Difference between revisions of "User:Alec"

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Hi, I'm the admin of this site and creator of most of the content. Write a note on my talk page for requests!
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Hi, I'm Alec; I've done {{M|99.9\%}} of the work on this site easy and I am the administrator. You can contact me on my talk page (I use this site regularly) or at "alec" {{M|\mathcal{A}\top}} unified{{M|\rightarrow}}mathematics{{M|\cdot}} com
 +
 
 +
The project has not gone entirely dormant. I've just been busy on other things [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 21:05, 8 May 2018 (UTC)
 +
 
 +
I must also remember to deal with pages tagged by [[Template:XXX]] as they have no grade/category system! Same for [[Template:Todo]] - I'm not sure how they're different!
 +
 
 +
: Don't forget about: [[:Category:Finished notes]]
 +
: Or [[User:Alec/BookTemplate]]
 +
: Or [[User:Alec/NewTodoTemplate]]
 +
: Or [[Characteristic property of the disjoint union topology/Proof]]
 +
: Or [[User:Alec/ParametricPages]]
 +
: Or [[/Modules]]
 +
: Or [[/Unnamed inequality]]
 +
: Or [[/Exam Qs]]
 +
: Or [[/Questions to do]]
 +
: Or [[/Pages to do]]
 +
: Or [[/Goals]]
 +
: Or [[/Manifolds pages]]
 +
: Or [[/Link templates]] added: [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 02:07, 31 December 2017 (UTC)
 +
: Or [[/Template redirect test]] added [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 19:26, 31 December 2017 (UTC)
 +
: Or [[:Category:Urgent work]], or {{C|<nowiki>{{</nowiki>[[Template:Alec's terminology|Alec's terminology]]{{!}}construct<nowiki>}}</nowiki>}} and my plan to make a template and version conventions, so pages made before a convention took effect can easily give a link to conventions they do follow, ideally with the ability to "do trials", eg version T7 is "trial 7", some base version + whatever trial 7 is, T8 would be potentially another trial/proposal + another base version, and V6 would be everything V5 is plus whatever new conventions V6 establishes. This way a page is everything at or before its convention. [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 11:46, 5 November 2018 (UTC)
 +
==[[User:Alec/Noticeboard|Noticeboard]]==
 +
{{:User:Alec/Noticeboard}}
 +
==[[User:Alec/Things not to forget|Things not to forget]]==
 +
{{:User:Alec/Things not to forget}}
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==[[User:Alec/Pages being worked on|Pages being worked on]]==
 +
{{:User:Alec/Pages being worked on}}
 +
==Notation==
 +
{| class="wikitable" border="1"
 +
|-
 +
! Symbol
 +
! Command
 +
|-
 +
! {{M|\trianglelefteq}}
 +
| {{C|\trianglelefteq}}
 +
|-
 +
! {{M|\triangleq}}
 +
| {{C|\triangleq}}
 +
|-
 +
! {{M|\ntrianglelefteq}}
 +
| {{C|\ntrianglelefteq}}
 +
|}
 +
==Current projects==
 +
Currently ensuring that all existing measure theory articles are "up to a decent standard" and working on Measure Theory, following Halmos' example (rings).
 +
* [[Notes:Halmos measure theory skeleton]] - notes for plan on definitions
 +
* [[Site projects:Patrolling measure theory]] - "patrol" being the "decent standard" project.
 +
* [[Site projects:Measure theory plan]] - implementation of plan.
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* [[Site projects:Split set theory into elementary set theory]] - some things classified as "set theory" (like [[set subtraction]]) would be best classified as "elementary set theory". This project endeavorers to do that.
 +
* [[Site projects:Patrolling topology]] - "patrol" being the "decent standard" project.
 +
 
