OpenLLM-France/wikimedia huggingface dataset:
# Vector space/Finitely generated/Length of every basis/Fact/Proof

Let ${\mathfrak {b}}=b_{1},\ldots ,b_{n}$ and ${\mathfrak {u}}=u_{1},\ldots ,u_{k}$ denote two bases of $V$. According to the basis exchange theorem, applied to the basis ${\mathfrak {b}}$ and the linearly independent family ${\mathfrak {u}}$, we obtain $k\leq n$. When we apply the theorem with roles reversed, we get $n\leq k$, thus $n=k$.
# Vector space/General distributivity law/Exercise

Let $V$ be a vector space over a field $K$. Let $s_{1},\ldots ,s_{k}\in K$ and $v_{1},\ldots ,v_{n}\in V$. Show
    ${\left(\sum _{i=1}^{k}s_{i}\right)}\cdot {\left(\sum _{j=1}^{n}v_{j}\right)}=\sum _{1\leq i\leq k,\,1\leq j\leq n}s_{i}\cdot v_{j}\,.$
# Vector space/Generating subspace/Remove representable vector/Exercise

Let $K$ be a field, and let $V$ be a $K$-vector space. Let $v_{i}$, $i\in I$, be a family of vectors in $V$, and let $w\in V$ be another vector. Assume that the family
    $w,v_{i},i\in I,$
is a system of generators of $V$, and that $w$ is a linear combination of the $v_{i}$, $i\in I$. Prove that also $v_{i}$, $i\in I$, is a system of generators of $V$.
# Vector space/Generating system/Inclusion/Exercise

Let $K$ be a field, and let $V$ be a $K$-vector space. Let $v_{i}$, $i\in I$, be a family of vectors in $V$ and $w_{j}$, $j\in J$, another family of vectors in $V$. Then, for the spanned linear subspaces, the inclusion $\langle v_{i},\,i\in I\rangle \subseteq \langle w_{j},\,j\in J\rangle$ holds, if and only if $v_{i}\in \langle w_{j},\,j\in J\rangle$ holds for all $i\in I$.
# Vector space/Generating system and spanned subspace/Fact/Proof/Exercise

Let $K$ be a field, and let $V$ be a $K$-vector space. Show that the following statements hold.
* For a family $v_{i}$, $i\in I$, of elements in $V$, linear span is a linear subspace of $V$.
* The family $v_{i}$, $i\in I$, is a spanning system of $V$ if and only if
    $\langle v_{i},\,i\in I\rangle =V\,.$
# Vector space/Generating system/Definition

Let $K$ be a field, and let $V$ be a $K$-vector space. A family $v_{i}\in V$, $i\in I$, is called a generating system (or spanning system) of $V$, if every vector $v\in V$ can be written as
    $v=\sum _{j\in J}s_{j}v_{j}\,,$
with a finite subfamily $J\subseteq I$, and with $s_{j}\in K$.
# Vector space/Generating system and spanned subspace/Fact

Let $K$ be a field, and let $V$ be a $K$-vector space. Then the following statements hold.
* For a family $v_{i}$, $i\in I$, of elements in $V$, the linear span is a linear subspace of $V$.
* The family $v_{i}$, $i\in I$, is a spanning system of $V$, if and only if
    $\langle v_{i},\,i\in I\rangle =V\,.$
# The Web Economy/06
## Community Is King

This is a lesson part of the module The Web Economy out of the Open Source ERP/Executive Masters course conducted by a private university.

## Topics

* Compiere enjoyed a growing community in 2003 that puts them as a defacto leader in Open Source ERP space. But in 2006 they received external funding about USD6 million and began to close up their source and alienate their community of users. The community forked as another project called ADempiere and I was nominated as its leader. I learnt many things since then especially the rule that Community is King.
* Even though Yahoo! was the first-mover in the search engine territory, today it is taken over and threatened by Google. But when Google took in funds and go public, it suffers problems that often affect large commercial giants.
* Open Source is now used to gain popularity and hold on a community. It seems to be a marketing ploy to gain following and then close off like a wolf shedding its sheep's clothing to rake in easy profits. Good example is Mambo that forked to Joomla, besides the Compiere/ADempiere later case.
* With such high growth and fast saturation of many fads, the Internet still offers blue oceans for new ideas that are real and possess leadership for the world.

