Set Theory and Logic


Relations Properties Compatibility

Authors: Misha Mikhaylov

It was shown here that just transitive relation may be considered as closure and its presence is necessary and sufficient to order a set linearly, and it is not possible to do this by using other relation’s property – neither reflexivity nor symmetry. By interaction, it occurs due to ambiguity of their definition – it was shown earlier (ref. [3]) they have various appearances. Among them just the only transitivity is determined uniquely. At the same time the last one doesn’t exist separately from any others. Circumstances of their joint existence are clarifying in this article.

Comments: 7 Pages.

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Submission history

[v1] 2014-09-25 14:54:50
[v2] 2014-09-28 13:34:49
[v3] 2016-02-25 11:57:16
[v4] 2016-02-27 04:59:59

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