 +
==Notes==
 +
Diagram for [[Characteristic property of the product topology]]:
 +
{| class="wikitable" border="1"
 +
|-
 +
|<center><span style="font-size:1.2em;"><m>\begin{xy}
 +
\xymatrix{
 +
& & \prod_{\alpha\in I}X_\alpha \ar[dd] \\
 +
& & \\
 +
Y \ar[uurr]^f \ar[rr]+<-0.9ex,0.15ex>|(.875){\hole} & & X_b
 +
\save
 +
(15,13)+"3,3"*+{\ldots}="udots";
 +
(8.125,6.5)+"3,3"*+{X_a}="x1";
 +
(-8.125,-6.5)+"3,3"*+{X_c}="x3";
 +
(-15,-13)+"3,3"*+{\ldots}="ldots";
 +
 
 +
\ar@{->} "x1"; "1,3";
 +
\ar@{->}_(0.55){\pi_c,\ \pi_b,\ \pi_a} "x3"; "1,3";
 +
\ar@{->}|(.873){\hole} "x1"+<-0.9ex,0.15ex>; "3,1";
 +
\ar@{->}_{f_c,\ f_b,\ f_a} "x3"+<-0.9ex,0.3ex>; "3,1";
 +
\restore
 +
 
 +
}
 +
 
 +
 
 +
\end{xy}</m></span></center>
 +
|-
 +
! Diagram
 +
|}
 +
Characteristic property of the subspace topology:
 +
* {{MM|1=\forall S\in\mathcal{P}(X)\left[\forall Y\forall\mathcal{K}\in\mathcal{P}(\mathcal{P}(Y))\left(\overbrace{\mathcal{T}(Y,\mathcal{K})\implies}^{\text{if }(Y,\mathcal{K})\text{ is a topology then} }\Big[\underbrace{\forall f\in\mathcal{P}(Y\times X)}_{\text{relations from }X\text{ to }Y}\big(\overbrace{\mathcal{F}(f)\implies}^{\begin{array}{c}\text{if }f\text{ is a}\\\text{function then} \end{array} }[\mathcal{C}(f)\iff\mathcal{C}(\iota_S\circ f)]\big)\Big]\right)\right]}}
 +
==Things I want to use==
 +
Linked list documentation diagram:
 +
<syntaxhighlight lang="c">
 +
            /*
 +
            * B is the node to be removed.
 +
            * We do this by binding A forward to C
 +
            *
 +
            * BEFORE:
 +
            * ---> +---+---------> +---+---------> +---+-----
 +
            *....  | A |          | B |          | C |    ....
 +
            * -----+---+ <---------+---+ <---------+---+ <---
 +
            *
 +
            * AFTER:      ,------------------.
 +
            * ---> +---+--'        +---+-------'-> +---+-----
 +
            *....  | A |          | B |          | C |    ....
 +
            * -----+---+ <-.-------+---+        ,--+---+ <---
 +
            *              `------------------'
 +
            *
 +
            *  Note that B.previous.bindForwards(B.next) is the same
 +
            *  as B.next.bindBackwards(B.previous)
 +
            *  A nice side-effect of this is that provided one has a
 +
            *  ref counting scheme in place (which you need basically
 +
            *  need for safe multi-threaded schemes anyway) any iterators
 +
            *  "pointing" to B remain valid.
 +
            *  Make sure that this "rail-road" situation where going
 +
            *  forward and back MIGHT not be inverses is well documented
 +
            *  and expected.
 +
            */
 +
</syntaxhighlight>

Latest revision as of 11:46, 5 November 2018

Hi, I'm Alec; I've done [ilmath]99.9\%[/ilmath] of the work on this site easy and I am the administrator. You can contact me on my talk page (I use this site regularly) or at "alec" [ilmath]\mathcal{A}\top[/ilmath] unified[ilmath]\rightarrow[/ilmath]mathematics[ilmath]\cdot[/ilmath] com

The project has not gone entirely dormant. I've just been busy on other things Alec (talk) 21:05, 8 May 2018 (UTC)

I must also remember to deal with pages tagged by Template:XXX as they have no grade/category system! Same for Template:Todo - I'm not sure how they're different!