### Discussion

After some research, have a discussion on the following, safe as sub-page and link it under Student Notes.
* Why do you think Google can easily beat Yahoo!?
* What did Google did that Yahoo! did not?
* Do you think there will be another dotcom that can beat Google in future?
* Why is Google losing trust after it went public and commercialised?
* Why does Mambo's community fork to form Joomla? Also ADempiere.
* What does the majority of the community wants out of a dotcom or site?
* Who is actually King, the site product or the community?
* Discuss the last statement in the topics above.

### Activities

* Publish your works in an attractive manner in your user page, stating your own views and findings providing links to your sources. Use the talk page here to score marks.
* Create or edit sub-pages of course materials within wikiversity.
* Discuss in the forum (link shall be provided) by offering your ideas and answering or comment on others' postings.
# The Web Economy/14
## Critical Tools And Skills

This is a lesson part of the module The Web Economy out of the Open Source ERP/Executive Diploma course conducted by a private university.

## Topics

* Today's knowledge worker in a community open source must know certain basic tools and skills to perform efficiently
* Among the further tools they have to handle are Chatroom client, Sourceforge repository, and Wikimedia.
* Skills involve soft skills such as been able to follow forum threads and response to them, and editing wikis.
* In an Open Source Software project, the contributors have to possess a high level of programming ability and be familiar with the subject matter.

### Assignment Tasks

* Create our own user account in this Wikiversity project. Take a tour here if you are a newbie.
* Research other user pages and dress up your own user page with relevant information about yourself and what you do.
* Create also an account in the the ADempiere Open Source ERP project wiki ADempiere Wiki and introduce yourself in the Community Portal.
* Create your discussion pages as sub pages in the wikiversity project. Create your classroom page as Open Source ERP/Classroom/09/1 etc.
* Try to edit some of the ADempiere Wiki such as typo and grammar mistakes.
* Comment in the talk pages on any point that is fitting. Remember to sign your name.
* Create a user account in http://sf.net/
* Browse through the trackers of http://sf.net/projects/adempiere
* How is open source software contribution different from a Wikipedian article contribution?

### Activities

* Publish your works in an attractive manner in your user page, stating your own views and findings providing links to your sources. Use the talk page here to score marks.
* Create or edit sub-pages of course materials within wikiversity.
* Discuss in the forum (link shall be provided) by offering your ideas and answering or comment on others' postings.
# The Web Economy/07
## Email and Mailing List

This is a lesson part of the module The Web Economy out of the Open Source ERP/Executive Diploma course conducted by a private university.

## Topics

* Email is the killer application. It is what everyone is using. It is a must and it becomes the Single Window that all users looks at each time they logon to the Web.
* By suscribing to maillists or trackers you can stream all needed activities into your single mailbox without visiting back those websites. You also need not remember every site to visit again.

### Workshop

* Suscribe to SourceForge ADempiere project CVSLogs tracker
* Monitor its forums

### Activities

* Publish your works in an attractive manner in your user page, stating your own views and findings providing links to your sources. Use the talk page here to score marks.
* Create or edit sub-pages of course materials within wikiversity.
* Discuss in the forum (link shall be provided) by offering your ideas and answering or comment on others' postings.
# The Web Economy/09
## Second Life

This is a lesson part of the module The Web Economy out of the Open Source ERP/Executive Diploma course conducted by a private university.

## Topics

* There is a website that offers Second Life for you to build a complete virtual life in a virtual world that tries to be as real as the real world, and of course it failed.
* It tries to get everyone into the same room and that is what Open Source does for software.
* Today you can start creating a new virtual environment just be merely visiting and commenting on blogs or forums that can backlink to you. By having your name occuring more often in the web will get it showing up more in the search results. And that is all free. All it need is our time and passion.
* Interest is built through conversation. That is the viral cause for you to keep returning with a passion.
* As you build your own content and presence on the web, you are building your own virtual credit account. More people will come to know you and your interests and perhaps some small fortune in the not so distant future.
* This carries alot of benefit such as increase in knowledge, networking and resources to depend on as well as market oppurtunities, all via the web.

