User talk:Paul August/Archive1

Welcome to the Wikipedia

Here are some links I thought useful:

Feel free to ask me anything the links and talk pages don't answer. You can sign your name by typing 4 tildes, like this: ~~~~.

Be Bold!

Sam [Spade] 21:04, 23 Jul 2004 (UTC)

"pi"

If you must write out pi instead of using the lower-case Greek letter, why in the world would you capitalize it? I've never seen it done that way. It's always lower-case even when it's at the beginning of a sentence. Michael Hardy 22:13, 23 Jul 2004 (UTC)

Hi Michael, I only changed the title of the page because it was displaying as "&pi". Anyway pi is fine with me, as would be π. As to why I capitalized it, I don't really know. After looking around a bit there are lots of examples of Pi on Wikipedia as well as other places on the web, but I have no strong feeling about which is standard. Paul August 00:59, Jul 24, 2004 (UTC)

Category problem

There are currently severe technical problems with categories, so please be patient about your mistaken link (from the Helpdesk). Once the category problems are solved your problem will be too. -Erolos 11:26, 29 Jul 2004 (UTC)

Erolos: Thanks Paul August 13:54, Jul 29, 2004 (UTC)

Maeander River stubness

Hi Adam, how much more info needs to be added to the article Maeander River before we remove the stub tag? My opinion was that this is an adequate amount for the topic, but i'm new ;-). Regards Paul August 04:25, Aug 6, 2004 (UTC)

Hi! I'm not sure how much more could be added...I guess stubs are kind of subjective, and it just looked like a stub to me. You can remove the notice if you think it's as complete as it can be. Adam Bishop 04:35, 6 Aug 2004 (UTC)

Hi Adam, I wouldn't say I thought it was "as complete as can be" but I do think it's complete enough. Is that enough? ;-) Paul August 04:39, Aug 6, 2004 (UTC)

Finished mathematics ?

Hi Michael, have you ever heard of this term before? Does it have wide usage? Paul August 22:03, Aug 11, 2004 (UTC)

I have not frequently (if ever) encountered it other than in this Wikipedia article. It seems the first 20 or so Google hits on it come from that article as well. So if it's frequently used, I'd guess it's only within a relatively small philosophy-of-mathematics community. Michael Hardy 01:41, 12 Aug 2004 (UTC)

I've never heard of it either. It was created by the same guy who created Folk mathematics, and who both may be User:JRR Trollkien. I'm wondering if this is a made up term. Paul August 06:54, Aug 12, 2004 (UTC)

FYI: I've VfD'ed it. Wikipedia:Votes for deletion/Finished mathematics. Gadykozma 14:14, 17 Aug 2004 (UTC)

Naming convention for television articles

Hi. Seeing as you were once previously interested in a naming convention, I'd like to invite you to vote on adoption of Wikipedia:Naming conventions (television). Voting is taking place on the Talk page and ends on Sep 13 2004. -- Netoholic 23:25, 22 Aug 2004 (UTC)

Diagrams in set theory

Oh, my creations are finally get rid of by you! Nice drawings, thanks. :P -wshun 13:18, 2 Sep 2004 (UTC)

Thankyou, I'm glad you like them ;-) However I seem to be having a problem with them not "floating" properly, under some browsers (they look fine to me with Safari), unless I "thumb" or "frame" them. Does the image placement look ok to you? Framing doesn't seem quite right for diagrams see subset for an example. Any ideas? Paul August 13:29, Sep 2, 2004 (UTC)

Since these images:

[[:image:Subset.png|50px|left|thumb|was in subset]]

[[:image:Set_union.png|50px|left|thumb|was in union (set theory)]]

[[:image:Set_intersect.png|50px|left|thumb|was in intersection (set theory)]]

[[:image:Set_complement.png|50px|left|thumb|was in complement (set theory)]]

[[:image:Set-comp2.png|50px|left|thumb|was in complement (set theory)]]

are no longer being used should we delete them? Paul August 15:39, Sep 3, 2004 (UTC)

No objection for deletion. -wshun 15:45, 3 Sep 2004 (UTC)

Mathematical Vigilance

Thank you for being alert and moving quicker than I to reverse the imaginary notion, presumptuously delivered as fact, by "Lupin" that zero can be defined as an integer both positive and negative. Wikipedia would degrade into gibberish if someone did not catch such irresponsible remarks wherever they occurred. --OmegaMan

TV Naming conventions.

At some point in the past you expressed an opinion on Wikipedia talk:Naming conventions (television). I have instigated a new poll on that page. I am hoping that this poll will properly allow all users who have an interest in the subject to express their views fairly before we come to a consensus. I have scrapped the poll that was previously in place on that page because I believe that it was part of an unfair procedure that was going against the majority view. I am appealing to all users who contribute to that page to approve my actions. I would appreciate it if you could take the time and trouble to read the page carefully and express an opinion and vote as you see fit. Mintguy (T) 16:43, 13 Sep 2004 (UTC)

