Answer by user21820 for Bijection between collection C and proper class PC...
It is conceptually simpler if you work in a class theory such as NBG or MK, in which classes are actually objects. However, if you want to see how the issue looks like in ZFC, you have to always...
View ArticleAnswer by Noah Schweber for Bijection between collection C and proper class...
The answer by eyeballfrog perfectly explains - at least, assuming a set-and-class theory in which replacement holds for sets (so, any set-and-class theory extending ZF, for example) - why the answer to...
View ArticleAnswer by eyeballfrog for Bijection between collection C and proper class PC...
If $C$ is a set, then its image by any class function is also a set (Axiom of Replacement). Since $PC$ is the image of $C$ by a class function (the hypothesized bijection) and $PC$ is not a set, we can...
View ArticleBijection between collection C and proper class PC makes C a proper class?
If there exists a bijection between a collection $C$ and a proper class $PC$, is $C$ necessarily a proper class as well? I've read and have been told by math professors that the answer is yes, but...
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