Don't forget about: Category:Finished notes
Or User:Alec/BookTemplate
Or User:Alec/NewTodoTemplate
Or Characteristic property of the disjoint union topology/Proof
Or User:Alec/ParametricPages
Or /Modules
Or /Unnamed inequality
Or /Exam Qs
Or /Questions to do
Or /Pages to do
Or /Goals
Or /Manifolds pages
Or /Link templates added: Alec (talk) 02:07, 31 December 2017 (UTC)
Or /Template redirect test added Alec (talk) 19:26, 31 December 2017 (UTC)
Or Category:Urgent work, or {{Alec's terminology|construct}} and my plan to make a template and version conventions, so pages made before a convention took effect can easily give a link to conventions they do follow, ideally with the ability to "do trials", eg version T7 is "trial 7", some base version + whatever trial 7 is, T8 would be potentially another trial/proposal + another base version, and V6 would be everything V5 is plus whatever new conventions V6 establishes. This way a page is everything at or before its convention. Alec (talk) 11:46, 5 November 2018 (UTC)

Noticeboard

As of Thursday, 5/Dec/2024 at 02:04:

Watchdogs

Things not to forget

Pages being worked on

Notation

Symbol Command
[ilmath]\trianglelefteq[/ilmath] \trianglelefteq
[ilmath]\triangleq[/ilmath] \triangleq
[ilmath]\ntrianglelefteq[/ilmath] \ntrianglelefteq

Current projects

Currently ensuring that all existing measure theory articles are "up to a decent standard" and working on Measure Theory, following Halmos' example (rings).

Notes

Diagram for Characteristic property of the product topology:

[ilmath]\begin{xy} \xymatrix{ & & \prod_{\alpha\in I}X_\alpha \ar[dd] \\ & & \\ Y \ar[uurr]^f \ar[rr]+<-0.9ex,0.15ex>|(.875){\hole} & & X_b \save (15,13)+"3,3"*+{\ldots}="udots"; (8.125,6.5)+"3,3"*+{X_a}="x1"; (-8.125,-6.5)+"3,3"*+{X_c}="x3"; (-15,-13)+"3,3"*+{\ldots}="ldots"; \ar@{->} "x1"; "1,3"; \ar@{->}_(0.55){\pi_c,\ \pi_b,\ \pi_a} "x3"; "1,3"; \ar@{->}|(.873){\hole} "x1"+<-0.9ex,0.15ex>; "3,1"; \ar@{->}_{f_c,\ f_b,\ f_a} "x3"+<-0.9ex,0.3ex>; "3,1"; \restore } \end{xy}[/ilmath]
Diagram

Characteristic property of the subspace topology:

  • [math]\forall S\in\mathcal{P}(X)\left[\forall Y\forall\mathcal{K}\in\mathcal{P}(\mathcal{P}(Y))\left(\overbrace{\mathcal{T}(Y,\mathcal{K})\implies}^{\text{if }(Y,\mathcal{K})\text{ is a topology then} }\Big[\underbrace{\forall f\in\mathcal{P}(Y\times X)}_{\text{relations from }X\text{ to }Y}\big(\overbrace{\mathcal{F}(f)\implies}^{\begin{array}{c}\text{if }f\text{ is a}\\\text{function then} \end{array} }[\mathcal{C}(f)\iff\mathcal{C}(\iota_S\circ f)]\big)\Big]\right)\right][/math]

Things I want to use

Linked list documentation diagram: 

            /*
             * B is the node to be removed.
             * We do this by binding A forward to C
             * 
             * BEFORE: 
             * ---> +---+---------> +---+---------> +---+-----
             *....  | A |           | B |           | C |    ....
             * -----+---+ <---------+---+ <---------+---+ <---
             * 
             * AFTER:       ,------------------.
             * ---> +---+--'        +---+-------'-> +---+-----
             *....  | A |           | B |           | C |    ....
             * -----+---+ <-.-------+---+        ,--+---+ <---
             *               `------------------'
             * 
             *  Note that B.previous.bindForwards(B.next) is the same
             *  as B.next.bindBackwards(B.previous)
             *  A nice side-effect of this is that provided one has a 
             *  ref counting scheme in place (which you need basically
             *  need for safe multi-threaded schemes anyway) any iterators
             *  "pointing" to B remain valid.
             *  Make sure that this "rail-road" situation where going
             *  forward and back MIGHT not be inverses is well documented
             *  and expected.
             */
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