17 Summary

This concludes our discussion of Bridge to Abstract Mathematics. We started with an introductory look at set theory then studied how sets relate to each other through relations. We looked at a very important relation known as a function and discussed how to determine whether a function is one-to-one, onto, neither, or both. We then applied the idea of one-to-one, onto functions to finite and infinite sets, determining the cardinality of sets and determining whether an infinite set is denumerable and countable or uncountable. Now that we have crossed the bridge, we are ready to enter into the world of abstract math, starting with real analysis.