### Discussion

* Look for forums or blogs of your choice or related topics.
* Draft some answers or comments that are positive and generate goodwill.
* Keep track and see if it solicit any response from others.
* Look for examples of single individuals with just simple publishing acts but are catapulted suddenly to fame and fortune.

### Activities

* Publish your works in an attractive manner in your user page, stating your own views and findings providing links to your sources. Use the talk page here to score marks.
* Create or edit sub-pages of course materials within wikiversity.
* Discuss in the forum (link shall be provided) by offering your ideas and answering or comment on others' postings.
# The Web Economy/12
## Bazaar Spirit

This is a lesson part of the module The Web Economy out of the Open Source ERP/Executive Diploma course conducted by a private university.

## Topics

* Eric Raymond wrote about The Cathedral and The Bazaar. He points out 2 different models to modern software development.
* Since then it is been greatly refered to as a definition of the merits of Open Source development.
* If you do not contribute, someone else will.

### Discussion

* Read and discuss the article concerning the Bazaar model of software development.
* Research whether Linux development today still uses the model and what are its challenges and constraints.
* If you have a chance to do what Linus did back then, would you give it away? What would be your concerns?
* What if you have a big company with alot of costs and have produced a perfect software. Would you give your software away? What would be your concerns now?

### Activities

* Publish your works in an attractive manner in your user page, stating your own views and findings providing links to your sources. Use the talk page here to score marks.
* Create or edit sub-pages of course materials within wikiversity.
* Discuss in the forum (link shall be provided) by offering your ideas and answering or comment on others' postings.
# The Web Economy/15
## Levels of Participation

This is a lesson part of the module The Web Economy out of the Open Source ERP/Executive Diploma course conducted by a private university.

## Topics

* There are different type of user participation in any online project.
* They are
** Lurkers - who only reads and hardly said a word or contribute anything. They comprise a high percentage of visitors and contribute to the hitrate.
** Trolls - who lurks but occasionaly fire up.
** Newbies - who are new and would try to ask around and get what they want.
** Geeks - those who are experts and may be busy or impatient to answer too many questions. But they are the most helpful in a forum or project
** Poison - those who may divert the attention of a project with drawn out arguments or debates.
* Debian was a highly succesful project with 1,000 developers and faces issues giving rise to forks such as Ubuntu.
* Information is free, people are not, contributors are priceless.
** Web Economy for FOSS is a new medium and paradigm that many do not know how to fit in. For example in the old economy, people hide or sell information. However here we cannot do that and regard information as free. We can only sell people's time as a service and it is charged in dollars for man-hours or man-days.
** However there are those who still manipulate information such as delaying it unless the users pay and separate such users as to time phased consumers where those who pay shall get the information earlier.
** The Web perpetually threatens information hiding as another party can or will expose earlier or easier information to forge ahead. Therefore any profiteering model has to rely on top of the rule that information must be free.

### Assignment Tasks

* See if you can identify any such character in ADempiere SourceForge project.
* What are the reasons for even taking part in an FOSS project in the first place?.
* Find out how best to convert lurkers to more active users.
* Investigate what is happening with Debian and its forks, and if there are more recent ideas on better community management.
* When you given free information in forums, sometimes users still bother your time privately and refuse to go through public forums. What should you do?

### Activities

* Publish your works in an attractive manner in your user page, stating your own views and findings providing links to your sources. Use the talk page here to score marks.
* Create or edit sub-pages of course materials within wikiversity.
* Discuss in the forum (link shall be provided) by offering your ideas and answering or comment on others' postings.
# The Web Economy/08
## Forums and Blogs

This is a lesson part of the module The Web Economy out of the Open Source ERP/Executive Diploma course conducted by a private university.

## Topics

* If things are not said in a forum, then it is not considered said at all. Forums play an important role in putting all discussions in one place and public. For Open Source, forums are vital.
* Blogs or social sites activity can segregate online activity into a more focused and personalised structure.
* However social sites also allow segregation where certain members kept to their own culture and norm without interfacing with anyone else.
* Just like in olden days, the marketplace or town hall is where people congregate and important decisions made, today it is happening in forums and blogs.
* Linux was created when its creator Linus Torvalds submitted to a mailing list his first code contributions. Forums began to spread the word in a viral manner.
* When ADempiere was first discussed in red1.org forum it attracted more than 500 visitors a day and important decisions were made there.

