OpenLLM-France/wikimedia huggingface dataset:
# Vector space/Bidual/Natural mapping/Fact/Proof

Let $v\in V$ be fixed. First of all, we show that $\Psi (v)$ is a linear form on the dual space ${V}^{*}$. Obviously, $\Psi (v)$ is a mapping from ${V}^{*}$ to $K$. The additivity follows from
    $(\Psi (v))(f_{1}+f_{2})=(f_{1}+f_{2})(v)=f_{1}(v)+f_{2}(v)=(\Psi (v))(f_{1})+(\Psi (v))(f_{2})\,,$
where we have used the definition of the addition on the dual space. The compatibility with the scalar multiplication follows similarly from
    $(\Psi (v))(sf)=(sf)(v)=s(f(v))=s((\Psi (v))(f))\,.$
In order to prove the additivity of $\Psi$, let $v,w\in V$ be given. We have to show the equality
    $\Psi (v+w)=\Psi (v)+\Psi (w)\,.$
This is an equality inside of ${\left({V}^{*}\right)}^{*}$, in particular, it is an equality of mappings. So let $f\in {V}^{*}$ be given. Then, the additivity follows from
    $(\Psi (v+w))(f)=f(v+w)=f(v)+f(w)=(\Psi (v))(f)+(\Psi (w))(f)\,.$
The scalar compatibility follows from
    $(\Psi (sv))(f)=f(sv)=s(f(v))=s((\Psi (v))(f))\,.$
In order to prove injectivity, let $v\in V$ with $\Psi (v)=0$ be given. this means that for all linear forms $f\in {V}^{*}$, we have $f(v)=0$. But then, due to fact, we have
    $v=0\,.$
By the criterion for injectiviy, $\Psi$ is injective.
In the finite-dimensional case, the bijectivity follows from injectivity and from fact.
# Vector space/Direct/Definition

Let $K$ denote a field, and $V$ a set with a distinguished element $0\in V$, and with two mappings
    $+\colon V\times V\longrightarrow V,(u,v)\longmapsto u+v,$
and
    $\cdot \colon K\times V\longrightarrow V,(s,v)\longmapsto sv=s\cdot v.$
Then $V$ is called a $K$-vector space (or a vector space over $K$), if the following axioms hold (where $r,s\in K$ and $u,v,w\in V$ are arbitrary).
* $u+v=v+u$,
* $(u+v)+w=u+(v+w)$,
* $v+0=v$,
* For every $v$, there exists a $z$ such that $v+z=0$,
* $1\cdot u=u$,
* $r(su)=(rs)u$,
* $r(u+v)=ru+rv$,
* $(r+s)u=ru+su$.
# Vector space/Dimension n and n vectors/Equivalences/Fact

Let $K$ be a field, and let $V$ be a $K$-vector space with finite dimension $n=\dim _{\left(V\right)}$. Let $n$ vectors $v_{1},\ldots ,v_{n}$ in $V$ be given.
* $v_{1},\ldots ,v_{n}$ form a basis of $V$.
* $v_{1},\ldots ,v_{n}$ form a generating system of $V$.
* $v_{1},\ldots ,v_{n}$ are linearly independent.
# Vector space/Bidual space/Definition

Let $K$ be a field, and let $V$ be a $K$-vector space. Then the dual space of the dual space ${V}^{*}$, that is,
    ${({V}^{*})}^{*},$
is called the Bidual of $V$.
# Syllabus of Economics/Introduction to industrial organization - Q & A
## About this page

This page is a place for people to enter exam questions and answers for the syllabus module "Introduction to economics" that is part of the Introductory Microeconomics syllabus in Wikiversity's School of Economics. If you would like to help with this learning project, you might like to adding questions and answers (or by helping verify existing questions and answers) to the test bank of questions and answers below for this module. Just add the questions and answers to this page. Later, the plan is to convert these questions and answers on some linked pages using the WikiMedia quiz extension. Other ways you could help are by entering links to relevant Wikipedia entries or other useful learning materials into the Introductory Microeconomics syllabus page or by adding questions and answers for the other modules listed on the Introductory Microeconomics syllabus page.
Questions and Answers
# Syllabus of Economics/Scarcity and economic interactions

This page links to Wikipedia entries and other learning materials that are relevant to the list of topics in a module of the Introductory Microeconomics syllabus on the Wikiversity's School of Economics pages.

