Talk:Reflexive relation

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[edit] 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!

[edit] 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)

[edit] 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

[edit] 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)

[edit] Incorrect?

From my notes a reflexive relation is:

(x)((\existsy)(Rxy \lor Ryx) \to 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)

[edit] 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)