This question links to a former discussion on the board. I'm confused regarding this thread: http://https://www.physicsforums.com/showthread.php?t=3622 Specifically, towards the end of the thread, the asker states (in regards to the union notation originally cited): "....if we say that x is an element of the union of those sets, then we know x is an element of at least one of those sets. " I thought the "or" conditional of the union meant that one (and only one) match occurs for x for the notation to be true. I could be wrong....