This page has a long and tortuous history, but the short version is that Netoholic (who has gained something of a reputation for acting without the agreement of other users, and now has an RFC against him for that very reason) started moving pages before there was a general agreement, several users complained about this but Netoholic took no notice. I suggested that we hold a new poll to establish a true consensus. I suggested to User:Gtrmp that he prepare such a poll. While he was doing this, Netoholic once more acted without the consent of the majority and instituted his own poll which was configured to either endorse or reject his unilateral movement of pages, and did not offer users the chance to make other suggestions. This poll was defeated by a clear majority, but Netoholic took the decision to extend the deadline. At this point I created the poll that you now see on that page. The poll is open, and is open to further embellishment should you wish to extend the list of options. I have not set a close date as I believe I have already imposed myself too much on the process. I am therefore a little disappointed to see your name in the disapprove section. However as I've just indicated, I do not intend to impose myself too much on that page other than to stem Netoholic and his inability to treat other users with respect. So I invite you to discuss the matter of additional options, and the deadline for the poll on that page. BTW I should point out that I originally prepared a poll in a similar format to that on user:Gtrmp's page, but several users complained that it was overly complicated, so I simplified it to what you see now. Mintguy (T) 21:30, 16 Sep 2004 (UTC)

Hi Mintguy. I'm sorry if I've done something inappropriate. I probably just misunderstood the situation. I thought that part of the proposal for a new poll, was to achieve consensus on the wording of the new poll before voting started (the idea of making changes to the poll after voting has started seems strange to me). I thought that that was why there was an approve/disapprove section. Since It seemed to me that the poll on User:Gtrmp's page was better, I expressed an opinion to use it instead. You did actively seek out my opinion, and I gave it. Again if I've done something I shouldn't have then I apologize. Paul August 03:59, Sep 17, 2004 (UTC)

Data Management Wiki Committee

Thank you for your contribution to one, or more, articles that are now organized under Data management.

Because of your previous intrest, you are recieving an invitation to become a founding member of the Data Management Wiki Committee.

The members, of course, will form and solidify the purpose, rules, officers, etc. but my idea (to kick things off) is to establish a group of us who will take responsiblity to see that the ideas of Data management are promoted and well represented in Wikipedia articles.

If you are willing to join the committee, please go to Category_talk:Data_management and indicate your acceptance of this invitation by placing your three tilde characters in the list.

KeyStroke 01:04, 2004 Sep 25 (UTC)

Thank you

Thanks for the note you made on my user page. I'm attempting to do a re-author as we speak, which is more going to focus on my Wikipedia material, but is going to hopefully retain some text from me at the start. Just to let you know it's happening.

Matt

User 12.151.135.2 and Boston Opera edits

(To user 12.151.135.2, copied from his/her talk page. Paul August)

You are making inappropriate edits to: Boston Lyric Opera. Please stop. For example your last edit removed the following:

"It was founded in 1976. Its home base is the Schubert Theater in Boston.

It stages three to four productions a year with promising young singers, directors, conductors and designers.

The BLO attracts a public of some forty thousand people a year."

You give no reason for this deletion. Why did you remove it? Are these statements factually incorrect? Removing content without giving an appropriate reason is a violation of Wikipedia policy. Please see Wikipedia:Avoiding_common_mistakes. Knowingly, and repeated making edits of this sort is considered vandalism, and can result in being banned from Wikipedia.

Other of your edits appear to violate the policy that Wikipedia articles should be written from a neutral point of view please see: Wikipedia:Neutral point of view. Some of the information that you tried to add to this article might be useful, if it were written "neutrally", in accordance with the above policy. This also applies to the edits you've made to Opera Boston and Opera Company of Boston.

You are a new user and you're probably unaware of Wikipedia "standards and practices" for article edits. Hopefully, you're well-meaning rather than willfully malicious. If so, since you seem to know a lot about the Boston opera scene, you could probably make some valuable contributions.

If you would like to discuss any of this, you can do this on the article's talk page Talk:Boston Lyric Opera or mine Paul August 13:54, Sep 30, 2004 (UTC)

To the unpithy person who referes to himself as PAUL AUGUST....Cambridge is full of eccentric phonies such as yourself, who like to hide behind obscure and foolish titles...Your blocking of the truth behind the Opera Company of Boston exposes you as a Goebbels-type (see Nazi Germany) You are most likely under 30 years old, and therefore untrustworthy. My colleagues and I lived and suffered through the dapradations of Ms. Caldwell and her ilk.. If you wish to continue to censor our account, we will apply to the proper authority aand WIKIPEDIA< and have you barred!!! The OCB chorus (A.G.M.A.) (From user: 12.151.135.2 13:26, Sep 30, 2004. Moved from my User page . I only just discovered it today, since it was "buried" in a table and was not displaying on my User page. Paul August ☎ 16:00, Jan 26, 2005 (UTC))

(To user 12.151.135.2, copied from his/her talk page. Paul August)

Please stop. If you continue to vandalize pages, you will be blocked from editing Wikipedia. Paul August 12:30, Oct 5, 2004 (UTC)

to: Paul August and his crew of "balanced" POV types...It appears that you are more interested in the bland and unconvincing narrative that that the OCB/BLC/ OB are presenting on your site..they are hiding behind the lack of information, while, myself, and my colleagues who actually LIVED these artistic times, and know the entire truth, are being "edited" by guys who even admit that they haven't the knowledge to touch the material... I provided follow ups to the OCB material; why didn't you back check it,,or are you afraid to touch print media, or extend yourself beyond your butt on your chairs...no matter, my colleagues and I have the site, and will continually inject the truth, until you let it stand..., so that you will have to lose your precious time continuously editing back...we WILL outlast you!!! The artists of the Boston opera scene.... (from user 12.151.135.2, 13:40, Oct 5, 2004. Paul August)

GOOD LUCK, YOU WITH A PHONY NAME AND C/V! 02138 KMA KMA KMA KMA KMA KMA (from user 12.151.135.2, 14:17, Oct 5, 2004, copied from his/her talk page)

