If I do something, is it fair to say that I am also _choosing_ not to do one of an infinite number of other things that I am not considering at the time of the choice?
For example, if I ask somebody "What's your name?", is it accurate to say I am choosing not to ask them "Where are my walnuts?", even if the second question never even occurred to me?
No, it's a mistake to say that you are choosing not to do all those other things. When you decide to ask someone "What's your name?" it is not "accurate" or right to say that you have chosen not to ask that person "Where are my walnuts?" What is true is that you are not choosing to do the infinite number of things, and you are not choosing to ask where your walnuts are, but that is not at all the same thing as choosing not to ask where they are. Not choosing to ask my name is not a choosing, whereas choosing not to ask my name is. You can also see that it couldn't be right to say that you are choosing not to do infinitely many things - there just isn't time!