analysis ("the Book" within this book) written by Walter Rudin and wrote down where to find the definitions and theorems of the Book in the MML. If mathematical concepts differ between the Book and the MML, this is explained as well where appropriate. For example, in the Book it isn't explained what exactly a relation is, but rather what a function and (later) equivalence relation is, while both are a special kind of relation in Mizar.
Of course, since the MML doesn't contain all of mathematics, some definitions or theorems may have not been formalized yet. Additionally, as Wiedijk wrote, it is not necessarily easy to search the MML for a specific statement, so the authors of this book could have simply overlooked it despite their efforts. So if a statement is commented with "no reference" it means "no reference found".
For this book, the third edition of the Book and version 5.54.1341 of the MML are used, unless otherwise stated.
# Mizar Commentary on Walter Rudin's Principles of Mathematical Analysis/Sequences and Series of Functions

Note that sequences of functions can be seen as sequences over a normed space, which will mostly be left untouched in this chapter.

## Discussion of main problem

7.1 Definition Let $F$ denote $\{f_{n}\}$. $F$ being pointwise convergent is described by F is_point_conv_on E (SEQFUNC:20, see also SEQFUNC:def 10). Then $\lim _{n\to \infty }f_{n}$ is given by lim(F,E) (SEQFUNC:def 13). No reference for series.
7.2 Example No reference.
7.3 Example No reference.
7.4 Example No reference.
7.5 Example No reference.
7.6 Example No reference.

## Uniform Convergence

7.7 Definition $F$ being uniformly convergent on $E$ is F is_unif_conv_on E (SEQFUNC:def 12) or F is_uniformly_convergent_to f (MESFUN10:def 2. That uniform convergence implies pointwise convergence is SEQFUNC:22 or MESFUN10:20. No reference for function series.
7.8 Theorem No reference.
7.9 Theorem No reference.
7.10 Theorem No reference.

## Uniform Convergence and Continuity

7.11 Theorem No direct reference, but implicitly given in proof of TIETZE:20.
7.12 Theorem is TIETZE:20.
7.13 Theorem No reference.
7.14 Definition No reference.
7.15 Theorem No reference.

## Uniform Convergence and Integration

7.16 Theorem is INTEGRA7:31 or MESFUN10:21.
Corollary No reference.

## Uniform Convergence and Differentiation

7.17 Theorem No reference. #TODO show that $f'(x)=\lim _{n\to \infty }f_{n}(x)$
7.18 Theorem No reference. #TODO existence of continuous nowhere differentiable function

## Equicontinuous Families of Functions

7.19 Definition No reference for pointwise bounded, but for F is uniformly_bounded (MESFUN10:def 1).
7.20 Example No reference.
7.21 Example No reference.
7.22 Definition No reference.
7.23 Theorem No reference.
7.24 Theorem No reference.
7.25 Theorem No reference.

## The Stone-Weierstrass Theorem

7.26 Theorem No reference #TODO the Stone-Weierstrass theorem
7.27 Corollary No reference.
7.28 Definition The algebra of complex functions on a domain $E$ is CAlgebra(E) (CFUNCDOM:def 8), the real analogon of that is RAlgebra(E) (FUNCSDOM:def 9). A general algebra structure is found in POLYALG (not to be confused with the universal algebra from UNIALG_1). Subalgebras for complex algebras are defined in CC0SP1:def 1, for real algebras in C0SP1:def 9. No reference for uniformly closed or uniformly closure.
7.29 Theorem No reference.
7.30 Definition No reference.
7.31 Theorem No reference.
7.32 Theorem No reference.
7.33 Theorem No reference.

