Talk:Reflexive relation

prove this
How do you prove this?

If (X is a strict order of Y) AND (Y is a partial order of Z) => (X is a strict order of Z) You have to use asymmetry and antisymmetry from both definitions somehow to prove X STRICT Z

Please help!

Irreflexive
A relation that is not reflexive is irreflexive or aliorelative.

Is that really what irreflexive means? I thought it meant something stronger than not reflexive, namely that no element bears the relation to itself. Josh Cherry 3 July 2005 17:01 (UTC)

irreflexive
i agree,

In logic, a binary relation R over a set X is irreflexive if for all a in X, a is not related to itself. When you replace the "all" part for "some" you will get a relation that is not reflexive nor irreflexive. So, "irreflexive" is stronger than "not reflective". Example: if "a likes b" is irreflexive then someone cannot likes his/her selves; if some but not all people like themselves then "a Likes b" is neither reflexive nor irreflexive

Positioning of examples and properties
Oleg, i dunno whod get pissed because of the way headings are placed on this tiny page, but I put properties above examples cause examples is long, huge, and easily visible - while properties sorta gets lost in the haze down there. I'm pretty sure placing properties above didn't obscure the examples any. Fresheneesz 05:05, 1 December 2005 (UTC)


 * OK, I will put back. Oleg Alexandrov (talk) 05:30, 1 December 2005 (UTC)

Incorrect?
From my notes a reflexive relation is:

(x)((y)(Rxy Ryx)  Rxx)

which includes: "...is the same ___ as..." "... is equal to ...," "...is equal to or less than ...," "... is equal to or greater than ...," "...is a proper subset of ...,"

and a totally reflexive relation is:

(x)Rxx

which includes "...is identical to ..."

Gregbard 11:49, 28 August 2007 (UTC)

Incomprehensible line
The following line is incomprehensible to me and probably a lot of other people:

At least in this context, (binary) relation (on X) always means a subset of X×X, or in other words a function from a set X into itself.

I'm sure it's very precise, but for conveying an understanding of the reflexive relation, it fails miserably. Remember that this content is supposed to be accessible to everyone and not a dusty, old reference for those who are already familiar with the material.

indil (talk) 21:42, 5 December 2007 (UTC)

List of examples
Good example ? Division is not reflexive for all real (natural with 0) numbers. Why? You can't divide by zero. 86.61.232.26 (talk) 12:18, 13 April 2009 (UTC)

Rewrite
I've gone ahead and rewritten most of the article. It's missing a few minor details from the original, but has all the important stuff, and given the previous state of the article I think it's more than a fair trade. (And they can be worked back in later anyway.) 24.76.174.152 (talk) 09:38, 30 August 2009 (UTC)


 * It looks much better. By the way, you might want to consider registering a user name. Ironically, a username unrelated to your real identity is likely to be more anonymous than your IP address. And using a username helps other people communicate with you. &mdash; Carl (CBM · talk) 11:52, 30 August 2009 (UTC)


 * The lack of username isn't out of some misguided belief it's more anonymous this way, I'm just too lazy and don't really edit Wikipedia much anyway so it's not of much benefit. 24.76.174.152 (talk) 08:33, 31 August 2009 (UTC)

“≲”? ≤
The page says “the reflexive closure of x<y is x≲y” and “the reflexive reduction of x≲y is x<y”. Exactly what is the symbol “≲” supposed to mean here? I first assumed that it is just a typo and should be “≤” instead, but it occurs twice. — Miym (talk) 23:34, 30 August 2009 (UTC)


 * Yeah, that must have been some kind of error. The character in question was Unicode point 2272 (see Unicode_Mathematical_Operators and ). I fixed it. &mdash; Carl (CBM · talk) 23:49, 30 August 2009 (UTC)


 * It was, sorry about that. Thanks for fixing it. 24.76.174.152 (talk) 08:29, 31 August 2009 (UTC)

Graph theory
This article could be made much clearer if a reflexive graph were included. -Rlinfinity (talk) 19:11, 11 April 2010 (UTC)

Examples section
With the examples, shouldn't there be a definition of what set the relations are reflexive or irreflexive on? I would assume that it was the original authors intention that the examples refer to the set of real numbers, but I think that should be specified.

For example, on the set S = {5,3}, the relation divides is not reflexive, but is listed in the examples of being reflexive. Collinslyle (talk) 22:38, 14 January 2016 (UTC)


 * Huh? 3 divides 3 and 5 divides 5, so it's a reflexive relation.  Every reasonable definition of divisibility has that x divides x for all x. --JBL (talk) 23:07, 14 January 2016 (UTC)