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OpenLogicProject / OpenLogic

An open-source, customizable intermediate logic textbook
http://openlogicproject.org/
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problem 1.6 in open-logic-complete #303

Closed rishihho closed 2 years ago

rishihho commented 2 years ago

it might be helpful to mention that B is a set of sets because if there's an element in B that isn't a set, the union on all of B wouldn't be well defined.

rzach commented 2 years ago

I don't think that's necessary. \bigcup B is the set of all elements of elements of B. It doesn't matter if B happens to have an element that's not a set; it just isn't an element of \bigcup B. If B contains no sets at all, e.g., then \bigcup B = \emptyset. To give the proof, knowing that A \in B is all that's needed.

rishihho commented 2 years ago

just to clarify with an example, if B = {{1, 2}, 3, {4}}, then \bigcup B = {1, 2, 4}?