(to user 12.151.135.2, copied from his/her talk page. Paul August)

Thank you for replying to my message about your edits to Opera Company of Boston, Opera Boston and Boston Lyric Opera. I'm sure you do know more about the Boston Opera scene than I do. I think some of the information you have provided is quite interesting, especially concerning the history of the OCB, it could and should be incorporated into the article. But the problem with what you wrote is that it was not written from a neutral point of view (in fact as Viajero said on my talk page, it sounded like it was written by someone "with an axe to grind"). Unfortunately that kind of writing just isn't appropriate for an encyclopedia, and it is in violation of the policies and intent of Wikipedia. I think you do have some valuable information to contribute, and I would like to see it incorporated into the Boston Opera articles. If you would like, I'd be willing to help. If you would like to know in more detail what the problems are with the edits you made, I'd be happy to discuss that, perhaps together we could add some of your edits back. Wikipedia has allowed you the privilege of editing these articles, and in return you are expected to conform to the guidelines which have been developed by Wikipedia, it is only polite to do so. Regards Paul August 19:41, Oct 5, 2004 (UTC)

Young man, these days the blocks to the truth are not "neytral" If you seek to suppress the truth about anything, then nothing is true!!!..The fact is that my colleagues and I are working on our Opera News of Massachusetts, and we will find a page or two about you and your "editors" when we publish on OUR Internet..

Have a nice day...... :):):):):):):):):) !!!

P>S> conformity??? Are you a dinosaur of the Soviet Commisariat of Truth and Art??? You really do not think before you tap on your keys.... (from User 12.151.135.2 06:17, Oct 6, 2004 copied from his]her talk page)

(to user 12.151.135.2, copied from his/her talk page)

You seem to disagree with the policy stated in: Wikipedia:Neutral point of view (Is that true? Did you read it? If not it might be helpful if you did, also you might want to look at: Wikipedia:NPOV tutorial). If you don't want to follow this policy, then Wikipedia is not the place for you. Fortunately, there are lots of places on the internet which will allow you to write whatever you like ;-) By the way I'd like to say that I'm not unsympathetic to the particular point of view you have been expressing in your edits, I think I share some of it. In fact I might try to add some of the stuff you wrote back to the articles, but I will have to do some research - can you provide any other sources besides the ones already given? Paul August 13:27, Oct 6, 2004 (UTC)

Opera Company of Boston Edits

Hi, In case you're un-aware, I thought you might be interested in the the edits going on at Opera Company of Boston. You also might want to look at Opera Boston and Boston Lyric Opera. Paul August 21:04, Sep 30, 2004 (UTC)

Hi, thanks for your heads up about the Boston opera articles. I have reverted the changes, and removed the Boston Opera Company from Cleanup. This anon user clearly has an axe to grind; his/her contributions were highly unencyclopedic. Of course the articles could use some additional material, but that will have to wait until someone with a more balanced POV comes along. PS Whereabouts in Cambridge to you live? I was born and grew up there. -- Viajero 17:50, 1 Oct 2004 (UTC)

You're welcome. Some of the content added to Opera Company of Boston seemed useful, but I don't know enough to be able to NPOV it. I live off of Sherman street next to Danehy Park, in North Cambridge. Where did you live? Paul August 21:11, Oct 1, 2004 (UTC)

Attalus I

Brilliant job. The Successors are hard to get straight. I hope you'll worm your way through every one of them. Thanks for alerting me! Wetman 05:52, 11 Oct 2004 (UTC)

You'll find the answers to your questions on my talk page User talk:PHG. Regards

Good work on this article, I like this article's footnotes especially. Hopefully we can pursuade the Mediawiki coders to put in the ability to hide footnotes for those complainers who do not like them :o).

My way of doing fact checking is a little different, by quoting the fact then finding multiple sources. This way you dont have to have multiple footnoes after each fact going to difference sources.

As well, having the footnotes autonumber, quote the text in my way of doing it, and the ability to hide the footnotes and the footnotes markup will be good. The coders have not been that interested in putting this in, and frankly i dont really know who is in charge of putting in this feature. Hopefully they will find us :). --ShaunMacPherson 04:34, 15 Oct 2004 (UTC)

Infinity

Salutations Gene Ward Smith,

I think your edits to infinity, especially your most recent ones, are a vast improvement over what was there before.

I have a few concerns though about your edits and with what you wrote on the talk page, that I'd like to discuss with you.

In your first round of edits, you deleted large amounts of content with no discussion and without the benefit of a consensus. This is widely considered to be a violation of Wikipedian norms of conduct. It is also important to be especially careful about deleting content. If it is wrong, then it's generally held to be better to fix it. If it is out of place, then it's generally held to be better to move it. Being a relatively new Wikipedian, perhaps you are not aware of this.

Also, I don't think it is helpful to call lysdexia's edits "vandalism". His edits were no more "vandalism" than yours were. As I said above your edits would be considered by many to be contrary to established norms, but I don't think they would qualify as vandalism. Nor, in my view, were lysdexia's reverting your edits vandalism. He was merely trying to undo what he and many wikipedians would consider to be inappropriate edits.

As for the content of your edits, as I said above, and on Talk:Infinity, I like, for the most part, what you've added to the article, but I'm concerned about some of the content that you deleted. For example I'm not convinced (yet!) that all the mathematics should go. I think this should be discussed on the talk page, and a consensus reached.