## Wikipedia entries

Scarcity
Trade
Law of rent
Production–possibility frontier
Opportunity cost
Market economy
Price system

## Other learning materials

* YouTube: Economists Do It With Models: Introduction to the Production Possibilities Frontier
# Syllabus of Economics/Market and public policy

This page links to Wikipedia entries and other learning materials that are relevant to the list of topics in a module of the Introductory Microeconomics syllabus on the Wikiversity's School of Economics pages.
Wikipedia entries
Other learning materials
# Syllabus of Economics/Market institutions

This page links to Wikipedia entries and other learning materials that are relevant to the list of topics in a module of the Introductory Microeconomics syllabus on the Wikiversity's School of Economics pages.
Wikipedia entries
Other learning materials
# Syllabus of Economics/Scarcity and economic interactions - Q & A
## About this page

This page is a place for people to enter exam questions and answers for a syllabus module that is part of the Introductory Microeconomics syllabus in Wikiversity's School of Economics. If you would like to help with this learning project, you might like to adding questions and answers (or by helping verify existing questions and answers) to the test bank of questions and answers below for this module. Just add the questions and answers to this page. Later, the plan is to convert these questions and answers on some linked pages using the WikiMedia quiz extension. Other ways you could help are by entering links to relevant Wikipedia entries or other useful learning materials into the Introductory Microeconomics syllabus page or by adding questions and answers for the other modules listed on the Introductory Microeconomics syllabus page.
Questions and Answers
What generally drives consumers in economic theory is ___, while what generally drives producers is ___.
A. minimized cost; maximized profit.
B. maximized utility; maximized profit.
C. minimized cost; maximized sales.
D. maximized utility; maximized sales.
ANSWER: B
# Syllabus of Economics/Introduction to labour economics - Q & A
## About this page

This page is a place for people to enter exam questions and answers for the syllabus module "Introduction to economics" that is part of the Introductory Microeconomics syllabus in Wikiversity's School of Economics. If you would like to help with this learning project, you might like to adding questions and answers (or by helping verify existing questions and answers) to the test bank of questions and answers below for this module. Just add the questions and answers to this page. Later, the plan is to convert these questions and answers on some linked pages using the WikiMedia quiz extension. Other ways you could help are by entering links to relevant Wikipedia entries or other useful learning materials into the Introductory Microeconomics syllabus page or by adding questions and answers for the other modules listed on the Introductory Microeconomics syllabus page.
Questions and Answers
# Syllabus of Economics/Market institutions - Q & A
## About this page

This page is a place for people to enter exam questions and answers for the syllabus module "Introduction to economics" that is part of the Introductory Microeconomics syllabus in Wikiversity's School of Economics. If you would like to help with this learning project, you might like to adding questions and answers (or by helping verify existing questions and answers) to the test bank of questions and answers below for this module. Just add the questions and answers to this page. Later, the plan is to convert these questions and answers on some linked pages using the WikiMedia quiz extension. Other ways you could help are by entering links to relevant Wikipedia entries or other useful learning materials into the Introductory Microeconomics syllabus page or by adding questions and answers for the other modules listed on the Introductory Microeconomics syllabus page.
Questions and Answers
# Syllabus of Economics/Introduction to labour economics

This page links to Wikipedia entries and other learning materials that are relevant to the list of topics in a module of the Introductory Microeconomics syllabus on the Wikiversity's School of Economics pages.
Wikipedia entries
Other learning materials
# Syllabus of Economics/Market and public policy - Q & A
## About this page

This page is a place for people to enter exam questions and answers for the syllabus module "Introduction to economics" that is part of the Introductory Microeconomics syllabus in Wikiversity's School of Economics. If you would like to help with this learning project, you might like to adding questions and answers (or by helping verify existing questions and answers) to the test bank of questions and answers below for this module. Just add the questions and answers to this page. Later, the plan is to convert these questions and answers on some linked pages using the WikiMedia quiz extension. Other ways you could help are by entering links to relevant Wikipedia entries or other useful learning materials into the Introductory Microeconomics syllabus page or by adding questions and answers for the other modules listed on the Introductory Microeconomics syllabus page.
Questions and Answers
# Microsoft Office/Word/Customize options and views for documents

This lesson introduces customizing options and views for documents.

