Difference between revisions of "Talk:Equipotent sets"
From Encyclopedia of Mathematics
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(I deliberately used "family" to avoid the word "class" here, because of logical difficulties) |
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"Equipotence is an equivalence relation on a family of sets" — As for me, a "family" means, a mapping from an "index" set (to something). Here I'd say, on the class of all sets. But maybe dialects differ. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 20:30, 10 January 2015 (CET) | "Equipotence is an equivalence relation on a family of sets" — As for me, a "family" means, a mapping from an "index" set (to something). Here I'd say, on the class of all sets. But maybe dialects differ. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 20:30, 10 January 2015 (CET) | ||
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| + | Really, I see that the terminology is unstable. In "[[Centred family of sets]]" I see indexed family; but in "[[Upper bound of a family of topologies]]" I see that "family" is just another name for a set. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 20:38, 10 January 2015 (CET) | ||
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| + | :I deliberately used "family" to avoid the word "class" here, because of logical difficulties. An equivalence relation is defined as a subset of a certain set, but the class of all sets is a proper class, not a set, and so we have not defined an equivalence relation on a proper class of sets. On the other hands, to talk of a set of sets, while perfectly correct, seemed inelegant in this context. [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 21:17, 10 January 2015 (CET) | ||
Latest revision as of 20:17, 10 January 2015
"Equipotence is an equivalence relation on a family of sets" — As for me, a "family" means, a mapping from an "index" set (to something). Here I'd say, on the class of all sets. But maybe dialects differ. Boris Tsirelson (talk) 20:30, 10 January 2015 (CET)
Really, I see that the terminology is unstable. In "Centred family of sets" I see indexed family; but in "Upper bound of a family of topologies" I see that "family" is just another name for a set. Boris Tsirelson (talk) 20:38, 10 January 2015 (CET)
- I deliberately used "family" to avoid the word "class" here, because of logical difficulties. An equivalence relation is defined as a subset of a certain set, but the class of all sets is a proper class, not a set, and so we have not defined an equivalence relation on a proper class of sets. On the other hands, to talk of a set of sets, while perfectly correct, seemed inelegant in this context. Richard Pinch (talk) 21:17, 10 January 2015 (CET)
How to Cite This Entry:
Equipotent sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Equipotent_sets&oldid=36208
Equipotent sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Equipotent_sets&oldid=36208