OpenLLM-France/wikimedia huggingface dataset:
# Ordered field/Convergent sequences/Rules/1/Fact/Proof

Denote the limits of the sequences by $x$ and $y$, respectively. Let $\epsilon >0$ be given. Due to the convergence of the first sequence, there exists for
    $\epsilon '={\frac {\epsilon }{2}}\,$
some $n_{0}$ such that for all $n\geq n_{0}$ the estimate
    $\vert {x_{n}-x}\vert \leq \epsilon '\,$
holds. In the same way there exists due to the convergence of the second sequence for $\epsilon '={\frac {\epsilon }{2}}$ some $n_{0}'$ such that for all $n\geq n_{0}'$ the estimate
    $\vert {y_{n}-y}\vert \leq \epsilon '\,$
holds. Set
    $N={\max {\left(n_{0},n_{0}'\right)}}\,.$
Then for all $n\geq N$ the estimate
    ${\begin{aligned}\vert {x_{n}+y_{n}-(x+y)}\vert &=\vert {x_{n}+y_{n}-x-y}\vert \\&=\vert {x_{n}-x+y_{n}-y}\vert \\&\leq \vert {x_{n}-x}\vert +\vert {y_{n}-y}\vert \\&\leq \epsilon '+\epsilon '\\&=\epsilon \end{aligned}}$
holds.
# Ordered field/Bernoulli's inequality/Fact

Let $K$ be an ordered field and $n$ a natural number.
$x\in K$ with $x\geq -1$ the estimate
    $(1+x)^{n}\geq 1+nx\,$
# Ordered field/Convergent sequence/Bounded/Fact

Let $K$ denote an ordered field. If a sequence is convergent in $K$,
# Ordered field/Convergent sequence/Bounded/Fact/Proof

Let ${\left(x_{n}\right)}_{n\in \mathbb {N} }$ be the convergent sequence with $x\in K$ as its limit. Choose some $\epsilon >0$. Due to convergence there exists some $n_{0}$ such that
    $\vert {x_{n}-x}\vert \leq \epsilon {\text{ for all }}n\geq n_{0}.$
So in particular
    $\vert {x_{n}}\vert \leq \vert {x}\vert +\vert {x-x_{n}}\vert \leq \vert {x}\vert +\epsilon {\text{ for all }}n\geq n_{0}.$
Below $n_{0}$ there are ony finitely many members, hence the maximum
    $B:=\max _{n<n_{0}}\{\vert {x_{n}}\vert ,\,\vert {x}\vert +\epsilon \}\,$
is welldefined. Therefore $B$ is an upper bound and $-B$ is a lower bound for ${\left\{x_{n}\mid n\in \mathbb {N} \right\}}$.
# Ordered field/Convergent sequences/Rules/2/Fact/Proof

Let $\epsilon >0$ be given. The convergent sequence ${\left(x_{n}\right)}_{n\in \mathbb {N} }$ is bounded, due to fact, and therefore there exists a $D>0$ such that $\vert {x_{n}}\vert \leq D$ for all $n\in \mathbb {N}$. Set $x:=\lim _{n\rightarrow \infty }x_{n}$ and $y:=\lim _{n\rightarrow \infty }y_{n}$. We put $C:={\max {\left(D,\vert {y}\vert \right)}}$. Because of the convergence, there are natural numbers $N_{1}$ and $N_{2}$ such that
    $\vert {x_{n}-x}\vert \leq {\frac {\epsilon }{2C}}{\text{ for }}n\geq N_{1}{\text{ and }}\vert {y_{n}-y}\vert \leq {\frac {\epsilon }{2C}}{\text{ for }}n\geq N_{2}.$
These estimates hold also for all $n\geq N:={\max {\left(N_{1},N_{2}\right)}}$. For these numbers, the estimates
    ${\begin{aligned}\vert {x_{n}y_{n}-xy}\vert &=\vert {x_{n}y_{n}-x_{n}y+x_{n}y-xy}\vert \\&\leq \vert {x_{n}y_{n}-x_{n}y}\vert +\vert {x_{n}y-xy}\vert \\&=\vert {x_{n}}\vert \vert {y_{n}-y}\vert +\vert {y}\vert \vert {x_{n}-x}\vert \\&\leq C{\frac {\epsilon }{2C}}+C{\frac {\epsilon }{2C}}\\&=\epsilon \end{aligned}}$
hold.
# Ordered field/1 and 0/Exercise

Let $K$ denote an ordered field. Show, only using the axioms of an ordered field, that $1>0$ holds.
# Ordered field/Archimedean property/Definition

