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The following citation agrees on the phrase "serial relation" but differs from the concept of this article, so it was removed:
This article pertains to relatons R such that ∀x∃y xRy. — Rgdboer ( talk) 21:16, 7 April 2018 (UTC)
The article currently defines a serial relation as
However, Binary relation#Formal definition defines the domain of a binary relation R as
making the definition of a serial relation as it is currently worded vacuous or at least somewhat inconsistent with the definitions given at Binary relation (I think). – Tea2min ( talk) 07:07, 24 May 2018 (UTC)
Complete relation currently redirects to Serial relation, but the term "complete relation" is not mentioned there at all. Complete relation used to redirect to Total relation before that was turned into a redirect to Serial relation, and Total relation used to mention "complete relation" as a synonym (see old version of "Total relation"). – Tea2min ( talk) 13:52, 30 May 2018 (UTC)
"Serial relation" is little used while "Total relation" has come to the fore, especially in contrast to partial function. The concept of Totality is important in algebra as seen in the template on group-like structures. Thus it appears this article should be moved to Total relation (a redirect currently brings readers here). Does anyone object to such a Move? — Rgdboer ( talk) 23:53, 17 July 2019 (UTC)
References for Total have been supplied. Since the confusion with Connex should not be perpetuated, and a reference is not at hand, the following was removed:
Our efforts are coordinated to assist readers to find current terminology. — Rgdboer ( talk) 20:58, 19 July 2019 (UTC)
Serial relation is a generic term referring to various relation Russell used in 1903 to develop order theory through series. Today the topic was added as "Russell's series". Currently total relation is a disambiguation claiming that Connected relationis an alternative article. Yet the only reference given is Aliprantis and Border (2007) Infinite Dimensional Analysis. The Introduction and Characterization sections are more commonly called Total. Rgdboer ( talk) 23:41, 17 September 2021 (UTC)
The links to this article are being pruned and sent to Total relation, which is the commonly used term. Serial relation is a concept developed by B. Russell to discuss series, both infinite and finite. Rgdboer ( talk) 03:39, 13 April 2022 (UTC)
Well “total relation” and “total order” might be thought total for the same reason, but the adjective “total” has different meanings in these phrases. References are being assembled and note taken of the citation requested at homogeneous relation where “connected” is described as possibly being “total”. Rgdboer ( talk) 03:16, 14 April 2022 (UTC)
but the adjective “total” has different meanings in these phrases" That's exactly my point. We should try to avoid such ambiguous words, in order to prevent confusion. - Jochen Burghardt ( talk) 08:45, 14 April 2022 (UTC)
An order may be total as a relation, but not be a total order!! This difficulty in descriptive language suggests these notes: heterogeneous relations may be total, but orders are endorelations, and the connectedness axiom needs that context. General readers may be interested in relations per se, or orders, and the texts of articles ought to direct them accordingly. A redirect total relation (order) for Connected relation provides an expedient for order theory contexts. Rgdboer ( talk) 03:51, 17 April 2022 (UTC)
Seems to be a duplicate article. 1234qwer 1234qwer 4 17:32, 4 May 2022 (UTC)