I hate to frustrate you, but I don't know what f:X \to Y means, and I haven't learned about metric spaces yet. This is a mathematical logic book and only the second chapter at that. Perhaps I won't be able to learn logic and foundational material first, but I'm not ready to give up yet. If you feel like helping, what I have in mind is if I let y be a/the value of the 0ary function from X to Y, is y an arbitrary element of Y, so that I can generalize from y to every element of Y, or is y a particular element of Y, so that I cannot generalize from it?
