Actually, in my Graduate Math Analysis class at a top 10 Engineering School, my world renowned professor, as we were moving to proving various infinite sets and aspects of the number line, answered a question the following way "In Math, there are many things we can prove, but at the foundations of Math we start with some assumptions and frankly you just have to take them by faith." Don't ask me the particulars because i was an Engineer taking Math Analysis simply to develop "proof" skills. As soon as I left that class, I proceeded to block out everything about Math Analysis.