## Exercises

1. No reference. 2. No reference. 3. No reference. 4. No reference. 5. No reference. 6. No reference. 7. No reference. 8. No reference. 9. No reference. 10. No reference. 11. No reference. 12. No reference. 13. No reference. 14. No reference. 15. No reference. 16. No reference. 17. No reference. 18. No reference. 19. No reference. 20. No reference. 21. No reference. 22. No reference. 23. No reference. 24. No reference. 25. No reference. 26. No reference.
# Mobility 2050

Mobility 2050 is a vision of everyday personal mobility as it can and should be in 2050. It is written by uniquely qualified authors: engineering students who have the technical education they need to conceive of, review, and evaluate sociotechnical alternatives in mobility, but who – unlike many people of comparable qualifications – are also young enough to expect to be working citizens in the future they write about, perhaps with decades still ahead of them. These qualifications give these authors a direct, personal stake in the success of mobility visions they propose.
Especially in the US, mobility policies and practices in the 2020s remain much as they were 25 or 50 years ago. Passenger transport, land use policies and practices, and transportation engineering standards have changed little since the 1990s and even the 1970s. At 29 percent, the share of total greenhouse gas emissions attributable to transportation in the US is higher than the share of any other major sector of the national economy, and higher than in other high-income nations. The endurance of such policies and practices may be due in part to a paucity of visionary, long-term planning.
If the mobility of 2050 in the United States is to be more affordable, inclusive and sustainable than the mobility of the 2020s, the planning must begin now. The authors themselves determine the ideas and values that the mobility of 2050 will serve. They will also consider how the technology of the mid-21st century may permit new mobility possibilities.
Mobility 2050 is divided into three parts: 1. Normalizing Walking and Micromobility 2. Making Transit Practical 3. Land Use Planning and Urban Design for Inclusive Sustainability
Within each section, chapters will consider more specific subsets of these subjects. Authors are invented to consider each of them broadly, without regard in inherited assumptions.

## Table of Contents
#### Normalizing Walking and Micromobility

* Learning from Success Stories
* Lightweight Electromobility
* Tech's Place in Micromobility

#### Making Rail and Transit Practical

* New Transit Modes
* Battery-Free Electromobility
* Trains Instead of Planes

#### Land Use Planning and Urban Design for Inclusive Sustainability

* The Future of the 15-Minute City
* Recovering Land Lost to Parking Craters
* Retrofitting Parking Garages
* Retrofitting Suburbia
# Pinyin/Mark
## Noun

* a mark is a sign marking on something, such as a line or a point.
** biaojih shih moouwuh shahng d jihhaoh, rur 1-tiaor xiahn huoh 1'g diaan.
# Pinyin/Marriage

See also
# Pinyin/Man

Search Pinyin man
* narnrern
* rern
# Pinyin/Married

See also
# Pinyin/Mango

See also
A mango is a sweet tropical fruit with smooth yellow or red skin, soft yellow or orange flesh and a very large seed inside.
Mángguǒ shì tián de rèdài shuǐguǒ. Guǒpí guānghuá, huángsè huò hóngsè. Guǒròu róuruǎn, huángsè huò chéngsè. Guǒhé hěn dà.
# Muggles' Guide to Harry Potter/Magic/Herbology
## Overview

Herbology is the study of magical plants and how to take care of, utilize and/or combat them. Herbology lessons are shown in each of the first six books.
The subject is depicted as closely related to Potions, due to the nature of the plants, many of which are cultivated for extracting useful ingredients. Throughout the series, Herbology is taught by Pomona Sprout.

## Extended Description

Herbology is a core subject; it is one of the seven academic subjects taught in the first year. Harry, who chooses to pursue a career as an Auror, takes Herbology at NEWT-level.
Being located in greenhouses on the grounds, trips to and from Herbology lessons are written to depict the weather at the time (for example, Harry Potter and the Half-Blood Prince, chapter 14). There are at least three greenhouses described in the books, holding a variety of magical plants of varying degrees of lethality, including mandrakes, bubotubers, and Snargaluffs (which are valued for their pods).
Herbology is also, initially, the only subject in which Neville Longbottom excels. Neville will later show aptitude for Charms and Defence Against the Dark Arts.

## Analysis

As mentioned, Herbology and Potions are reasonably closely related. We see one interaction between Professor Sprout and Professor Slughorn, where they are discussing the properties of a plant that Slughorn needs for his first-year Potions class. We have to assume there are similar, though possibly not as cordial, interactions earlier between Professor Sprout and Professor Snape.
Like Charms, Herbology is a practical class, with lots of noise and activity going on. As a result, it is a class where Harry, Ron, and Hermione can discuss their plans. It is likely for this reason that we see as much of Herbology as we do, and also possibly why all three of the Trio are able to continue Herbology studies at NEWT level.