Also, you may not have noticed, but after lysdexia reverted your original edits, I added back your "Use of infinity in Physics" section edits, with some additional edits of my own. You have now eliminated all of my edits. Was this intentional? If so would you mind telling me what you found wrong with them? Reverting edits without discussing why tends to make people unhappy.

It's great to have another math PhD, contributing to Wikipedia. There are several professional mathematicians working on wikipedia, by the way, three good ones that I know are: AxelBoldt, Charles Matthews, Michael Hardy. I myself, have a PhD in categorical topology, as well as "a background in philosophy", so we should get along famously ;-)

Paul August 06:27, Nov 1, 2004 (UTC)

I don't know how to correspond other than by editing this page, so here I am. You wrote "In your first round of edits, you deleted large amounts of content with no discussion and without the benefit of a consensus. This is widely considered to be a violation of Wikipedian norms of conduct." However, we are told "be bold", and it doesn't take much boldness to see that removing material which is simply wrong is a good idea. Can you point to one single sentence in the introduction I removed which has any value? If so, we could talk about restoring that content, but if not, what would be the point in worrying about it? I think a concrete discussion focused on "You removed X, but X actually made sense and you didn't replace it with Y doing the same job" would be where to start.

Also, I don't think it is helpful to call lysdexia's edits "vandalism".

I wrote a lot of good stuff and he took it out, and replaced it with what I regard as garbage. Why is that not vandalism? In any case delicacy with my manners went out the window when he introduced the adjective "stupid".

For example I'm not convinced (yet!) that all the mathematics should go. I think this should be discussed on the talk page, and a consensus reached.

It is impossible to have an intelligent philosophical discussion of the concept of infinity and ignore mathematics, so this is a red herring.

Also, you may not have noticed, but after lysdexia reverted your original edits, I added back your "Use of infinity in Physics" section edits, with some additional edits of my own.

I didn't think I eliminated your edits, so I'd better check. Certainly, that was not my plan.

It's great to have another math PhD, contributing to Wikipedia. There are several professional mathematicians working on wikipedia, by the way, three good ones that I know are: AxelBoldt, Charles Matthews, Michael Hardy. I myself, have a PhD in categorical topology, as well as "a background in philosophy", so we should get along famously ;-)

Good! I've not made as many contributions as AxelBoldt or Charles Matthews, but mine are pretty substantial by now. Gene Ward Smith 07:23, 1 Nov 2004 (UTC)

Hi Gene Ward Smith,

Thanks for responding to my post on your talk page. I've copied your response (above) to make it easier to follow the discussion.

Yes we are told to be bold, but sometimes what one editor thinks is "simply wrong" another editor thinks is "a lot of good stuff", so we have to work together here by striving for consensus. We can discuss specific X's removed and/or replacement Y's, but much of my concern has to do with process.

For example your edit of 19:14, Oct 16, removed the following:

Use of infinity in mathematics
[edit]

In mathematics, infinity is an unbounded quantity that is greater than every real number. [1]

This definition is wrong, and in particular "unbounded quantity" makes no sense. The substance was retained in the discussion of infinity in real analysis.

A distinction is made between different "sizes" of infinity because it can be shown that some infinite sets have greater cardinality than others. Georg Cantor developed a system of transfinite numbers, in which the first transfinite cardinal is aleph-null ( $\aleph _{0}$ ), the cardinality of the set of natural numbers.

This was rewritten and retained.

All of the text in this section was deleted by you on Oct 16th (see: edit history) leaving this version of the article [2] correct? Your edits on Oct 31st added back this content. My concerns were about edits of Oct 16th. Paul August 20:09, Nov 1, 2004 (UTC)

The modern mathematical conception of the infinite developed in the late nineteenth century from work by Cantor, Gottlob Frege, Richard Dedekind and others, using the idea of sets. Their approach was essentially to adopt the idea of one-to-one correspondence as a standard for comparing the size of sets, and to reject the view of Galileo (which derived from Euclid) that the whole cannot be the same size as the part. An infinite set can simply be defined as one having the same size as at least one of its "proper" parts.

Again, this was not removed, it was edited.

This was removed on Oct 16th, it was edited and added back on the 31st, correct? (see above) Paul August 20:09, Nov 1, 2004 (UTC)

Thus Cantor showed that infinite sets can even have different sizes, distinguished between countably infinite and uncountable sets, and developed a theory of cardinal numbers around this. His view prevailed and modern mathematics accepts actual infinity. Certain extended number systems, such as the surreal numbers, incorporate the ordinary (finite) numbers and infinite numbers of different sizes.

Ditto.

Our intuition gained from finite sets breaks down when dealing with infinite sets. One example of this is Hilbert's paradox of the Grand Hotel.

Didn't change a word of this.

It is worth mention that the infinite cardinal numbers (relating to set theory) and the infinity commonly encountered in algebra and calculus are two completely different concepts. In algebra and calculus, 2^∞ is not technically a number, but taking a limit yields 2^∞ = ∞. Real numbers are not used to measure the sizes of sets, so ∞ can be used for any quantity that grows indefinitely at a limit. The corresponding statement in set theory is that 2^ℵ₀ > ℵ₀ because the former term is uncountable, while the latter is countable. Exponents in set theory are not the same as regular exponents in high school mathematics, the former using cardinals or sizes and the latter using ordinals or amounts, and ∞ is not the used or treated same as aleph null.

This repeated stuff already discussed, and was removed as redundent. The discussion of exponents in set theory was irrelevant to the topic.