Let $K$ be an ordered field. $K$ is called Archimedean, if the following Archimedean axiom holds, i.e. if for every $x\in K$ there exists a natural number $n$ such that
    $n\geq x\,.$
# Ordered field/Bernoulli's inequality/Fact/Proof

We do induction over $n$. Suppose that the statement is already known for $n$. Then
    ${\begin{aligned}(1+x)^{n+1}&=(1+x)^{n}(1+x)\\&\geq (1+nx)(1+x)\\&=1+(n+1)x+nx^{2}\\&\geq 1+(n+1)x,\end{aligned}}$
since squares in an ordered field are nonnegative.
# System development/Domains/Overview/Case management/Ontology

* Case
* Worklist
# System development/Domains/Overview/Communication
## Index

* Best practices
* Business objectives
* Case studies
* Ontology
* Processes
* Software
* Subdomains
* To-do
* Vision
# System development/Domains/Overview/Facility management/Software

On this page you can find an overview of tooling that is used to support facility management.
# System development/Domains/Overview/Contract management

Contract management or contract administration is the management of contracts made with customers, vendors, partners, or employees.

## Index

* Best practices
* Case studies
* Ontology
* Processes
* Software
* Subdomains
* To-do
* Vision
# System development/Domains/Overview/Contract management/Ontology
## Concepts

* Contract
* Contractholder
* ContractType
* Organization
* Supplier
# System development/Domains/Overview/Event management
## Index

* Ontology
* Processes
* Software
* Subdomains
* To-do
* Vision
# System development/Domains/Overview/Facility management

Facility management (or facilities management or FM) is an interdisciplinary field devoted to the coordination of space, infrastructure, people and organization, often associated with the administration of office blocks, arenas, schools, sporting complexes, convention centers, shopping complexes, hospitals, hotels, manufacturing, shipping, etc..

## Index

* Best practices
* Case studies
* Ontology
* Processes
* Software
* Subdomains
* To-do
* Vision
# System development/Domains/Overview/Case management
## Index

* Ontology
# System development/Domains/Overview/Customer service
## One liners

* “In the digital age, every point of engagement with a customer – from a service call to a marketing email – serves as a ‘Moment of Truth’.

## To-do

* Pega researched how telco- and broadband provider can improve their customer service. See http://www.pega.com/telco-moments-of-truth for more info.
** Most telco- and broadband providers feel...
# Student Projects/Earthquake

An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth, resulting from the sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in size from those that are so weak that they cannot be felt to those violent enough to toss people around and destroy whole cities. The seismicity, or seismic activity, of an area is the frequency, type and size of earthquakes experienced over a period of time. The word tremor is also used for non-earthquake seismic rumbling. An earthquake is a violent movement of the rocks in the Earth's crust which create waves of energy travelling through the Earth. Earthquakes are usually quite brief (and even somewhat repeated itself, known as an aftershock), but may repeat over a period of time. The study of earthquakes is called seismology. Earthquakes usually occur where tectonic plates are in constant motion, in which these areas of constant motion (or violent motion) are usually at the edges of the plates. For example, several and several earthquakes have been recorded in the Western part of South America due to the constant motion between the South American plate and the Nazca plate. Earthquakes usually occur on faults, which are breaks in the Earth's crust formed by the sliding, pushing, or pulling of tectonic plates.
# Student Projects/DNA

DNA stands for Deoxy Ribo Nucleic Acid. It is an organic chemical of complex molecular structure that is found in all prokaryotic and eukaryotic cells and in many viruses. DNA codes genetic information for the transmission of inherited traits.They are found inside every cell.Cell has nucleus which has a nuclear membrane, chromosome, nucleoplasm,nucleolus.Chromosome consists of strings of DNA.
Discovery of DNA:
James Dewey Watson (born April 6, 1928) is an American molecular biologist, geneticist and zoologist.
Francis Harry Compton Crick (8 June 1916 – 28 July 2004) was a British molecular biologist, biophysicist, and neuroscientist.These two scientists,Watson &Crick in 1953 designed the structure for DNA as double helix which they realised could carry biological information and was awarded Nobel prize in 1962.
Structure of DNA:
There are three classes of macromolecules: proteins, lipids, and carbohydrates. There is a fourth class of macromolecules: nucleic acids. Like other macromolecules, nucleic acids are composed of monomers, called nucleotides, which are polymerized to form large strands. Each nucleic acid strand contains certain nucleotides that appear in a certain order within the strand, called its base sequence. The base sequence of deoxyribonucleic acid (DNA) is responsible for carrying and retaining the hereditary information in a cell. The building blocks of nucleic acids are nucleotides. Nucleotides that compose DNA are called deoxyribonucleotides. The three components of a deoxyribonucleotide are a five-carbon sugar called deoxyribose, a phosphate group, and a nitrogenous base, a nitrogen-containing ring structure that is responsible for complementary base pairing between nucleic acid strands. The deoxyribonucleotide is named according to the nitrogenous bases. The nitrogenous bases adenine (A) and guanine (G) are the purines; they have a double-ring structure with a six-carbon ring fused to a five-carbon ring. The pyrimidines, cytosine (C) and thymine (T), are smaller nitrogenous bases that have only a six-carbon ring structure.
# System development/Domains/Overview/Project management/Vision

