We'll agree to disagree on this point then. My stance is you're using the word construction in a more layman like manner whereas I am using it in the more formal sense. It's not a particularly big deal either way.
The answer to all of these questions is obviously "yes".
Is BB(745) one of those constructible numbers? This is harder to answer, except that you have firmly taken the position that it is. Hence it must be constructible.