"bounded" versus "unbounded"
[edit]

In mathematics, the term bounded is use to designate a set whose elements in a container of finite size. More formally, the set $Z=\left\{z_{1},z_{2},z_{3},\ldots ,z_{n}\right\}$ is said to be bounded if there exists at least one point c (center) and a positive real number r (radius) such that the set $U_{r}\left(c\right)$ , where $U_{r}\left(c\right)$ is the set that contain all the points than are less or equal to distance r from c, in both directions, contains all the elements of Z; $Z\subset U_{r}\left(c\right)$ . Z is unbounded if, for any c and any r, $U_{r}\left(c\right)$ does not include all elements of Z.

This is wandering off the topic; if something like this is to be included, it should be much more concise.

This is the mathematical way of answering the riddle, "How long is a piece of string?" by showing that the [imaginary] string has a length shorter than a[n imaginary] string of longer length.

This is just bad.

For the above definitions to make sense, we have to have define what we mean by distance, We must define a metric to be in metric space. If it is not, the terms "bounded" and "unbounded" are meaningless. However, the term '"infinity" is meaningful even without a metric.

Again, metric spaces are off-topic.

These definitions of bounded and unbounded are the same, regardless of whether point c is part of Z, or whether or not $U_{r}\left(c\right)$ is exactly equal to Z.
It can be easily shown that

If a set is finite, it is bounded.

If a set is unbounded, is infinite.

However,

If a set is bounded, it is not necessarily finite. For example, a segment is bounded but has an infinite number of elements.

If a set is infinite, it may not be unbounded.

If a set is bounded, we can define a diameter of the set:
$diam\left(Z\right)=Max_{z\in Z,y\in Z}d(z,y)$
Where $d(z,y)$ is the distance between z and y in set Z. We take the maximal $d(z,y)$ returned after considering all permutations of z and y.
The diameter of a set is always a positive real number or zero, if the set is bounded. It can be zero if and only if the set is empty or has only one member.
If the set Y is unbounded, we can write $diam\left(Y\right)=\infty$ but it must be understood that this is only a convention for stating that Y is unbounded. It does not literally mean that the diameter is infinite.

This isn't a very good discussion, but the main thing wrong with it is that it is off-topic.

Calculus and mathematical analysis
[edit]

A very common use of infinity is in calculus and mathematical analysis, for example:

$\lim _{t\to \infty }\,f(t)=0$

$\int _{0}^{1}\,f(t)dt\ =\infty$

$\int _{0}^{\infty }\,f(t)dt\ =\infty$

$\int _{0}^{\infty }\,f(t)dt\ =1$

The article isn't about freshman calculus, even if that is where a lot of this discussion seems to be coming from. This is included to the extent it needs to be in the real analysis stuff.
Infinity is not part of the set of real numbers; $\infty \not \in \mathbb {R}$ and cannot be used in places where a real number can normally be used. For example, $a-a=0\ \ \forall a\in \mathbb {R}$ is true, but $\infty -\infty =0$ is undefined. Over the mathematical explanation and by logic, arithmetic operations, those based on counting, are undefined for infinity within arithmetic mathematics for expression and solution. But within logic the statement $\infty -\infty =0$ is also true; however, infinity not being bound produces indeterminate solutions wherein a 0 or any other solution may be or already is true if the expression is defined, which is an arbitrary task. This explanation is absent from any maths level treatise of infinity.

This could be worked up into a discussion of the arithmetic of infinity used as a symbol for a limit, but as it is it isn't up to snuff, and is misleading at best.

There are only few cases when you can consider ∞ as a regular number. In these unusual cases, you are in the so-called extended real number field, denoted by ${\bar {\mathbb {R} }}$

Good link, but needs editing. "Regular number"?

In limit analysis, we can make statements which include the theoretical case that we almost put infinity in the place of a real number, for example $\lim _{x\to \infty }\,{\frac {1}{x}}=0$ . This states that as x continues to grow in magnitude (tends towards infinity), 1/x becomes closer and closer to zero (tends toward zero). The limit case, $1/\infty =0$ is undefined; however if x was the largest finite value known to us, 1/x would be the closest finite value to zero known to us. Here, "undefined" means that the solution is not in the set of real numbers; this only repeats the axiom that infinity is not a number.

Is a discussion of limits carried on to this extent relevant to the topic? It's not "limits", its "infinity".

Limits do not literally consider the case of x=∞ If the definition did include ∞, the properties of the definition change, and some properties that were valid before may no longer be valid. For example, when you extend the definition of integrals, you get improper integrals. Without fully understanding this and correctly assessing the consequences of using infinity in place of a real number, error and paradox may occur. For an example, see the explanation of why the mean of the Cauchy distribution is undefined.
It is important to note that not all limits, series and integrals are convergent.
In the usual ordered real number field, it is common to distinguish between +∞ and -∞.

Ditto.

Can't you see that, even if some of the above is less than perfect (which I think it clearly is;-) removing such a large amount of content without discussion might upset the many editors who may have collaborated in writing it?

Good point, but this got dumped in after I made my edits, and without regard to them, and I did not create that mess. Why was my edit allowed to be butchered, but I am under an obligation to deal with a lot of stuff, much of it irrelevant or badly written or even wrong? All of this greatly expanded the size of the article but didn't really add much that was relevant and correct.

Perhaps I've made a wrong assumption. Looking at the edit history, I've assumed that your first edit to this article occurred on Oct16. Is that correct? If so then this did not get "dumped in after" you made your edits. This content was present in the article well before Oct 16th. Did you perhaps make edits before the 16th under a different user name? Paul August 20:28, Nov 1, 2004 (UTC)

As I said above, in my opinion (an opinion shared by many other editors) if content has any value at all, it is better to try to fix or move it rather than delete it.