## Questions

Study questions are meant to be left for each student to answer; please don't answer them here.

## Greater Picture

Herbology seems to the uninitiated to be a relatively straightforward and harmless branch of magic, but we are somewhat disabused of that notion by the appearance of the Venomous Tentacula, first mentioned in Harry Potter and the Chamber of Secrets. Professor Sprout's offhanded treatment of the plant in that episode is misleading; much later, we see a Death Eater being reeled in by Tentacula. Many plants are only handled with protective gear, and in the climactic battle at Hogwarts we see many magical plants being used as weapons.
In the Epilogue, it is revealed that Neville has become the Professor of Herbology at Hogwarts.
# Muggles' Guide to Harry Potter/Magic/Hippocampus
## Overview

Hippocampi are the equine equivalent of Muggle "mermaids": forequarters and head of a horse, and tail of a fish.

## Extended Description

The Hippocampus is largely a Mediterranean beast, though a single example was caught off the coast of Scotland by Mermen in 1949.

## Analysis

While the Hippocampus does not appear in the main story, it does appear in the stated form in Muggle mythology. The name has also been used to identify a part of the structure of the brain which is apparently somehow involved with the creation and storage of memories.

## Questions

Study questions are meant to be left for each student to answer; please don't answer them here.
# Muggles' Guide to Harry Potter/Magic/Homenum Revelio
## Overview

Homenum Revelio is a spell which will reveal to the caster whether any other (presumably living) humans are within its area of influence.

## Extended Description

When they first arrive at Number 12, Grimmauld Place after leaving Bill and Fleur's wedding, Harry, Ron, and Hermione are concerned that there may be Death Eaters lurking. Hermione casts Homenum Revelio to determine that the house is, in fact, empty.
When Harry, Ron, and Hermione are betrayed by Xeno Lovegood, the two Death Eaters, Selwyn and Travers at first do not believe Xeno's protestations that he actually has Harry Potter. Selwyn determines that there is, in fact, someone else there by using this charm.
In both cases, the person casting the spell reports to the others there present what has been discovered, and Harry, Ron, and Hermione are only aware of the spell because they hear it being cast.

## Analysis

The fact that Hermione reported nobody present at Grimmauld Place, and that Selwyn had to tell Travers that there was someone "up there," leads us to believe that the response to the spell is local to only the caster; other than the person casting the spell, nobody is aware of the results of the spell.

## Questions

Study questions are meant to be left for each student to answer; please don't answer them here.
# Muggles' Guide to Harry Potter/Magic/Hand of Glory
## Overview

The Hand of Glory, a desiccated, severed human hand, is a candle holder; the person holding it is able to see in complete darkness by its candlelight, but to anyone else, the light is invisible.

## Extended Description

First seen at Borgin & Burkes, a shop in Knockturn Alley dealing in Dark objects. Harry, using Floo Powder for the first time, accidentally lands in Borgin & Burke's. As he prepares to exit, he sees Draco Malfoy and his father, Lucius Malfoy, entering the shop. Harry hides and overhears Borgin explaining the Hand of Glory and its function. It is, he says, a thief or plunderer's best friend; Lucius replies that he hopes Draco will be better than a thief or a plunderer...though unless his grades improve, that may be the best he can hope for.
Draco evidently does purchase a Hand of Glory, because Ginny sees him carrying it as he guides the Hogwarts invaders from the Room of Requirement; the hand apparently allows him to see where he is leading the Death Eaters despite the Darkness Powder he tosses after spotting the D.A. members.

## Questions

Study questions are meant to be left for each student to answer; please don't answer them here.
# Muggles' Guide to Harry Potter/Magic/Heliopath
## Overview

Heliopaths, a magical creature apparently springing entirely out of the mind of Xeno Lovegood, are supposedly "spirits of fire", giant flaming creatures.

