Definition talk:Idempotence

Probably no point in defining an "idempotent algebraic structure" as this has already been implicitly covered in "idempotent operation". What we have got is Definition:Idempotent Semigroup which is significantly more useful because it combines the concepts of closure, assoc and idemp in one definition, and this grouping is significant enough, and crops up frequently enough, to be treated as a type of object in its own right. It also makes definitions of objects which have these three properties somewhat shorter and (IMO) easier therefore to comprehend. (It is assumed that anyone making an investigation into e.g. semilattices will be sufficiently familiar with abstract algebra to be able to take semigroups and idempotence in their stride - and those who don't have a link to some easy pages to familiarise themselves with. --prime mover 05:37, 28 January 2012 (EST)


 * And another philosophical point: is there any direct need to introduce a "set" as such? The definitions "mapping" and "binary operation" should be enough, as the fact that they themselves are defined with relation to "sets" already means that it is already implicit that $S$ is a set. However, I have introduced the concept at the top of the page. --prime mover 05:42, 28 January 2012 (EST)


 * I feel there is a need to introduce a set; if only for the fact that the definitions of mapping and binary operation may be generalised in the future to cover more than mere sets. Also, readers should not be bothered with even the remote question as to what $S$ is; for all they could know, there could be an omission stating that $S$ is some specific type of set. Clarity above everything.


 * As to your first point, I will look through the various definitions of algebraic structures and link them together where I can. --Lord_Farin 06:16, 28 January 2012 (EST)