And this was not done with my edit.

you know what they say about two wrongs not making a right ;-) Paul August 20:28, Nov 1, 2004 (UTC)

Are you really saying that all of the above is "simply wrong", has no "value", makes no "sense" and that you regard it as "garbage"?

Sorting out the good and bad would be a bit of a problem. Easier would be to try to add more on the same topic but more concisely and correctly, but I am not sure that addresses your concerns.

I am pleased to see that in your recent edits you have reincorporated some of the deleted content above, often improving on what was there before. Perhaps other deleted content might also be profitably reincorporated? I would be happy to be specific if you are interested in discussing this any further ;-) I would like to help in any way I could ;-)

I'm trying. Some of the comments about the history of set theory were wrong as stated, so I created an article Dedekind infinite, and then restored a corrected version. I've been adding in other stuff also.

You should, however, consider that you played your own role in this debacle; despite recognizing the value of my edits, you allowed them to be reverted, and then futher editing work took place on this reverted version. This was obviously the wrong plan, and that it lead to problems was predictable. I think it would be helpful in the future not to allow such things to happen. Gene Ward Smith 21:03, 1 Nov 2004 (UTC)

Also if you wish to construe what lysdexia did as vandalism fine, but then don't you see that, by the same token, what you did above might also be construed in the same way? I was just trying to convince you that, just like it is unhelpful for lysdexia to use the word "stupid" the use of "vandalism" might also be unconstructive. (see Wikipedia:Vandalism for what most wikipedians mean by that term, you might also want to look at Wikipedia:Wikilove) I'm not trying to defend lysdexia, some of his actions and remarks (IMHO) have been less than than polite. But if you are simply trying to get back at lysdexia, by "responding in kind" please notice that calling his edits "vandalism" and "garbage", can be seen to tar with the same brush, the five dozen or so other editors who have worked on this article, like me ;-) Was that your intention?

Paul August 17:10, Nov 1, 2004 (UTC)

Re: Set theory format changes?

OK, I changed A′ to A^C in the image as well.
The reasons why I started changing to A^C are these:

To make Wikipedia's notation for set complement uniform: A^C was used in the article for De Morgan's Laws.

A′ should be reserved for Boolean complement,

A^{C^{for set complement.}}

The A^C notation has been adopted by PlanetMath ([3]).

The A^C notation is also used at the University of Cambridge (e.g. [4] hosted by Churchill College).

The A^C notation is more unique: the meaning of A′ is already overloaded: e.g. A′ as derivative of A.

A^C is more visible; it looks better on the page.

By the way, there appear to be five different ways of denoting the complement of set A: (1) A′, (2)

{\overline {A}}

, (3) A^C, (4) ~A, (5) comp(A). A′ is probably the most frequent one, so if you want to change from A^C back to A′, I would not oppose it.

>>Why are you changing "A ∩ B" to "A ∩B", this looks better to you? <<

This way the ∩ appears centered between the A and the B (at least on my browser). Which brings me to my question: the character for ∅ shows up as an empty square on my browser, not as an empty set character Ø. Does ∅ appear correctly on your browser and what did you do (if anything) to make it appear correctly? --AugPi 22:57, 1 Nov 2004 (UTC)

For all the browsers I use (Safari, IE, Omniweb, Forefox) the former looks centered, the latter does not. Also the using former which uses "non-breaking spaces" means that "A ∩ B" will always appear on the same line, that is it won't break across two lines. Also both empty set symbols show up correctly for me in all browsers, you might try changing your Wikipedia "math rendering preference" Paul August 23:33, Nov 1, 2004 (UTC)

Red-link recovery

Howdy and many thanks for your work on that list of mis-punctuated links. The list's pretty much completed now - I'll be generating a new version of it in due course, taking all the lessons learned from the last one into account. In the meantime, if you enjoyed working through the list (or at least found it a worthwhile distraction), you may want to have a look at the similar list of plural discrepancies which highlights red-links that might be red because they (or the article they are aiming for) are improperly pluralised. Again, thanks for your efforts - award yourself a wikimedal for janitorial services if you haven't already got one! - TB 11:28, 2004 Nov 8 (UTC)

Economy of Ireland

I've tried to address your comments on WP:FAC - note the articles title has been changed to Economy of the Republic of Ireland. CGorman 22:57, 10 Nov 2004 (UTC)

I think you are doing excellent work on Economy of Republic of Ireland. Hope my comments haven't been bugging you ;-) FAC can be a grueling process ;-) I just went through the "gauntlet" myself recently on Attalus I. Paul August 19:49, Nov 11, 2004 (UTC)

I went through with Celtic Tiger earlier in the month - they picked on everything! - even my cute little tiger image! Anyways I suppose the criticism will benifit wikipedia in the long run. As for the time changeable nature of the article - I don't see any way around it, all those figures are relevent and necessary to fully describe an economy. Thanks for your constructive criticism. CGorman 19:58, 11 Nov 2004 (UTC)

I agree that the article has to have this time dependent content in it. I'm just concerned about the problems inherent in this, and in ways to ameliorate it, Did you look at Avoid statements that will date quickly? It contains some suggestions for this problem. Also some of the words phrase which contain words like "now" and "recently" and "past decade" could be dated? Anyway I'm not objecting to this article on this (or any) basis. I think it's great! My only concern is to make the article as good as it can be ;-) By the way did you see my comment about the newer intro in the CIA factbook? Paul August 20:26, Nov 11, 2004 (UTC)