### Assignment & Discussion

* Suscribe to popular social sites such as FaceBook and BlogSpot. Think about content that you like to share.
* Create your own Wiki User page. Focus on your interests.
* Link your online assets to your User Page.
* Track and monitor the activity through your email box.
* How much are cultural differences affecting the way you interact with strangers on the Web?

### Activities

* Publish your works in an attractive manner in your user page, stating your own views and findings providing links to your sources. Use the talk page here to score marks.
* Create or edit sub-pages of course materials within wikiversity.
* Discuss in the forum (link shall be provided) by offering your ideas and answering or comment on others' postings.
# The Web Economy/10
## History of Open Source

This is a lesson part of the module The Web Economy out of the Open Source ERP/Executive Diploma course conducted by a private university.

## Topics

* Open Source was the original way software was written and shared among university students and professionals.
* It was then closed by commercial vendors, forcing Richard Stallman to start the Free Software movement.
* Open Source has evolved and mature with different players and philosophies.
* This fine line between the two looks like a long religious one. Even the combination acronym FOSS that stands for Free and Open Source Software is not accepted by Stallman.

### Discussion

* Research on the statement that software was originally free.
* How does such software companies make money back then?
* What did Richard Stallman fight for and how is it different from Open Source?
* How is Microsoft working with Open Source?.

### Activities

* Publish your works in an attractive manner in your user page, stating your own views and findings providing links to your sources. Use the talk page here to score marks.
* Create or edit sub-pages of course materials within wikiversity.
* Discuss in the forum (link shall be provided) by offering your ideas and answering or comment on others' postings.
# The Web Economy/11
## Birth of Linux

This is a lesson part of the module The Web Economy out of the Open Source ERP/Executive Diploma course conducted by a private university.

## Topics

* Andrew Tanenbaum created a classroom version of Unix, called Minix to teach his students
* Linus Torvalds, a student at that time, improved it and called it Freax.
* An ISP operator in Germany store it so that more can access it and called it Linux.
* Linux became very successful and Linus was shot to fame. Today Linux is growing too fast. However Prof Tanenbaum has issues with how Linux is been hailed.

### Discussion

* Go through and discuss the debate here.
* What are the basic points of contention between them?
* How has others commercialise Linux?
* How would you capitalise on Linux?
* What are the famous mantras of Linus and what do they mean in Open Source development?

### Activities

* Publish your works in an attractive manner in your user page, stating your own views and findings providing links to your sources. Use the talk page here to score marks.
* Create or edit sub-pages of course materials within wikiversity.
* Discuss in the forum (link shall be provided) by offering your ideas and answering or comment on others' postings.
# The Web Economy/13
## MS vs The World

This is a lesson part of the module The Web Economy out of the Open Source ERP/Executive Diploma course conducted by a private university.

## Topics

* Many see Microsoft business model of swallowing other competitors as evil. The major weapon that MS uses to built its wealth is the patents it holds over its Windows Operating System and the Office tools.
* MS is now threatened by Linux and even so by the recent explosive Google. It attempts to slow the imbalance by attempting to buy up Yahoo! Inc.
* Sun produces Java that is very popular but wasn't open source until lately when it is suffering a downfall.
* IBM succesfully invest more than a billion USD per year in Linux and Apache and derive more in profit back.
* Freebies and Open Source are disruptive forces that brings a net result of vast advancement and quantum leaps to the market.

### Discussion

* What are Microsoft good and bad points?
* How does it confronts Open Source?
* What are the new disruptive technologies out there that are Open Source?
* What do you predict would happen and who will survive? Why?
* Should there be only free software and no proprietary ones?

### Activities

* Publish your works in an attractive manner in your user page, stating your own views and findings providing links to your sources. Use the talk page here to score marks.
* Create or edit sub-pages of course materials within wikiversity.
* Discuss in the forum (link shall be provided) by offering your ideas and answering or comment on others' postings.
# Woodworking/Tools
## Hand tools
### Hand saw

A hand saw is a tool used to cut wood into different shapes by hand.

### Hammer

A hammer is a used to drive nails into wood, to shape metal and to destroy objects.

