User talk:L0mars01

Welcome
Welcome to ProofWiki! Since you're new, you may want to check out the general help page. It's the best first stop to see how things are done (next to reading proofs, of course!). Please feel free to contribute to whichever area of mathematics interests you, either by adding new proofs, or fixing up existing ones. If you have any questions please feel free to contact one of the administrators, or post your question on the questions page.

Here are some useful pages to help get you started:
 * Community Portal - To see what needs to be done, and keep up to date with the community.
 * Recent Changes - To keep up with what's new, and what's being added.
 * Check out our house style if you are keen on contributing.
 * Main Page talk - This is where most of the main discussions regarding the direction of the site take place. If you have any ideas, please share them!

Cheers!


 * --Your friendly ProofWiki WelcomeBot 19:50, 6 September 2012 (UTC)

On Definition:Characteristic Function
Please refrain from outright deletion of material in the future. While it may be true that the definition for a relation is an instance of that for sets, this doesn't imply that there is no added value in mentioning the special case. A relation is conceptually a lot different from a set (while it still is one) and so the distinction is merited. In fact, even if there was only one source mentioning the specific definition for a relation, for completeness' sake we at PW would aim to include that definition. Compare Definition:Neighborhood (Metric Space) which is an instance of Definition:Neighborhood (Topology). Thank you for your anticipated cooperation. --Lord_Farin (talk) 07:52, 22 September 2012 (UTC)


 * I'll endorse this. There was a specific reason for including the definition for a relation: it was a crucial step along the way towards the Gödel theorems (still unfinished while I work on other stuff).
 * ProofWiki is not so much an encyclopedia, it is more akin a dictionary. As such it includes a lot of small details which would in a more discursive presentational strategy be ignored. Users have expressed delight at such inclusivity as it can provide essential clarification of intellectual stumbling-blocks. --prime mover (talk) 08:02, 22 September 2012 (UTC)


 * A good definition is concise and clear. The issue was the article presented a characteristic function for a relation apart from that for a set by recreating the entire definition. This is like defining 'telephone' and 'red telephone' separately, without saying a red telephone is 'a telephone that is red'. This is problematic to the reader on a number of grounds.
 * It doesn't say one 'definition' is derived from the other when it should. This misleads the reader ('you mean to tell me a red telephone is completely different from a telephone?') with the illusion they are logically unrelated, proper definitions and that distinct definitions are needed for completeness, which isn't clear or concise.
 * Logical consequences aren't definitions. A reader will reasonably expect the broadest definitions (possibly broken into parts) on the main page. To present a derived instance as a definition is either incorrect or a source of confusion to a reader reasonably expecting the broadest definitions. Either detracts from clarity. ('I looked up telephone. Why are you telling me about red telephones?')
 * This misleads a reader who would need to read through both 'definitions', and make the correct associations to discover the distinction was illusory when the author could have just told them. Such preventable guesswork diminishes clarity. ('Why did you write all of that instead of tell me a red telephone is a telephone that is red?') A better approach is to direct the reader to the set definition of a relation and tell them a characteristic function for a relation is one for a set. ('Red is color, a feature independent of telephones. A red telephone is a telephone. And it's red.') As a convenience, an author could present that instance of the general definition as a consequence, not a new definition as the original presentation's appearances suggest.
 * Extra information not clearly classified as such can burden a reader rather than help them. Redundancy creates 'noise' that detracts from brevity, and confuses a reader who doesn't yet know the statement is redundant and parses it very closely to 'comprehend the new idea'. As a result, they may either discover the redundancy and fault the author for not stating so before wasting their time ('Oh, a red telephone is just a telephone that is red. Thanks a lot, genius.'), OR trust the redundancy was meaningfully put there and waste their time testing for 'different' cases ('hrm, I guess red telephones aren't ordinary telephones.'). Neither is a service to the reader.
 * That, in abundantly verbose fashion, is why I felt the definition for relations needed to go or something different needed to be written in its place.--L0mars01 (talk) 02:36, 23 September 2012 (UTC)


