This doubt has been bothering me for ages. \[\]I had learnt that if we have 2 intervals \((a,b)\cup(c,d)\), we can merge these together to form \((a,d)\) as long as \(a<d\) and \(b>c\). However, I saw one of the teachers at my coaching institute do this: \[\]\[(a,b)\ \cup(b,c)=(a,b)\] \[\]How can we merge these two intervals together? Was what I had learnt incorrect? \[\]And in general, when can we merge \(2\) or \(more\) intervals (of all 4 types: \((a,b],(a,b),[a,b),[a,b]\)) together to form a single interval?\[\] Any help would be really, really appreciated! Thanks very, very much in advance!