Talk:Symmetric relation

Properties "containing" relation

I think it is a good category to have. This page is small, its true, but categories help people find exactly what they're looking for. Most people are looking for something specific and don't want to read the entire article - no matter how small. I know it was a badly written title, but i hoped that people would *fix* it - not delete it. Can I put the title back in as "Combinations of Symmetric property and other properties" ? Wordy but i can't think of anything better right now. I sorta actually like my original better - more succinct. Fresheneesz 05:19, 1 December 2005 (UTC)

There is nothing wrong with using the metaphor of containment to describe relations among properties corresponding to conjunction of predicates. Jdthood 2 December 2005

Merging symmetric and antisymmetric

User 68.6.112.70 merged Antisymmetric relation. I've reverted the merge, because I'm not convinced that this is a good idea. Please diiscuss here before remerging these two articles. Thanks. Paul August ☎ 03:33, 22 November 2005 (UTC)

Hey, I merged the articles to resemble the merged pages "reflexive relation" and "irreflexive relation". It would be fine for them to be separate pages - but they are hard to read as it stands - and the asymmetric part of the antisymmetric page doesn't really fit since it is the combination of two relational properties.

- I'm open to comments and would like to know why you think my organization isn't helpful. Fresheneesz 05:02, 22 November 2005 (UTC)

Hi Fresheneesz. Thanks for coming here to discuss your proposed changes. Yes, I'm not particularly happy with the merge of "reflexive" and "irreflexive" either. Among other things, I think that having them in the same article unfortunately reinforces the misimpression (which naturally comes form their names) that every relation is either symmetric or antisymmetric, (or reflexive or irreflexive) I would prefer to keep the articles separate. I did like some of the things you did in the merge, for example having a separate Examples section. Can you elaborate on what you think the problems are with this page as it is now? Let's see if together, we can fix them. Thanks again. Paul August ☎ 17:11, 22 November 2005 (UTC)

Well one inherint problem with having many, but short, articles is that they become more cumbersome to switch between. I think that strongly noting the misimpressions in a merged article would be a good way of doing it. But another good way to do it would be to keep them separate, and touch them up - also link them to eachother *while* noting the misimpressions. Yet another way to go would be to merge ALL types of relations (or perhaps split the properties into subcategories).

I think for starters we should probably just organize the relation property pages with one or two headers for examples and such. It would probably also be useful to standardize the format of these pages. I have already made some tables for the example relations for a couple different types of relation properties (i'm waiting for Amane) Fresheneesz 21:15, 22 November 2005 (UTC)

I still think it is more concise and easier to read if the pages are merged. One can directly compare reflexivity and irreflexivity (noting that irreflexive is not merely the lack of reflexivity) without jumping between pages. Can I merge again? I'll have to say no answer means yes. Fresheneesz 18:37, 28 November 2005 (UTC)

I prefer to have separate articles for separate things. Yes having both properties in the same article, would make it easier to compare these two properties, but I think the vast majority of readers will simply want to know either about symmetric relations or antisymmetric relations, not both. I find it annoying when I want to look up something like "antisymmetry", and I get the "symmetry" page, and I have to read down the page to find what I'm looking for. Paul August ☎ 20:16, 28 November 2005 (UTC)

Alright, you wanna fix up the reflexive and irreflexive page? Fresheneesz 21:16, 28 November 2005 (UTC)

I'm going to merge the symmetric relation page, and the antisymmetric relation page again. I think this is the best way to exemplify that they are not exact opposites. I'll wait a bit for comments before i proceed. Fresheneesz 03:01, 13 December 2005 (UTC)

I still have the same objections noted above. Paul August ☎ 04:46, 13 December 2005 (UTC)

well crap. Then if you don't want to split up reflexive and irreflexive, i'll have to do it... later. Fresheneesz 11:01, 13 December 2005 (UTC)

I hope your "well crap" was of the friendly and good natured kind ;-) If you are feeling frustrated with me them I'm sorry, please accept my apologies. I will be happy to split up reflexive and irreflexive if you want. In fact I have been thinking about rewriting all of these articles, but I just haven't gotten around to it yet. i've been (and am) a bit busy in real life I'm afraid. Paul August ☎ 15:40, 13 December 2005 (UTC)

Not logical opposites...

