I'm trying to understand How can an ordered pair be expressed as a set? and I don't know what the big cap/cup notations mean when placed next to an ordered pair: $\bigcap(a,b)$ and $\bigcup(a,b)$.
[Math] What does the big cap notation mean
elementary-set-theorynotation
Best Answer
This is actually answered in the linked question, but for clarification, if by definition $(a,b)=\{\{a\},\{a,b\}\}$ then $$\bigcap(a,b) = \bigcap\{\{a\},\{a,b\}\} = \{a\} \cap \{a,b\} = \{a\}$$ and $$\bigcup(a,b) = \bigcup\{\{a\},\{a,b\}\} = \{a\} \cup \{a,b\} = \{a,b\}.$$