## Objectives and Skills

Objectives and skills for the customize options and views for documents portion of Microsoft Word certification include:
* Changing document views, using zoom, customizing the quick access toolbar, customizing the ribbon, splitting the window, adding values to document properties, using show/hide, recording simple macros, assigning shortcut keys, managing macro security
# Microsoft Office/Word/Headers

Upon creating the first numbered page in a header, scroll down to the second (2nd) page and use Microsoft word 2007 Alt+Shift+P and watch your page transform to the APA format. If the Running Head copies the same and you don't want the same Phrase on all pages. Go back to the first page, insert a numbered-page first. Position the page number to your desire, again scroll down to page 2. and insert the header; be sure the first page is checked (every page except the first) the program should direct you to type in the text you wish to use, type in the new text that you want to appear on every page thereafter. Tab over to the far right margin and press the following sequence: Alt+Shift+P. You can be creative, but the command will still be the same.
# Microsoft Office/Word/Navigate through a document

This lesson introduces navigating through a document.

## Objectives and Skills

Objectives and skills for the navigate through a document portion of Microsoft Word certification include:
* Searching for text within document, inserting hyperlinks, creating bookmarks, using Go To

## Readings

* Read Microsoft: Move around in a document using the Navigation pane
# Microsoft Windows/Windows XP

Windows Experience (XP)
Windows XP, has many editions Professional and Home Edition are the main ones. It was released in October 2001.
Built-in User Accounts
Windows XP Home has three built-in user accounts; Administrator, Guest, and SUPPORT_388945a0. Windows XP Professional has three built-in user accounts; Administrator, Guest, and SUPPORT_388945a0. Home Edition's Administrator account is defaultly disabled in the local policy which cannot be changed, you can only access it in Safe Mode. Home Edition's SUPPORT_388945a0 account; is defaultly disabled in the local policy and cannot be access. Professional's user accounts has full access.
Local Security Policy Accounts: Administrator Account Status; is the security policy that Home edition has that restricts the administrator account. It is defaultly disabled. Local Security Policy is only in Professional. You cannot add it. Local Security Policy (secpol.msc) is in Windows XP Professional.
Active Directory Active Directory is used in Windows Server 2003, it is for users and computers on a network. Most schools use active directory for students and staff. Active Directory (AD), can have Group Policies add for groups of users. There is Active Directory in schools. Windows XP Professional and Windows Server 2003 are on the OS built platform.
# Microsoft Office/Word/Format a document

This lesson introduces formatting a document.

## Objectives and Skills

Objectives and skills for the format a document portion of Microsoft Word certification include:
* Modifying page setup, changing document themes, changing document style sets, inserting simple headers and footers, inserting watermarks, inserting page numbers

## Multimedia

* Watch Microsoft: Format a document.
* Watch Microsoft: Add headers, footers, margins, and rulers to a page.
# Microsoft Windows/Active Directory
## Active Directory in Schools
### History

High Schools used to use Apple/Mac(s). Then they upgraded to Windows. Now they have Windows XP Professional, Embeded, 7, 98, Server 2008/2003 and Linux. Linux is for networking classes. Windows Embedded is for Cafe Machines. Windows Server 2003 Enterprise is at the main downtown center. Windows 7 Enterprise is what is being installed on new computers.

##### Active Directory in Schools

Most of each school has active directory on the server. It is connected with an underground trunkline that goes as a Wide Area Network (WAN). Each student and staff member have a Roaming User Profile (RUP) which is stored on the server. Each user can logon a client computer running windows xp professional.
Group Policy Object Editor is where the administrative IT staff secure the computers. They can restrict the start menu, C drive, CMD, more. They force classic start menus on RUP(s). There are different policies for each user on the server.

