I've been trying to wrap my brain around sets lately. Please bear with me, as I've been trying to teach myself. So, from what I've read, you can construct most everything in modern mathematics from sets. You can form the natural numbers from the successor function, you can construct the integers from the natural numbers, and the rationals from integers. Functions(well, relations) as a set of ordered pairs pairing elements from the input set and the output set. I think I understand this part pretty well. So here is where my question comes in. You can create a set of the latin alphabet as a set of naturals 0-25. Suppose I want to construct a set consisting of integers(Z) and letters(A). The intuitive thing to do would be the union of Z and A. But of course, this isn't meaningful. Since the alphabet is defined as natural numbers, how do I tell 0 from 'A'? Is there some operator similar to a union but preserves the different 'types'? Thanks for any suggestions!