In Agile methodologies, like scrum, a lot of project activities are considered waste.

## Challenges

* What are challenges in project management?
* You want to be in control. This means:
** You want to have an overview of all projects and the status of those projects.
** You want to know if a project is on budget, on time.
** You want to see who is responsible for a certain project.
** You want to see which activities are performed? who is performing the activity? and what is te status?
** You want to know which risks are involved.
* You want a project to be structured in a certain way.
* What are the deliverables of a project?
# System development/Domains/Overview/Retail/Ontology
## Concepts

* Cart
* Customer
* Product
* ProductCatalog
# System development/Domains/Overview/Retail/To-do/Develop a WEM application for a retail platform
## Index

* Mockups
* Projectplan
# System development/Domains/Overview/Risk management
## Index

* Ontology
* Processes
* Software
* Subdomains
* To-do
* Vision
# System development/Domains/Overview/Sales/Ontology
## Concepts

* Customer
* Invoice
* Order
* Orderline
* Product
# System development/Domains/Overview/Project management/Software

On this page you can find information about solutions that support project management.

## Selecting the right solution

For many teams one of these solutions will support their needs. The disadvantage of these solutions is that they are not easy to customize.

## Overview

| Name | URL |
| Asana | https://asana.com |
| Projectplace | https://www.projectplace.nl |
| Microsoft Project | https://products.office.com/en-us/project/project-and-portfolio-management-software |
| Trello | https://trello.com |
# System development/Domains/Overview/Retail

Retail is the process of selling consumer goods and/or services to customers through multiple channels of distribution to earn a profit.

## Index

* Best practices
* Case studies
* Ontology
* Processes
* Software
* Subdomains
* To-do
* Vision
# System development/Domains/Overview/Sales
## Index

* Best practices
* Business objectives
* Case studies
* Ontology
* Processes
* Software
* Subdomains
* To-do
* Vision
# Motivation and emotion/Tutorials/Goals and self/Self-constructs
## Self-constructs

* Brainstorm self-constructs that people have heard of e.g.,:
** Self-awareness
** Self-confidence
** Self-concept
** Self-efficacy - Belief in one's ability to perform a task, particularly under difficult conditions
** Self-esteem - Note Reeve's arguments about self-esteem as a symptom not a cause of psychological health and well-being
** Self-worth
* Group similar self-constructs together and then discuss, define and distinguish between them
# Motivation and emotion/Tutorials/Growth psychology/Fully functioning person

* A growing openness to experience – moving away from defensiveness and having no need for subception (a defence that involves unconsciously applying strategies to prevent a troubling stimulus from entering consciousness).
* An increasingly existential lifestyle – living each moment fully – not distorting the moment to fit personality or self-concept but allowing personality and-self concept to emanate from the experience. This results in excitement, daring, adaptability, tolerance, spontaneity, and a lack of rigidity and suggests a foundation of trust. "To open one's spirit to what is going on now, and discover in that present process whatever structure it appears to have" (Rogers, 1961)
* Increasing organismic trust – trusting one's own judgement and ability to choose behaviour that is appropriate for each moment. Not relying on existing codes and social norms but being open to experiences and trusting one's sense of right and wrong.
* Freedom of choice – not being shackled by the restrictions that influence an incongruent individual; able to make a wider range of choices more fluently. Belief that one plays a role in determining one's behaviour and so feel responsible for one's own behaviour.
* Creativity – feeling more free to be creative. Also more creative in the way one adapts to one's circumstances without feeling a need to conform.
* Reliability and constructiveness – can be trusted to act constructively. An individual who is open to all his/her needs will be able to maintain a balance between them. Even aggressive needs will be matched and balanced by intrinsic goodness in congruent individuals.
* A rich full life – the life of a fully functioning individual is rich, full and exciting; they experience joy and pain, love and heartbreak, fear and courage more intensely. Rogers' description of the good life:
* This process of the good life is not, I am convinced, a life for the faint-hearted. It involves the stretching and growing of becoming more and more of one's potentialities. It involves the courage to be. It means launching oneself fully into the stream of life.
* — Rogers (1961),
# Motivation and emotion/Tutorials/Growth psychology/Meaning and coherence
## Meaning and coherence