Yes I read Avoid statements that will date quickly and saw your comment about the newer intro in the CIA factbook, i'll try and act on this soon. CGorman 20:30, 11 Nov 2004 (UTC)

LNS

hey there paul i think it would be great if you could edit the intro back to what it was i just don't have the time now i gotta run pretty quick here--Larsie 03:51, 11 Nov 2004 (UTC)

Re: "Topological space" edit

Thanks for the heads-up about open-ended formulae - I've innocently made the same mistake in Stochastic process and Topologist's sine curve while trying to help out on the Wiki Syntax Project, so will revert them myself. Cheers & Sorry, Danog 19:22, 11 Nov 2004 (UTC)

GNAA Popeye

Hi Paul. After receiving no answer from Silsor and being quite rudely ignored by Arminius about the permanent blocking of GNAA Popeye, I have eventually written this RFC. I hope Silsor will not consider this a personal attack, but it seems like the only way to get the questions answered. Since your questions to Silsor were unanswered as well, I was wondering whether you would consider certifying the RFC? Of course I would understand if you preferred not to be involved, or if you did not feel that strongly about the issue. Thanks. Sam Hocevar 03:16, 14 Nov 2004 (UTC)

Hi Sam. I'm not sure yet exactly what involvement I want to have in all this. I do think the issue of possible abuse of administrator blocking powers is an important and serious matter, as well as a possible attempt to stifle unpopular speech. It's also quite easy for me to imagine that GNAA Popeye might have done things which would warrant an indefinite block. I've asked Silsor on his talk page to please explain to me the reasons and grounds for the block. We'll see where that leads. Regards, Paul August 05:40, Nov 14, 2004 (UTC)

Thanks Paul, Silsor has now answered on the RFC page and I have good hopes that he will answer the real questions. Regards, Sam Hocevar 14:00, 14 Nov 2004 (UTC)

Well, unfortunately I have to withdraw that. Quoting him: I don't feel I need to defend myself any further, as this RFC will be deleted in about 24 hours. Sam Hocevar 13:34, 15 Nov 2004 (UTC)

LNS

hey there paul i believe it was to be definitive, sorry about the late response. --Larsie 17:52, 17 Nov 2004 (UTC)

Clearing the air

Hi Paul,

Sorry for not responding for so long, I have been trying to give User:Sam Hocevar enough rope to hang himself which not being too bright he proceeded to do. You can read about it at User:Silsor/Sam Hocevar. Popeye and Sam worked together on the RFC and hoped to use you as their dupe in the RFC process, which was a troll attempt. If you have any questions that aren't answered there I'll be happy to answer them without delay. silsor 22:37, Nov 18, 2004 (UTC)

I don't remember calling you names, Silsor. If I did, give me a chance to apologise. If I did not, please don't call me "not too bright", it serves no purpose, especially on a public place I'm not supposed to actively follow. Despite your behaviour, I honestly think I have always been of the most absolute courtesy to you. Also, before accusing me of deceiving Paul, which I consider an insult to both of us, please read how I asked Paul to certify the RFC. It is still present two sections above. I presented the facts. I carefully left every possible way for Paul to kindly decline my request, without forcing him to anything. I think it was the most polite way to do it. See how optimistic I was to see you answer. See how I assumed that Paul's certifying was no longer needed since you had decided to answer beforehand. And stop accusing me of working with Popeye on the RFC, I thought and wrote every single line of it. The only communication relevant to this issue that I had with Popeye before that was asking him whether his account was still blocked. I honestly don't think he even knew what the RFC process was before I gave him the link to the one I wrote, and it was not a troll, until you decided to troll yourself into evading the questions again and again. Sam Hocevar 02:12, 19 Nov 2004 (UTC)

no original research

thanks for the suggestion, and the encouragement! Slrubenstein 22:12, 8 Dec 2004 (UTC)

request

Would you look at the recent history of "Postmodernity" and the discussion and comment?[5] Thanks, Slrubenstein 23:03, 8 Dec 2004 (UTC)

The Humungous Image Tagging Project

Hi. You've helped with the Wikipedia:WikiProject Wiki Syntax, so I thought it worth alerting you to the latest and greatest of Wikipedia fixing project, User:Yann/Untagged Images, which is seeking to put copyright tags on all of the untagged images. There are probably, oh, thirty thousand or so to do (he said, reaching into the air for a large figure). But hey: they're images ... you'll get to see lots of random pretty pictures. That must be better than looking for at at and the the, non? You know you'll love it. best wishes --Tagishsimon (talk)

Village Pump archives format change

Hi JessW, I wanted to let you know that I've changed (for the better I hope) the format of the Village Pump archives slightly. I hope you don't mind ;-) Paul August 15:06, Dec 10, 2004 (UTC)

By the way, I forgot to mention, what a good job you've been doing there ;-) Paul August 15:08, Dec 10, 2004 (UTC)

Looks great. Took me a sec to figure it out, as I put the listings at the bottom so they would be easier to find, but actually, your way makes the ToC clearer and is generally better. Good job. JesseW 19:46, 10 Dec 2004 (UTC)

Thanks, glad you like it. Paul August 19:54, Dec 10, 2004 (UTC)

