Union of two REL is closed under union. I don't understand how is it closed. I followed this link. The have stated:
Here the trick is to simulate both M1 and M2 “simultaneously”. In other words, we design a machine that executes one step of M1, followed by one step of M2, then again one step of M1 and so on.
My question is if the word doesn't belong to either of the machines then how did they decide that the output will be closed? Both the machines can be in an infinite loop and we cannot decide if the word belongs to the language accepted by M1 of M2.
What am I missing here? Also, is there any relation between halting and closure properties of turning recognizable languages?