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“Xả” chính là buông  xả,  trí  tuệ  đích  thực. Tại  sao  người  thế  gian  không  chịu  buông xả vậy? Vì không có trí tuệ. Họ vẫn cứ là tự tư tự lợi,  cho nên họ không thể buông xả. Trí tuệ đích thực là cái có  được từ tâm thanh tịnh. Trí tuệ mở rồi thì pháp thế xuất thế gian tất cả thông đạt viên mãn.   Các  bạn  xem  trong  “Ảnh  Trần  Hồi  Ức  Lục”, Pháp  sư  Đàm Hư kể về Pháp sư Phơi Đèn Cầy. Bạn xem, vị pháp sư  này  không  biết  chữ, chưa từng đi học, làm  hương đăng ở  trong  tự  miếu. Ông  là  người  thành  thật, thường  hay  bị  người lừa gạt, đạo hữu đồng tu trêu chọc ông, họ nói với ông:  “Thầy Hương Đăng, khoảng tháng sáu, thầy thấy mọi  người đều phơi quần áo, đèn cầy của thầy cũng nên đem ra  phơi đi, không phơi sẽ bị mốc đấy” . Ông liền đem hết đèn  cầy ra ngoài sân để phơi nên đều bị chảy nước hết, ông ngu  si đến như vậy. Thời khóa tối, khi thắp đèn cầy thì chỉ có  tim đèn, còn sáp thì không còn nữa. Thầy [https://en.wiktionary.org/wiki/Duy-na Duy-na] nhìn thấy  rất  khó chịu,  nói: “Ông làm trò gì vậy?”.  “Họ bảo tôi đi  phơi đèn  cầy, tôi bèn phơi. Phơi xong thì biến thàn h như  thế  này  đây”, thầy  Hương  Đăng  trả  lời.  Sau  khi  khóa  tối  xong, thầy  Duy-na  bèn  đem  sự  việc  trình  với  Lão  hòa  thượng và nói không nên để ông làm hương đăng nữa. Lão  hòa thượng thương xót ông, người thành thật, bèn gọi ông  lên  mà  bảo  rằng:  “Chú  không  nên  làm  hương  đăng  nữa, chú đến Chùa Dục Vương để lạy xá lợi của Phật Thích Ca  Mâu  Ni, một  ngày  chú  lạy  3.000  lạy” .  Ông  rất  thật  thà,  nghe lời đi tu khổ hạnh, mỗi ngày lạy 3.000 lạy, lạy được  ba  năm  ông  liền  khai  ngộ. Ông  có  thể  làm  thơ, làm  kệ, giảng Kinh thuyết pháp, mặc dù ông chưa hề học qua. Tại  sao ông làm được vậy? Vì trí tuệ mở rồi, giống như Đại Sư  Huệ Năng vậy, bởi vì ông không phải học hành nhồi nhét, ông  không  phải  do  người  khác  dạy, cho  nên  đến  lúc  này  học  cái  gì  cũng  nhanh  chóng  vì  chướng  ngại  không  còn  nữa. Chúng ta hiện nay học cái gì cũng khó khăn, do trùng  trùng chướng ngại, trí tuệ không mở, tâm không thanh tịnh,  đạo lý là như vậy. Ông, con người thành thật này tâm thanh  tịnh.  Khó  khăn  của  ông  chúng  ta  hiện  nay  hiểu  rõ, ông  không có phiền não của người bình thường, ông chỉ có vô  minh che đậy chính mình. Lão hòa thượng dạy ông phương  pháp này hay. Ông một lòng một dạ đi lạy Phật, mỗi  ngày  lạy  3.000  lạy, ý  niệm  gì  cũng  không  còn. Lạy  Phật  là  tu  định, tu  tâm  thanh  tịnh, tu  tâm  chân  thành.  Một  khi  khai  ngộ thì pháp thế xuất thế gian tất cả đều thông đạt. Cho nên có huệ mới có thể xả, không có huệ thì không chịu xả. Để biết thêm chi tiết gỗ huyết rồng là gì, xem tại [https://phapduyen.com/danh-muc/chuoi-vong/hat-go/huyet-rong-huyet-long/ https://phapduyen.com/danh-muc/chuoi-vong/hat-go/huyet-rong-huyet-long/]
+
{{Notebox|'''Account creation disabled due to spam. To create an account...  ''' [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 20:36, 28 November 2017 (UTC)|Email me at "alec" the usual email symbol here, then "unifiedmathematics.com" if you want one, I'll create it and email you back with credentials. The accounts created and sifting the spam - even with my Quick-Block modifications is too great!}}
 +
<div style="float:right;">__TOC__</div>
 +
==Making full use of the site==
 +
'''The best interface by far is the search box''' this project is intended to create a ''queriable resource'' for looking up things and learning from them (and those pages will link to related and required topics), for some examples try searching for the following:
 +
* Norm
 +
* Inner product
 +
* Category
 +
* Linear map
 +
* Dynkin system
 +
Some pages may be rather sparse, containing little more than a definition, but there is always some information even if it is minimal. This site follows the doctrines of [[Doctrine of monotonic definition|monotonic definition]] and of [[Doctrine of least surprise|least surprise]]. For example the term "ring without unity" violates monotonic definition, we only ever ''add'' properties. And the notation [[R+ (notation)|{{M|\mathbb{R}_+}}]] is ambiguous and can violate the doctrine of least surprise.
 +
 