* Two key psychological theorists about the importance of meaning, historically have been:
** Viktor Frankl, sense of meaning and logotherapy. Frankl survived a German concentration camp during WWII and observed that those with a reason to live beyond the camp were more likely to survive.
** Aaron Antonovsky, salutogenesis (the opposite of pathogensis) and sense of coherence (SOC). Antonovsky investigated the long-term health impacts for German concentration camp survivors. Whilst there considerable health issues, he was struck that some survivors were relatively healthy and investigated further. Those who emerged relatively health appeared to have, what he termed, a sense of coherence.
* According to Antonovksy, SOC is “The extent to which one has a pervasive, enduring though dynamic, feeling of confidence that one’s environment is predictable and that things will work out as well as can reasonably be expected.” It has three components:
** A sense of comprehensibility:
*** Do you feel that you can understand things, that things make sense and are not confusing?
*** Do you feel that things are predictable or can be expected? In other words, do you feel like you know what’s going to happen next, or that you know what’s coming?
** A sense of manageability:
*** Do you feel that things are manageable or within your control, that things can be handled or taken care of?
*** Do you feel you have the skills or ability, the support, the help, or the resources necessary to take care of things?
** A sense of meaningfulness:
*** Do you feel that things are interesting or fascinating, a source of pleasure or satisfaction?
*** Do you feel that things are really worth it, that there is good reason or purpose to care about what happens?
* Complete the SOC13 and compare with UC student item means (SOC29, Abou-Abou-Hamdan, 2008, N = 355):
| Scale | M | SD | Skew | Kurtosis |
| Overall SOC | 4.19 | 0.78 | -0.36 | 0.29 |
| Comprehensibility | 3.96 | 0.90 | -0.02 | -0.19 |
| Manageability | 4.71 | 0.94 | -0.38 | -0.10 |
| Meaningfulness | 5.01 | 1.06 | -0.62 | 0.22 |
Note that in scoring the SOC-13, reverse the scoring for Items 1, 2, 3, 7, 10, then add the items for each factor and work out the means.
Motivation and emotion/Tutorials/Growth psychology
# Motivation and emotion/Tutorials/Growth psychology/Problems for discussion
## Problems for discussion

* In general, do you think that evil resides in human nature or is it a product of a sick culture?
* As a parent raising a child who expresses a somewhat socially undesirable temperament, which option would you recommend - Explain/defend your answer:
** raise the child in his or her natural temperament or
** raise the child to conform to the more socially-desirable temperament?
* Do you mostly agree or mostly disagree with the following statement by Rogers: Learning does not follow from teaching. Rather, learning follows having one’s interests identified, facilitated, and supported.
* Explain the following concepts:
** growth-seeking and validation-seeking.
** Maslow’s distinction between growth and deficiency needs
** Rogers’ distinction between congruence and incongruence
** Autonomy and control causality orientations
* Discuss what types of social interactions
** support growth-seeking, growth needs, congruence, and an autonomy causality orientation?
** lead to validation-seeking, deficiency needs, facades, and a control causality orientation.
# Motivation and emotion/Tutorials/Growth psychology/Happiness - Practical exercises
## Happiness - Practical exercises

Choose one of the following out-of-classroom "happiness exercises" from positive psychology therapy to try and report about your experience and the results in your e-portfolio:
* Gratitude visit. Write a letter or visit and share about your gratitude to someone who has been especially kind to you but never really thanked.
* Three good things in life. Each day, write down three things that go well and identify the cause of each.
* You at your best. Write about a time when you functioned at your best. Reflect on the personal resources that made that functioning possible.
* Beautiful day: See Seligman's TED talk.
* Identify signature strengths: Noting signature strengths and using them more often.
* Using signature strengths in a new way. Identify up to five personal signature strengths (from a list such as the one in Reeve, 2009, Table 15.3) and find a way to use each in a new way.
For more information\, see Positive psychology progress: Empirical validation of interventions (Seligman et al., 2005)
# Motivation and emotion/Tutorials/Growth psychology/Optimal human functioning

What are the psychological characteristics of an optimally functioning human?
Brainstorm: What characterises "self-actualisation" or a "fully functioning person"?
# The sojourn in the lands of my ancestors by may angel