#### Single Sign-on

Most schools use a single sign-on tool to manage settings and documents. This is for clients and servers. Administrators manage the passwords and the single sign-on. It provides access to Internal Drives, Special start menus that are there, but not apart of (documents and settings) folder.
My Computer
Local C drive has NTFS File System.

### Domain Forests

Students have one. Staff have one. Administrator have one (Built-in accounts).
Local User Profile
Local User Profile (LUP) is a locally stored user profile that was initially stored on a server as a roaming user profile. It has saved profile settings. Everytime a student or staff login to client with roaming user profile their account creates a LUP on the local client.
Quota(s)
Quota(s) are the limits that students and staff get. Some schools allow 20MB disk storage on the network drive. My Documents is where the files are stored. Most school restrict the C drive. My Documents's target is stored on the server under the user account.
Group Policy in Active Directory
Each user is also called a "object". Each object on a server domain can have a group policy set for a group of objects. Group policy is not configured locally most of the time.
Domain Server
The server is the main point of the system. The domain is where the objects are and the Forests connect. Administrative Software Most schools have software for maintance purposes. Bootwiz, SQL2000, Aclient, showname and more.
Rapideploy
Imaging bootworks/RAPIDEPLOY. Version: 6.1.5813.0. Author: Altiris RapiDelpoy. It staff create images of the hard drives and store them on a external HDD. Then they can go to the client and extract the image the HDD. Some images are split into two images.
Rapid Install Package (RIP) Rip(s) are supposed to run Exe(s) they can be created. RIP Conflict editor is an administrative software.

## See Also

Windows Server Administration - Active Directory
# Microsoft Windows/Windows 7

Windows 7 is a personal computer operating system developed by Microsoft.

## Objectives and Skills

Objectives and skills for Windows 7 include:
* Learn about your computer
* Desktop fundamentals
* Programs, files, and folders
* Internet, e‑mail, and networking
* Pictures and games
* Help and support

## Multimedia

* Watch YouTube: Computer Basics - The Operating System.
* Watch YouTube: The Windows 7 Desktop Explained For Dummies.
* Watch YouTube: Learn Basic Computer Skills : Windows Explorer Tutorial.

## Activities

* Complete the tutorial DigitalLearn: Using a PC (Windows 7).
* Complete the tutorial GCFLearnFree: Windows 7.
* Complete the tutorial Microsoft: Windows Basics: All Topics.

## See Also

* Using an Operating System
* Wikipedia: Windows 7
# Microsoft Technology Associate

Microsoft Technology Associate (MTA) was a set of entry-level IT certification exams offered by Microsoft. Exams were available in three different tracks: IT infrastructure, database, and development. Microsoft stopped offering MTA exam vouchers on June 30, 2021. Purchased exam vouchers must be used by June 30, 2022.

## IT Infrastructure Track

* Exam 98-349: Windows Operating System Fundamentals - Retired
* Exam 98-365: Windows Server Administration Fundamentals - Retired
* Exam 98-366: Networking Fundamentals - Retired
* Exam 98-367: Security Fundamentals - Retired
* Exam 98-369: Cloud Fundamentals - Retired

## Database Track

* Exam 98-364: Database Fundamentals - Retired

## Development Track

* Exam 98-361: Software Development Fundamentals - Retired
* Exam 98-362: Windows Development Fundamentals - Retired
* Exam 98-363: Web Development Fundamentals - Retired
* Exam 98-372: Microsoft .NET Fundamentals - Retired
* Exam 98-373: Mobile Development Fundamentals - Retired
* Exam 98-374: Gaming Development Fundamentals - Retired
* Exam 98-375: HTML5 Application Development Fundamentals - Retired
* Exam 98-381: Introduction to Programming Using Python - Retired
* Exam 98-382: Introduction to Programming Using JavaScript - Retired
* Exam 98-383: Introduction to Programming using HTML and CSS - Retired
# System development/Modelling/Concepts/Customer

* Domain:
* Wikipedia

## Properties

| Sequence | Property name | Datamodel | Datatype | Definition/ example | Dutch | French | German | Spanish |
| 1 | | | | | | | | |
| 2 | | | | | | | | |
# System development/Modelling/Concepts/Assessor