Regarding this:

   Note that symmetry is not the logical opposite of antisymmetry....
   There are  no relations which are both symmetric and antisymmetric...,
   there are relations which are neither symmetric nor antisymmetric...,
   there are relations which are symmetric and not antisymmetric...,
   and there are relations which are not symmetric but are anti-symmetric....

In order to show that two terms are not logical opposites of each other, it suffices to show that something either satisfies both or fails to satisfy both. Showing that something satisfies one and not the other does not serve the purpose of showing that the terms are not logical opposites of each other.

Jdthood 18:27, 5 December 2005 (UTC)

The equivalence relation is an example of a symmetric and anti-symmetric relation. 131.111.184.91 (talk) 19:20, 18 November 2015 (UTC)

Marriage

[User:Arthur Rubin]: "is married to" is not the same as "is married to the same person as". "is married to" is a (typically) binary relation between spouses. So I was wrong to put it in the antisymmetric column. I'm changing that example. "is married to the same person as" implies there are at least 3 people married to each other. Libcub (talk) 20:51, 29 August 2014 (UTC)

If a relation is symmetric and antisymmetric, it is coreflexive. "Is married to" is not.

x is married to the same person as y iff (exists z) such that x is married to z and y is married to z.

Given the usual laws about marriage:

If x is married to y then y is married to x. (symmetric)

x is not married to x (irreflexive)

A person is married to at most one other person.

It follows that "x is married to the same person as y" iff x is married and x = y. — Arthur Rubin (talk) 20:56, 29 August 2014 (UTC)

The third law is not valid in the case of polygamy. GeoffreyT2000 (talk) 04:05, 28 September 2015 (UTC)

Relative to transitivity/antitransitivity

@Jochen Burghardt I noticed you reverted an edit with the comment:

> imo, names are pretty similar - symmetric:unsymmetric:antisymmetric is much like transitive:intransitive:antitransitive

That's fine, I just had some questions. Did you see at least my intention in the comment? The concepts of symmetric/not symmetric and symmetric/antisymmetric are orthogonal, as discussed in the article. The concepts of transitive/intransitive and transitive/antitransitive are not; antitransitive implies intransitive.

I also didn't see a definition of unsymmetric. I assume this means the same as not symmetric?

It would be nice to get at least some link to the other article in here, whether to highlight the differences or the similarity. Not the end of the world though. Davidvandebunte (talk) 16:04, 1 March 2023 (UTC)

I think I got your intention, and I find your remark quite interesting. Indeed I meant "not symmetric" by "unsymmetric" (this may be an unusual term - I'm not a native English speaker).

As for the implication: antisymmetry also implies unsymmetry, with few expections. On the non-strict side, a relation can be both antisymmetric and symmetric, but only if it is coreflexive, i.e. if it implies equality of its arguments. On the strict side, a relation that is both symmetric and asymmetric, must necessarily be empty. With these exceptions, the similarity "symmetric : unsymmetric : antisymmetric is much like transitive : intransitive : antitransitive" from my edit summary applies. So there are three grains of salt to be taken with the similarity: (1) the strict/non-strict distinction is present on the symmetry, but absent on the transitivity side, (2) in the non-strict case each coreflexive relation is an exception, (3) on the strict side, the empty relation is an exception.

I'm not sure if my clumsy explanations can be summarized to a nice little remark in the article. - Jochen Burghardt (talk) 16:54, 1 March 2023 (UTC)

The word "unsymmetric" is uncommon but doesn't sound like a completely invented word, at least to me. If we were to invent a word then insymmetric would be appropriate, but it sounds even stranger.

I see what you were trying to say much better now, and agree that although your explanation makes sense, it would be a bit distracting in the context of the article. We can leave it as "less is more" for now. Davidvandebunte (talk) 18:00, 1 March 2023 (UTC)