Difficult: One concept I wan't sure on is when do you want to use induction as opposed to other proofs? We learned some of the basic key indicators of when to use direct, contrapositive, and contradiction proofs. Are there similar components of proofs requiring induction? Is it any time you would have to do an infinite number of proofs?
Also, the example with proving the cardinality of a power set is 2^n was tricky to follow, so an example in class would help a lot on that one.
Oh, and do we need to write "By the Principle of Mathematical Induction..." at the end of each of our proofs?
Interesting: I am really glad we are learning induction, as it is one of the main proof techniques we use in our Putnam class. I find it interesting that we are able to do so many different types of proofs using induction. From even/odds, to divisibility, to sets, they all work out!
No comments:
Post a Comment