Wikipedia:Reference desk/Archives/Mathematics/2012 June 4

= June 4 =

definition of set
set is a well defined collection of objects. but is {1,2,a,b} can be called a set? do the elements in the set need not have any relation among them? — Preceding unsigned comment added by Sateesh shivaraju (talk • contribs) 15:53, 4 June 2012 (UTC)


 * Well, they do have a relationship - they're members of the same set. There could also be other relationships. For example, the set of items listed by Sateesh shivaraju is {1,2,a,b}. But my guess is that you're approaching this from a computer science perspective, where numbers and characters have different "types" and containers are typically limited to only holding a single "type" of object. That, however, is a limitation of computers, not of mathematics. The divisions in mathematics aren't as "predefined" as those in computer science. To some extent you could argue that all members of a set are of the same kind, but that's a little facile, because in mathematics you can shrink or expand the definition of "the same kind" to include or exclude whichever objects you feel like at the time. For example, the set I gave above only contains items of the type "things that can be listed by Sateesh shivaraju". Such mathematical "types" don't have to be rigidly predefined like the integer/float/string types in programming. -- 71.35.105.132 (talk) 17:07, 4 June 2012 (UTC)


 * Yes, that is a set, it's just not a commonly predefined set, like the set of all integers. Arbitrary sets are also sets.  Or, to put it in math terms, "the commonly predefined sets are a proper subset of the universe of all sets". :-) StuRat (talk) 19:47, 4 June 2012 (UTC)
 * Nay, the commonly predefined sets are rather a class than a set, lest we be a-venturin' too close to certain paradoxes. :) 24.92.85.35 (talk) 00:25, 6 June 2012 (UTC)