* question: how do you call someone who checks whether a task is performed? can you call this person an assessor?
* https://en.wiktionary.org/wiki/assessor
# System development/Modelling/Concepts/Call

* index:
* wikipedia

## Properties

| Sequence | Property name | Datamodel | Datatype | Definition/ example | Dutch | French | German | Spanish |
| 1 | Call number | CallNumber | sequence | | | | | |
| 2 | | | | | | | | |
# System development/Modelling/Concepts/Complaint

index: complaint, complaints

## Attributes

* Inquire
* Description
# System development/Modelling/Concepts/Contract

* Domain: contract management
* Wikipedia: https://simple.wikipedia.org/wiki/Contract
A contract is a legal agreement.

## Contract timeline

Remark: you also have contracts who have a montly or yearly notice period. You can add an attribute notify me on date dd/mm/yyyy.

## Attributes

| Sequence | Property name | Datamodel | Datatype | Dutch |
| 1 | Contract ID | ContractID | Sequence | |
| 2 | Description | Description | Text | Omschrijving |
| 3 | File | File | File | Bestand |
| 4 | Contractparty | ContractParty | Reference to Organization | |
| 5 | Start date | StartDate | Date | Startdatum |
| 6 | End date | EndDate | Date | Einddatum |
| 7 | Notice Period | NoticePeriod | Whole number | Opzegtermijn |

## Fact types

* A contract is concluded between contracting parties (Is this sentence correct English?).
# Programming Challenges

This learning project provides resources for programming challenges.

## Individual Programming Challenges

Only resourses which do not require registration are listed.
* CodeChef
* Codeforces
* CodePen
* Coderbyte
* CodinGame
* Edabit
* Engage CSEdu: Materials
* FreeCodeCamp
* InterviewBit
* GitHub: Karan Projects
* LeetCode
* Practice Python
* Project Euler
* UVA Online Judge
* W3Resource: Python Exercises

## Competitive Programming Challenges

As listed on Wikipedia: Competitive programming:
* ACM-ICPC
* ACSL
* CodeChef
* Codeforces
* Codewars
* Facebook Hacker Cup
* Google Code Jam
* HackerRank
* IEEEXtreme Programming Competition
* International Olympiad in Informatics
* Topcoder Open
* Yandex

## See Also

* Computer Programming
* Wikipedia: Competitive programming
# Professor Knopfloch/Intelligence development/Exercise

At the begin of the university studies, Professor Knopfloch is double as clever as the students. Within one year of studies, the students are getting more clever by a percentage of $10\%$. Unfortunately, the professor looses a percentage of $10\%$ of his cleverness each year.
* Show that after three years of studies, the professor is still more clever that his students.
* Show that after four years of studies, the students are more clever than the professor.
# Program/Two registers/Bijective mapping/Exercise

We consider a computer with only two memory units, each can represent a natural number. At the start of every program (a sequence of commands), the initial entries are $(0,0)$. The computer can empty a memory unit, it can increase a memory unit by $1$, it can jump to another command (unconditional Goto) and it can compare the two entries of the two memory units. Moreover, it can jump to another command in case the comparing condition is fulfilled (conditional Goto). There is a printing command which prints the entries at the moment. Write a computer-program such that every pair $(n,m)\in \mathbb {N} ^{2}$ is printed exactly once.
# Profit

Profit relates to business and earning money. This area of this site is meant to help teach about profit in the realm of business. Organizing learning, teaching, and research related to the idea of profit can be organized here. In business, profit occurs when you earn more money than you spend to build your business.

## Readings
### Wikipedia

| Profit (accounting) Gross profit Profit margin Income statement Earnings before interest, taxes, depreciation, and amortization Earnings before interest and taxes Earnings before taxes Dividend | Dividend payout ratio Net income per employee Undistributed profits tax Sales (accounting) Earnings before interest and taxes Net profit Profit (economics) Productivity Nonprofit organization |

## Discussion questions

* How can profit drive success business?
* Is profit more important than a purposeful mission in business?
* What are the advantages and disadvantages of running a for profit or not for profit business?
* How do benefit corporations approach the need for profit?