## Extended Description

In Harry Potter and the Order of the Phoenix, during the initial meeting of the Defence Association in the Hog's Head, Luna says that Cornelius Fudge has an army of Heliopaths, telling Neville that they are spirits of fire, "great flaming creatures that gallop over the ground burning everything in front of them". Hermione states that they do not exist; Luna then angrily counters this by saying that there are plenty of eyewitness accounts of them. The incipient argument is only broken up when Ginny imitates Professor Umbridge.

## Analysis

It is interesting to note Hermione's anger at this invention. Hermione, as we've seen, is somewhat hidebound, believing what she is told by "authority," whether that is teachers or books, and finds Luna's belief in this, and other apparently nonsensical creatures, aggravating. Curiously, this seems to be the last time in the series that one of Luna's invented creatures angers Hermione; after this, she seems wryly amused rather than upset at Luna's beliefs. No explanation is visible for this, but we can speculate that the abuse of authority she sees in Umbridge weakens Hermione's faith in authority in general. Alternately, of course, it may be simply that Hermione, maturing, sees much less in the world as being pure black or white, and becoming more accepting of unusual viewpoints.

## Questions

Study questions are meant to be left for each student to answer; please don't answer them here.
# Muggles' Guide to Harry Potter/Magic/Hinkypunk
## Overview

A Hinkypunk is a small, one legged creature that appears to be made out of smoke. It carries a lantern that is used to lure unsuspecting travelers into bogs.

## Extended Description

The term is first introduced in Harry Potter and the Prisoner of Azkaban. When Professor Snape substitutes for Professor Lupin in Defense Against the Dark Arts, he instructs the class to turn to the section on Werewolves; Hermione protests "We're due to start hinkypunks."
Later in the year Professor Lupin sets up an obstacle course for the third years' final exam. One of the obstacles is to "squish their way across a patch of marsh while ignoring misleading directions from a hinkypunk."

## Questions

Study questions are meant to be left for each student to answer; please don't answer them here.
# Muggles' Guide to Harry Potter/Magic/History of Magic
## Overview

History of Magic is the course in which students at Hogwarts learn, appropriately enough, about the history of magic. It is a core subject, and is required for all students from first to fifth years. We presume that NEWT-level studies are available, but as the viewpoint character does not progress in this course past year five, we don't see them. This may imply that it may only be continued at NEWT level with a written OWL examination. It is taught by Professor Binns, a ghost.

## Extended Description

Very nearly all of the exposure we have to the course is involved with mentioning how boring it is. Harry is obviously not alone in his inability to stay awake in this class; of all the Trio, it seems Hermione alone is able to stay awake long enough to make notes. Harry does note at one point that with any other teacher, the subject matter (the Goblin Wars) could be much more exciting.
Possibly the main reason for the existence of this course is in Harry Potter and the Chamber of Secrets, where Hermione manages to get the story of the Chamber of Secrets from Professor Binns. Additionally, there is one time when Harry is aroused from his stupor in this class by the arrival of an injured Hedwig at the window. All other sessions of this class are uniformly dull and eventless.

## Analysis

Harry's experience in this class clearly mimics the experience many students have had in one class or another. It is possible that this course is included for the purpose of balance, as if to say, yes, magic and learning about magic can be fun, but it's not all fun, there's tedious part of it as well. Selection of history as the subject in question is probably premeditated. Of all the courses that are required learning, History is by far the most commonly seen as not only tedious, but useless. Particularly at the teenage level, few students can see the value of learning about things that happened long ago. Making the instructor a ghost emphasizes that the subject material is basically unchanging, and also allows for his delivery of the material to be, if we may be permitted the pun, dry and dead.
There are points in history that have a great influence on Harry and his actions; however, he does not perceive, and perhaps Binns does not adequately teach, the background that led to the separation of Muggles and the Wizarding world, with its concomitant Decree for the Reasonable Restriction of Underage Sorcery. This decree, with its constraints on what Harry is allowed to do outside school and the consequences he suffers therefrom, is a part of a larger picture that Harry remains unaware of, despite its stemming from a critical juncture in Wizarding history.