Article Licensing

Hi, I've started a drive to get users to multi-license all of their contributions that they've made to either (1) all U.S. state, county, and city articles or (2) all articles, using the Creative Commons Attribution-Share Alike (CC-by-sa) v1.0 and v2.0 Licenses or into the public domain if they prefer. The CC-by-sa license is a true free documentation license that is similar to Wikipedia's license, the GFDL, but it allows other projects, such as WikiTravel, to use our articles. Since you are among the top 1000 Wikipedians by edits, I was wondering if you would be willing to multi-license all of your contributions or at minimum those on the geographic articles. Over 90% of people asked have agreed. For More Information:

Multi-Licensing FAQ - Lots of questions answered
Multi-Licensing Guide
Free the Rambot Articles Project

To allow us to track those users who muli-license their contributions, many users copy and paste the "{{DualLicenseWithCC-BySA-Dual}}" template into their user page, but there are other options at Template messages/User namespace. The following examples could also copied and pasted into your user page:

Option 1

I agree to [[Wikipedia:Multi-licensing|multi-license]] all my contributions, with the exception of my user pages, as described below:

OR

Option 2

I agree to [[Wikipedia:Multi-licensing|multi-license]] all my contributions to any [[U.S. state]], county, or city article as described below:

Or if you wanted to place your work into the public domain, you could replace "{{DualLicenseWithCC-BySA-Dual}}" with "{{MultiLicensePD}}". If you only prefer using the GFDL, I would like to know that too. Please let me know what you think at my talk page. It's important to know either way so no one keeps asking. -- Ram-Man (comment| talk)

fix-up

Hi Paul, Thanks for removing that tag from the Harvard science center article and marking it as a stub. The polaroid-style architecture and collections of old scientific instruments housed there might make the building worthy of an independent article, but the link was just a test I meant to only preview and forgot. Tobacman 23:35, 16 Dec 2004 (UTC)

http://en.wikipedia.org/wiki/Asbestosis_-_Compensation_and_Liability_Disputes

Thanks for your contribution.

Significant revision in progress. Please re-visit and comment, if you consider appropriate.

Cayley-Newbirth operation matrix

Hi, I'm trying to figure out what's going on with regards to Cayley-Newbirth operation matrix. On VFD, you wrote: "Delete This is a hoax. —ExplorerCDT 13:31, 24 Dec 2004 (UTC)". Why do you think this article is a hoax? Previously you wrote: "If it is a hoax, it's at least 40 years old. It appears (albeit as the Cayley Operational Matrix, without Newbirth credited) via several mentions and footnotes in my 1964 edition of Handbook of Mathematical Functions from the U.S. National Bureau of Standards. That alone leads me to think it isn't a hoax. —ExplorerCDT 07:56, 22 Dec 2004 (UTC)" Why did you change your mind? And can you tell me where in Handbook of Mathematical Functions "Cayley Operational Matrix" is mentioned. Thanks. Paul August ? 23:06, Dec 24, 2004 (UTC)

(The above copied from User talk:ExplorerCDT Paul August ☎ 23:38, Dec 24, 2004 (UTC))

What's going on? I misread Handbook of Mathematical Functions, thinking it wasn't a hoax. Now, after being told by several people it is, I retract my vote saying it's a hoax. For some stupid power-mad reason, I have User:Charles Matthews accusing me of planting it, or having conspiratorial knowledge without any proof, and harassing me to no end. I wish you people, pardon the expression, would just go fuck off. —ExplorerCDT 23:11, 24 Dec 2004 (UTC)

Thanks for your reply. I'm sorry if I'm bothering you, but I think it is important to get to the bottom of this. I have spent countless hours editing, trying to make Wikipedia a better encylopedia, I presume, so have you. "Hoax" articles are very bad for Wikipedia. So, are you saying that there are no mentions of "Cayley Operational Matrix" in Handbook of Mathematical Functions that you are aware of? Can you tell me what passages from Handbook of Mathematical Functions you misread, which made you think there were? Paul August ☎ 23:37, Dec 24, 2004 (UTC)

You're not too much of a bother. I disagree on the importance of it, however. I can't remember off hand what the passages were, unfortunately I'm in the middle of a move and I packed up HoMF a few days ago...otherwise I would check. —ExplorerCDT 23:46, 24 Dec 2004 (UTC)

Blunsdon United

Hello Fennec, on Dec 13th, the FVD discussion for Blunsdon United: Wikipedia:Votes for deletion/Blunsdon United was deleted (by you) from the Wikipedia:Votes for deletion/Old. What was the result? Blunsdon United was not deleted but it still has a VFD tag, and no result is indicated on Wikipedia:Votes for deletion/Blunsdon United. Thanks. Paul August ☎ 20:40, Dec 30, 2004 (UTC)

Sorry to be a bother, but I'm trying to understand the vfd process better. Can I assume that no concenus was reached to delete Blunsdon United? How can I tell who determined the result? Can I remove the vfd tag from that article (I'm not a sysop)? Is Wikipedia:Votes for deletion/Blunsdon United supposed to be updated to reflect a result? Can anyone do that? should I? Paul August ☎ 20:17, Dec 31, 2004 (UTC)

Dreadfully sorry about this- I believe I was in the middle of dealing with multiple articles at once when either Wikipedia or my Internet connection failed. Yes, it survived VFD. I have removed the tag and placed the appropriate note on the talk page. Thanks for bringing this to my attention. -Fennec (はさばくのきつね) 20:27, 31 Dec 2004 (UTC)

Thanks for your reply and taking care of Blunsdon United. I would have been glad to have fixed things myself, but was unsure of whether I had the authority to do so. Paul August ☎ 20:36, Dec 31, 2004 (UTC)