Okay so what then? If I can't use what I stated before, where do I even start tackling this proof? The closest thing I saw to this proof in the chapter on induction was proving that Power sets have 2n elements if there are "n" elements in a set. The other problems had to do with series and sums.
Okay so I did some reading on induction in my textbook. The one problem I see with proof by induction for this problem is that there is no base case that is true unless I'm not seeing it.
Well I know the set of integers is closed under multiplication and addition and that's about it. Wait...is that what the problem is asking me to prove?
I just started taking a foundations of math course that deals with proofs and all that good stuff and I need help on a problem that I'm stuck on:
Prove: Z={3k:k\inZ}\cup{3k+1:k\inZ}\cup{3k+2:k\inZ}
Z in this problem is the set of integers
This is all that's given. I thought maybe I...