Talk:Tychonoff's Theorem

Various questions
a) The definition for "tree":


 * In the definition for "tree", the symbol for the ordering given is for a generic strict ordering, while the definition for a partially ordered set as given on ProofWiki calls for a standard partial ordering which includes reflexivity.


 * Similarly, there is a mention of "strictly bounded from above". I have never seen the term "strictly bounded" before and I have had difficulty finding a reliable citation for its definition.

Question is: how important is the "strictly bounded" and the "strict ordering" in the above definition?

b) There's more things, but I have to go and do something else now, I will be back. --prime mover 03:16, 31 December 2011 (CST)


 * I assume that there are two equally good definitions of a partially ordered set --- with or without strict inequality. The definitions of a well-order relation and of a tree in Wikipedia use strict order.  Since one is expressible in terms of the other, i do not think this is an issue, maybe a note needs to be added to the definition of poset in ProofWiki.


 * It's a good point, but as you say not important (and the fact that it is not important is also a good point!) so the definitions in the pages are to be amended so as to allow for such ordered sets to be defined using strict orderings. Another page may then be added to explain that the two styles of definition are equivalent.--prime mover 07:29, 31 December 2011 (CST)


 * I put "strict" in parenthesis to show that it can be omitted from the sentence without change of meaning. I put it because "open" intervals are often used in the proof.  You are right that these definitions need to be removed from the article and it needs to be linked to other articles. --Cokaban 04:57, 31 December 2011 (CST)


 * This last exercise is under way. --prime mover 07:29, 31 December 2011 (CST)

Style
To have equations flushed left, it would be easier to set an option like \documentclass[fleqn], and then use \[ \], is this possible? --Cokaban 05:17, 31 December 2011 (CST)


 * Not as far as I know. This is not a full $\LaTeX$ environment. Instead it uses $\LaTeX$ structures within a MediaWiki environment, and as such uses MediaWiki page formatting.


 * In order to get equations to flush left, use this technique:
 * $d := b^2 - 4 a c$
 * Simple as that. Colons are used to indent.


 * We do have a technique for aligning equations, which is used on most pages on this site. Click "Random proof" and it will (eventually) take you to a page where you will see it used.


 * I plan to work through the page and convert it to house style (e.g. each definition and lemma on its own page, dollar-signs not backslash-bracket for delimiters, equations are deliberately not centered on the page, sentences are kept short, and one sentence per line, and so on), but it takes time to do. --prime mover 06:44, 31 December 2011 (CST)