THE CASK OF AMONTILLADO levern hill
Montresor tells the story of the night that he took his revenge on Fortunato, a fellow nobleman. Angry over some unspecified insult, he plots to murder his friend during Carnival when the man is drunk, dizzy, and wearing a jester's motley. He baits Fortunato by telling him he has obtained what he believes to be a pipe of Amontillado (about 130 gallons), a rare and valuable sherry wine. He claims he wants his friend's expert opinion on the subject. Fortunato goes with Montresor to the wine cellars of the latter's palazzo, where they wander in the catacombs. Montresor offers De Grave, a wine, to Fortunato; at one point, Fortunato makes an elaborate and — to the narrator's eyes — grotesque gesture with an upraised wine bottle. When Montresor appears not to recognize the gesture, Fortunato asks, "You are not of the masons?" Montresor says he is, and when Fortunato, disbelieving, requests a sign, Montresor displays a trowel he had been hiding. Montresor warns Fortunato, who has a bad cough, of the damp, and suggests they go back; Fortunato insists on continuing, claiming that "[he] shall not die of a cough." During their walk, Montresor mentions his family coat of arms: a foot in a blue background crushing a snake whose fangs are embedded in the foot's heel, with the motto Nemo me impune lacesst (No one attacks me with impunity). When they come to a niche, Montresor tells his victim that the Amontillado is within. Fortunato enters and, drunk and unsuspecting, does not resist as Montresor quickly chains him to the wall. Montresor then declares that, since Fortunato won't go back, he must "positively leave [him]." Montresor walls up the niche, entombing his friend alive. At first, Fortunato, who recovers from his drunken state faster than Montresor anticipated he would, shakes the chains, trying to escape. The narrator stops working for a while so he can enjoy the sound. Fortunato then screams for help, but Montresor mocks his cries, knowing nobody can hear them. Fortunato laughs weakly and tries to pretend that he is the subject of a joke and that people will be waiting for him (including the Lady Fortunato). As the murderer finishes the topmost row of stones, Fortunato wails "For the love of God, Montresor!" Montresor replies, "Yes, for the love of God!" He listens for a reply but hears only the jester's bells ringing. Before placing the last stone, he drops a burning torch through the gap. He claims that he feels sick at heart, but dismisses this reaction as an effect of the dampness of the catacombs. In the last few sentences, Montresor reveals that it has been 50 years since the murder, he has never been caught, and Fortunato's body still hangs from its chains in the niche where he left it. The murderer, seemingly unrepentant, ends the story by remarking: In pace requiescat
# The universe as a false vacuum and quantum suicide

The universe as a false vacuum and quantum suicide
On Wikipedia there is the following article.
Possibility that the universe is a false vacuum
Some of it was taken from an earlier version of Chaotic inflation theory Is the article valid?
In particular is the comparison with Quantum suicide and immortality valid? I wrote the material relating to that comparison.
See Many worlds quantum mechanics
# Theatre

Theatre or theater is a collaborative form of fine art that uses live performers to present the experience of a real or imagined event before a live audience in a specific place. The performers may communicate this experience to the audience through combinations of gesture, speech, song, music, and dance.

## Resources

* Makeup
* Musical
* Musical Direction

## See Also

* Collaborative play writing
* Wikipedia: Theatre
# The visible sky

Have you ever looked carefully and curiously at the night sky far was from a city? If so, at first glance you may have found no order in the stars, and no way to judge their distances, except to say that they are far away. What patterns emerge from a careful long term scrutiny?

## Objective

Describe the daily motions of the sun, moon, stars and planets relative to the horizon.

## Constellations

Take the time to study the stars for a while; you'll find that they fall into patterns, designs imposed by your mind. Ancient skywatchers perceived stellar patterns and passed them on such patterns are called Constellations. Early named constellations marked a convenient group of stars, with ill-defined boundaries, that typically outlined a mythological or realistic figure. In Babylonian times the constellations came into use as signposts in the sky to mark the positions of the sun and moon. The constellations used today (there are 88 of them) are established by international agreement of astronomers.

### Wikipedia readings

* Andromeda
* Antlia
* Apus
* Aquarius
* Aquila
* Ara
* Aries
* Auriga
* Bootes
* Caelum
* Camelopardus
* Cancer
* Canes Venatici
* Canis Major
* Canis Minor
* Capricornus
* Carina
* Cassiopeia
* Centaurus
* Cephus
* Cetus
* Chamaeleon
* Circinus
* Columba
* Coma Berenices
* Coona Australis
* Corona Borealis
* Corvus
* Crater
* Crux
* Cygnus
* Delphinus
* Dorado
* Draco
* Equuleus
* Eridanus
* Fornax
* Gemini
* Grus