## Questions

Study questions are meant to be left for each student to answer; please don't answer them here.
# Modern History/Dawn of the Computer Age

| Wikibooks Modern History Population, Governance, Philosophy, Invention, Weapons, Combat, Trade, Exploration | Edit template |
Current status: This book does not yet contain much content. Work for expansion is beginning. Creation of stubs linking to Wikisource and Wikipedia is in progress.
Contributors: If you copy (instead of link) content from elsewhere into this book, for example content from Wikipedia or public domain sources, then you MUST CREDIT the source of such copied text.
As the need for rapid calculations increased, commercial organisations introduced the electronic calculator to the market. Then the computer appeared.
The price of computers decreased, and they started appearing in more businesses, and then also in schools, libraries, and wealthier governments.
The Internet connected computers together and provided more information to users, but there were also problems such as fraudulent websites, overabundant commercial emails, copyright violations, server outages, and lack of connectivity to poorer countries.
The dawn of the computer age brought about some disadvantages, such as incompatible file formats, fears about privacy, and error messages such as the Blue Screen of Death.
This page or section of Modern History is a stub. You can help Wikibooks by expanding it.
# Modern History/Earl Lincoln Poole

Earl Lincoln Poole (1891-1972) was an American bird artist and sculptor. Published versions of his illustrations appeared in Birds of Virginia (1913) and Bird Studies at Old Cape May (1937). He was born in Haddonfield, New Jersey, and was active in Pennsylvania.
# Modern History/Benjamin Disraeli

Benjamin Disraeli, 1st Earl of Beaconsfield, KG, PC (21 December 1804 – 19 April 1881) was an English statesman and literary figure. He served in government for three decades, twice as Prime Minister – the first and thus far only person of Jewish parentage to do so, although Disraeli was baptised in the Anglican Church at an early age. Disraeli's most lasting achievement was the creation of the modern Conservative Party after the Corn Laws schism of 1846.
Although a major figure in the protectionist wing of the Conservative Party after 1846, Disraeli's relations with the other leading figures in the party, particularly Lord Derby, the overall leader, were often strained. Not until the 1860s would Derby and Disraeli be on easy terms, and the latter's succession of the former assured. From 1852 onwards Disraeli's career would also be marked by his often intense rivalry with William Ewart Gladstone, who eventually rose to become leader of the Liberal Party. In this duel, Disraeli was aided by his warm friendship with Queen Victoria, who came to detest Gladstone during the latter's first premiership in the 1870s. In 1876 Disraeli was raised to the peerage as the Earl of Beaconsfield, capping nearly four decades in the House of Commons. He died in 1881.
Before and during his political career Disraeli was well-known as a literary and social figure, although his novels are not generally regarded as belonging to the first rank of Victorian literature. He mainly wrote romances, of which Sibyl and Vivian Grey are perhaps the best-known today. He was and is unusual among British Prime Ministers for having gained equal social and political renown.
# Modern History/Decolonisation

Decolonization is the process by which a colony gains its independence from a colonial power, a process opposite to colonization. Decolonization could be achieved by attaining independence, integrating with the administering power or another state, or establishing a "free association" status. The UN has stated that in the process of decolonization there is no alternative to the principle of self-determination. Decolonization may involve peaceful negotiation and/or violent revolt by the native population. Decolonization in the strict sense is distinct from the break-up of traditional empires, and in modern academic discourse the period of decolonization generally refers to two major waves of independence from European colonial rule:
From the late 18th century up through 19th century decolonization in the Americas occurred, beginning with American colonists' revolt against British rule in the present-day United States, and continuing through the collapse of the Spanish and Portuguese empires in Latin America.
In the 20th and 21st centuries "decolonization" usually refers to the achievement of independence by the various European colonies and protectorates in Asia and Africa following the end of World War II. This conforms with an intellectual movement known as Post-Colonialism. A particularly active period of decolonization occurred between 1945 to 1960, beginning with the independence of Pakistan and India from Britain in 1947.