### Screwdriver

A screwdriver is a tool for screwing and unscrewing screws.

### Spanner

A spanner is a tool to tie and untie nuts and bolts.

### Pliers

Pliers are used to bending and compressing materials.

### Hand plane

A hand plane is a used for shaping wood.

### Try square

A try square is a used to draw 90 degree lines on wood.

### Bevel gauge

A bevel gauge is a used to draw angles on wood.

### Speed square

A speed square is a used to mark and draw angles on wood.

### Combination square

A combination square is a tool to draw angles and to measuring parts on wood.

### Clamp

A clamp is used to hold or secure objects tightly together to prevent movement.

## Power tools
### Circular saw

A circular saw is used to cut wood and depths of wood.

### Drill

A drill is a used to drill holes.

## Other
### Drill bit

Drill bits used to drill holes in different sizes.

## More information

* Woodworking tools (Wikipedia)
* Woodworking hand tools (Wikipedia)
** Hand saw (Wikipedia)
** Hammer (Wikipedia)
** Screwdriver (Wikipedia)
** Spanner (Wikipedia)
** Pliers (Wikipedia)
** Hand plane (Wikipedia)
** Try square (Wikipedia)
** Bevel gauge (Wikipedia)
** Speed square (Wikipedia)
** Combination square (Wikipedia)
** Clamp (Wikipedia)
* Woodworking hand-held power tools (Wikipedia)
** Circular saw (Wikipedia)
** Drill (Wikipedia)
* Drill bit (Wikipedia)
# Woodworking/Wood
## Softwood - hardwood
### Softwood

* Pine
* Hickory
* Beech
* Birch
* Cedar
* Redwood
* Hemlock
* Fir
* Spruce

### Hardwood

* Oak
* Maple
* Mahogany
* Cherry
* Rosewood
* Teak

## Indoor

* Jarrah
* Tasmanian Oak
* Karri
* Teak
* Blackbutt
* Cypress Pine
* Spotted Gum
* Pacific Maple
* Brushbox
* Western Red Cedar
* Baltic Pine
* Radiata Pine
* Sydney Blue Gum
* Hoop Pine

## Exterior

* Merbau
* Teak
* Jarrah
* Tallowwood
* Cypress Pine
* Oregon
* Treated Pine
* Western Red Cedar
* Balau
* Blackbutt

## More information

* Wood (Wikipedia)
* Softwood (Wikipedia)
* Hardwood (Wikipedia)
* List of woods (Wikipedia)
# WordPress

* Category: CMS
* Learning community: Making beautiful websites
# WordPress/Functionality
## Index

* users
# WordPress/Learning WordPress

* You can install WordPress on you PC, you can also find a provider. See https://wordpress.org/hosting.
* http://codex.wordpress.org/First_Steps_With_WordPress
# WordPress/Links

On this page you can find useful links regarding WordPress.
* how can you change the layout of a WordPress site? http://codex.wordpress.org/Blog_Design_and_Layout
* http://codex.wordpress.org/
* http://buddypress.org/
# Wool

Wool is a protein fiber. It is crimped and elastic. Crimped makes wool bulky and helps it to retain heat, it also absorbs moisture and sound because it is hallow. Wool is normally creamy white in colour, but it can also be black, brown, or silver in colour. It is also hyperallergenic (in other words it causes few allergies in human beings). The main source of wool is sheep, the wool yielding animal bears a thick coat of hair on its body. The hair traps a lot of air in it, since air is a poor conductor of heat, it keeps the animal worm and dry allowing it to live in cold and harsh climates.The hairy skin of the sheep has two types of fibers: 1) The coarse beard hair 2) The fine soft hair close to the skin. The fine hair provides the fibers for making woolen clothes and the coarse hair provides wool for making carpets etc.
Wool yielding animals: Some animals other than the sheep also produce wool. They are Yalk, its wool is common in Tibet and Ladakh. Angora goat, it is found in hilly regions such as Jammu and Kashmir, the wool obtained from it is called as angora wool. Kashmiri goat, the wool obtained from it is very soft and it is used in weaving fine shawls, these shawls are popular as pashmina shawls in India. Camel, the fur on the body of the camel is also used as wool. Llama and Alapaca, they found in south america and they produce wool.