Talk:Equivalence class

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Mathematics rating:	Start Class	High Priority	Field: Foundations, logic, and set theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. A very important subject. Much work needed. And references too. Geometry guy 00:11, 17 June 2007 (UTC) Isn't the equivalence class fundamental to classification; and doesn't classification found many if not every field of study: not just those listed above? Geologist (talk) 07:40, 20 December 2007 (UTC)

I think some mention should be made of representative elements of an equivalence class and reduction relationships that lead to such representations.

My math is old, rusty and unused. Therefore I find the article a little confusing in some places. In particular the first paragraph of Properties: "that any two equivalence classes are either equal or disjoint."

I think it would be great if someone would add correct, simple examples. For example by elaborating the colored cars example.

As far as I can tell from the equivalence_relation page, there can be different equivalence relations leading to different equivalence classes, which may overlap between two equivalence relations. So the quotation above perhaps should continue "under the same equivalence relation".

Even the example given can be viewed in two ways: either partitioning the set of cars into a partition per color (x~y == color(x) = color(y)) , or one partition of green cars and one of non-green cars (x~y == color(x) = green iff color(y) = green). Is it somehow interesting that the equivalence class "red cars" is also an equivalence class within the subset of non-green cars?

It would also seem that the number of possible different equivalence classes over all possible equivalence relations on a non-empty set A is 2^|A|-1. But there could be fewer. Consider this set of cars (color,brand,model): { "blue Ford Galaxy", "blue Ford Focus", "silver Opel Zafira", "red Opel Astra", "red VW Polo" }. Partitioning on color and partitioning on brand both yield the set of blue Fords as one of the equivalence classes, so there are less than the 31 possible distinct equivalence classes, is that correct?

--Lasse Hillerøe Petersen 09:35, 17 July 2007 (UTC)

[edit] Who is the Wikipedia's audience?

There are (IMO) very few topics in the Wikipedia more important to more subjects than 'equivalence class'.

This articles raises the question of who articles are written for. Geology articles, I can assure you, are simplified to the level of inaccuracy. It was to this article I was about to refer discussions on classifying the sciences. My claim was that a physical science like chemistry was more abstract than a natural science like geology, because the former studied philosophically identical objects, like the element gold, whereas geology studied equivalence classes of specimens, like the mineral gold (which varies in properties). Were I to relate objective properties, equivalence, equivalence classes, abstract & concrete, a general reader would come here for a clear explanation of 'equivalence class'.

Classification founds science and many other unrelated fields. Perhaps this article could be broadened in scope, lengthened, offer the reader motivations by examples (as the previous discussion has done), proceed from the concrete to the abstract, and attempt to use intuitive English rather than offer an explanation in purely formal, symbolic logic. There would be plenty of room for that in a mathematics section. A reference would be nice. Geologist (talk) 09:01, 20 December 2007 (UTC)