Since exams are starting soon (for my university anyways), some of ours profs released sample questions
which would make a good review for some of the material covered in class. I'm having difficulties solving this question, and I'm not sure exactly what to start (this is a computer science course).
I need to show that the set of natural numbers can be decomposed into a union of infinitely many disjoint infinite sets. In other words, for each natural number n, i need to define a set A[n] which is a subset of N, such that Union(of_all A[n]) = N. Also, the intersection of each A[i] and A[j] must be the empty set, and each A[n] is an infinite set.
I suck at these types of questions, and I was wondering if someone could walk me through the logic/steps I would need to do in order to prove this, without giving me the full solution. Also, I just want to point out that this isn't a set theory course, so the material we covered in terms of set/cardinality/countable sets is somewhat basic.
Thank you in advance for the help,
This post has been edited by Nizbel99: 29 March 2010 - 10:54 AM