Definition talk:Set of Sets

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Set vs. set of sets

The elements of a set are by definition sets, so it's worth emphasizing here that a set of sets is just a set (in ZF). --barto (talk) (contribs) 05:00, 10 March 2018 (EST)

In ZF, where the concept of ur-elements is not supported.
In $\mathsf{Pr} \infty \mathsf{fWiki}$ we like to allow for concepts to be accessible to those who have not studied so deeply as to understand the fundamentals, but have been introduced to the most naive of theories in which, for example, a "set" can consist of elements as concrete as physical objects. In such contexts it makes sense to introduce, in a semi-formal way, the concept of a set which contains nothing else but other sets.
It is upon such simple abstract concepts that the very intellectual capacity of a person to even grasp ZF is based. --prime mover (talk) 05:15, 10 March 2018 (EST)
Indeed, which is why I certainly wouldn't merge this with Definition:Set. --barto (talk) (contribs) 05:18, 10 March 2018 (EST)
Where did you find the suggestion to do that? --prime mover (talk) 05:22, 10 March 2018 (EST)

I'm sorry, I don't follow the discussion here. It says right there, in the first sentence, "a set of sets is a set [...]". Maybe I miss something. — Lord_Farin (talk) 13:30, 12 March 2018 (EDT)