 +
'''This site goes through great effort to use a consistent, natural and unambiguous notation for everything, it also aims to document alternate notations'''
 +
 
 +
This site uses MathJax for mathematical rendering, which uses vector fonts to create sharp and all round superb renderings of mathematical equations. This site also uses XyJax for diagrams, (see [[Xypic]] for an example) allowing large diagrams, state machines and so forth to be rendered.
 +
===First years===
 +
Topics which first years are likely to cover (for example [[Sequence|sequences]], [[equivalence relation|equivalence relations]] and so forth) are so called "first-year friendly" pages. This means they are written verbosely and with plenty of explanation in order help those new to the topic. A good example is the [[Limit (sequence)|limit of a sequence]] page which gives two almost identical definitions, the experienced mathematician will both not care about the difference and also not need help interpreting the definition, the newcomer will need help, so very clear hand-holding proofs are presented (in a collapsed section, click expand to show) as well as an extended discussion as to why the definition works, including an animated diagram (albeit a low-res capture from a graphic calculator (at the time of writing))
 +
* The category [[:Category:First-year friendly]] contains {{PAGESINCATEGORY:First-year friendly|pages}} pages, this number is lower than the actual number as not all first-year friendly pages have been categorised. If you're a first year, and you search for stuff, it should be friendly.  
 +
===Undergraduates===
 +
This resource is useful to check definitions and theorem statements, to see discussion of notation, and to understand dependencies of a definition, for example if you encounter a [[Dynkin system]] you can see other names for it, but also 2 distinct definitions (with references) which are proved equivalent. Thus saving you the work of doing it yourself
 +
===Postgraduates===
 +
Definitions and theorem statements are always at the top of the page and not verbose, describing the conditions followed by the name of the object or outcome of the theorem. It will be very useful as a "refresher" or checking terminology, however it may not contain some of the rare material you look for. Feel free to request material or add to the project.
 +
 
 +
==Lists of covered items==
 +
(All the following statistics are as of {{CURRENTDAYNAME}}, {{CURRENTDAY}}/{{CURRENTMONTHABBREV}}/{{CURRENTYEAR}} at {{CURRENTTIME}})
 +
* There are {{NUMBEROFPAGES}} pages in total
 +
* There are {{NUMBEROFARTICLES}} pages in the main namespace that are counted as articles (I must find out what qualifies as an article)
 +
* [[:Category:All Definitions|All definitions]] - contains {{PAGESINCATEGORY:All Definitions|pages}} pages (across {{PAGESINCATEGORY:All Definitions|subcats}} subcategories)
 +
* [[:Category:Definitions|Definitions (mathematics)]] - contains {{PAGESINCATEGORY:Definitions|pages}} pages (across {{PAGESINCATEGORY:Definitions|subcats}} subcategories)
 +
* [[:Category:CS Definitions|Computer science definitions]] - {{PAGESINCATEGORY:CS Definitions|pages}} pages (across {{PAGESINCATEGORY:CS Definitions|subcats}} subcategories)
 +
** '''Note: ''' it's hard to tell just what is CS and what is mathematics (these get quite blurred) so CS usually refers to the things which are to do with computers, and was created to contains things like [[register based computing machine]]
 +
* [[:Category:Theorems|Theorems]] - containing {{PAGESINCATEGORY:Theorems|pages}} (across {{PAGESINCATEGORY:Theorems|subcats}} subcategories) (this is difficult to count, see [[:Category:Theorems, lemmas and corollaries]] for more, there are many more, some trivial and not worthy of their own page)
 +
Slightly related is the [[:Category:Exemplary pages|category of exemplary pages]] (containing {{PAGESINCATEGORY:Exemplary pages|pages}} pages), which showcases the best pages of this site.  
 +
 
 +
In the spirit of openness there is also the [[:Category:Dire pages|category of dire pages]] (containing {{PAGESINCATEGORY:Dire pages|pages}} pages), which contains pages that are not short, but woefully incomplete and in dire need of content.
 +
 
 +
==[[:Category:Index|Index category]]==
 +
This category contains indexing pages, these are used for things like notation, operators, structures and objects, so forth. This project is always changing, if you make particular use of something or think the current way is good, please comment on the appropriate talk page.
 +
* [[Index of notation]]
 +
==Mathematical subject index==
 +
(Note, if a link is read, it does '''not''' mean this site doesn't cover the subject, it just means that there is no introductory page to the subject
 +
{{:Site:Mathematical subject index/Index}}
 +
 