 * I see your point and appreciate your taking the time over this. In your opinion, would it be sufficient to add somewhere near the top of the Relations page that the c.f. on a relation is a specific example of a c.f. on a set?
 * The base that I'm trying to cover is the one where the reader is following through a thread of thought (from an external source which may not have been clearly-enough written - I have encountered some of these) where the c.f. of a relation is introduced without the general "set" definition having been introduced previously. In that case this will derail a possibly-already-out-of-depth reader with a concept which, on the surface, does not correspond to that which he/she is reading. So the existence of the definition for "relation" is there, deliberately for that reason.
 * I confess that I fell into the trap of making the assumption that a reader will automatically get the fact that they are instances of the same thing - you're right of course, this needs to be made obvious. --prime mover (talk) 08:19, 23 September 2012 (UTC)


 * Though I think that'd help, an uninitiated reader's opinion is more valuable. It'd be worth checking how other definitions treat this, too. Definition:Ring (Abstract Algebra) (maybe not the best example) places the definition under a section titled 'definition' and related ideas under separate sections that don't fall under the 'definition' section. It also has an 'also see' section that lists a link to Definition:Commutative Ring and other related definitions. Following that lead, the article's structure could change from
 * Definition
 * Set
 * Relation
 * Also known as
 * to something like
 * Definition
 * Characteristic function for a relation
 * Also known as
 * or
 * Definition
 * Also known as
 * Also See
 * Characteristic function for a relation [link to dedicated definition]
 * You may think of better ideas.--L0mars01 (talk) 13:30, 23 September 2012 (UTC)


 * If such a work hasn't presented the reader with sets yet, they're probably more likely to use the notations like $x \mathcal R y$, $\mathcal R \left({x,y,z}\right)$, etc. Also, though I've never come across characteristic functions before, I have seen contexts where relations are undefined terms, e.g. systems which don't use sets. If your aim is to address things like that, I recommend using that notation. --GFauxPas (talk) 13:38, 23 September 2012 (UTC)


 * "You may think of better ideas": Of those suggested, I think the system we have in place is optimal. --prime mover (talk) 16:07, 23 September 2012 (UTC)
 * ... and I'm not saying that "If such a work hasn't presented the reader with sets yet", that would be unfeasible. What I was attempting to communicate was: such a work may not have presented the characteristic function of a set yet, which is a different thing altogether. --prime mover (talk) 16:09, 23 September 2012 (UTC)
 * Oh, never mind what I said then. --GFauxPas (talk) 16:28, 23 September 2012 (UTC)


 * With the small amended line ("The concept of c.f. carries over directly to relations") I think that the issue is adequately dealt with. I thank L0mars01 for bringing this to our attention and investing the time necessary to explain his point thoroughly. There is an interplay here between generality on the one hand and specific instances on the other hand; going too much into the first would lead to malignant situations where, e.g., all proofs about matrices would be 'proofs by intimidation' using functional analysis results. The consequences of too specific subdivisions without clear references and explanation are sufficiently expressed in the red telephone analogy above.
 * LBNL, I hope you are willing to put some more of our (internally celebrated) constructions through the test of your unspoilt critical eye. Still, rather than deleting stuff outright, please use the associated talk pages to raise discussions of this type. --Lord_Farin (talk) 08:15, 24 September 2012 (UTC)

learning the ropes
A few quick points to mention ...

a) If a proof is different from that which is already in place, then add it as a separate proof rather than amend what's already there. This website was intended as a compendium, and we like to err on the side of inclusivity.

b) If this results in one part of a multipart proof (like this one) having more than one proof for it, then what we would like to do is separate out the parts into separate pages, each proving that small part. Then the multiple nature of that one part is easily modularised.

c) Using the "\def" command is something which we experimented with briefly at one time, but its use is not fully supported by MediaWiki. What we have found is that if you subsequently transclude a page into another one, the "\def" commands are not carried over, and the page suffers as a result. Hence all LaTeX needs to be written out in full. A slight inconvenience, but it has the advantage that all LaTeX is understandable at the base level.

d) Note the page style that has evolved, where full use of the screen space is exploited. The Equation template, for example, where one equation per line is de rigueur. We also make use of \displaystyle for \bigcup and the like.

You might want to familiarise yourself with this page: Help:Editing/House Style. Until then, you will probably find your pages will be enhanced by the "tidy" and "refactor" templates appearing on them. These are markers for us fussy types to go through and rearrange the pages to match the house style. --prime mover (talk) 19:42, 25 September 2012 (UTC)