 +
=OLD STUFF=
 +
===Old list of "areas"===
 +
* [[Topology]]
 +
* [[Linear Algebra]]
 +
* [[Set Theory]]
 +
* [[Differential Geometry]]
 +
* [[Abstract Algebra]]
 +
* [[Measure Theory]]
 +
* [[Manifolds]]
 +
* [[Notation]]
 +
 
 +
==Commonly needed things==
 +
* [[:Category:Shorthands|Shorthands]]
 +
* [[:Category:Definitions|Definitions]]
 +
* [[:Category:Theorems|Theorems]]
 +
* [[:Category:Subjects|Subjects]]
 +
* [[:Category:Motivations|Motivations]]
 +
* [[Special:AllPages|All pages]]
 +
* [[Useful inequalities]]
 +
* [[Index of notation]]
 +
* [[Index of terms]]
 +
 
 +
==Good (finished) pages==
 +
*[[Compactness]]
 +
*[[Topology]] - [[Motivation for topology]] - [[Continuity definitions are equivalent]]
 +
 
 +
==Editing tips==
 +
* [[Editing guide]]

Revision as of 03:04, 2 December 2017

Account creation disabled due to spam. To create an account... Alec (talk) 20:36, 28 November 2017 (UTC)
Email me at "alec" the usual email symbol here, then "unifiedmathematics.com" if you want one, I'll create it and email you back with credentials. The accounts created and sifting the spam - even with my Quick-Block modifications is too great!

Making full use of the site

The best interface by far is the search box this project is intended to create a queriable resource for looking up things and learning from them (and those pages will link to related and required topics), for some examples try searching for the following:

  • Norm
  • Inner product
  • Category
  • Linear map
  • Dynkin system

Some pages may be rather sparse, containing little more than a definition, but there is always some information even if it is minimal. This site follows the doctrines of monotonic definition and of least surprise. For example the term "ring without unity" violates monotonic definition, we only ever add properties. And the notation [ilmath]\mathbb{R}_+[/ilmath] is ambiguous and can violate the doctrine of least surprise.

This site goes through great effort to use a consistent, natural and unambiguous notation for everything, it also aims to document alternate notations

This site uses MathJax for mathematical rendering, which uses vector fonts to create sharp and all round superb renderings of mathematical equations. This site also uses XyJax for diagrams, (see Xypic for an example) allowing large diagrams, state machines and so forth to be rendered.

First years

Topics which first years are likely to cover (for example sequences, equivalence relations and so forth) are so called "first-year friendly" pages. This means they are written verbosely and with plenty of explanation in order help those new to the topic. A good example is the limit of a sequence page which gives two almost identical definitions, the experienced mathematician will both not care about the difference and also not need help interpreting the definition, the newcomer will need help, so very clear hand-holding proofs are presented (in a collapsed section, click expand to show) as well as an extended discussion as to why the definition works, including an animated diagram (albeit a low-res capture from a graphic calculator (at the time of writing))

  • The category Category:First-year friendly contains 18 pages, this number is lower than the actual number as not all first-year friendly pages have been categorised. If you're a first year, and you search for stuff, it should be friendly.

Undergraduates

This resource is useful to check definitions and theorem statements, to see discussion of notation, and to understand dependencies of a definition, for example if you encounter a Dynkin system you can see other names for it, but also 2 distinct definitions (with references) which are proved equivalent. Thus saving you the work of doing it yourself

Postgraduates

Definitions and theorem statements are always at the top of the page and not verbose, describing the conditions followed by the name of the object or outcome of the theorem. It will be very useful as a "refresher" or checking terminology, however it may not contain some of the rare material you look for. Feel free to request material or add to the project.

Lists of covered items

(All the following statistics are as of Friday, 29/Mar/2024 at 13:37)

  • There are 2,259 pages in total
  • There are 1,077 pages in the main namespace that are counted as articles (I must find out what qualifies as an article)
  • All definitions - contains 838 pages (across 2 subcategories)
  • Definitions (mathematics) - contains 819 pages (across 24 subcategories)
  • Computer science definitions - 0 pages (across 0 subcategories)
    • Note: it's hard to tell just what is CS and what is mathematics (these get quite blurred) so CS usually refers to the things which are to do with computers, and was created to contains things like register based computing machine
  • Theorems - containing 239 (across 16 subcategories) (this is difficult to count, see Category:Theorems, lemmas and corollaries for more, there are many more, some trivial and not worthy of their own page)

Slightly related is the category of exemplary pages (containing 7 pages), which showcases the best pages of this site.

In the spirit of openness there is also the category of dire pages (containing 18 pages), which contains pages that are not short, but woefully incomplete and in dire need of content.

Index category

This category contains indexing pages, these are used for things like notation, operators, structures and objects, so forth. This project is always changing, if you make particular use of something or think the current way is good, please comment on the appropriate talk page.

Mathematical subject index

(Note, if a link is read, it does not mean this site doesn't cover the subject, it just means that there is no introductory page to the subject


OLD STUFF

Old list of "areas"

Commonly needed things

Good (finished) pages

Editing tips