These are chat archives for RobertTalbert/mth225
The following are some overall comments and suggestions about HWB Proofs, for your consideration as you do any revisions you need to do. Not all problems are represented here; just ones that had widespread attempts.
Problem 1: General comment -- if you are taking square roots, it will end poorly. This proof can and should be done without any root-taking whatsoever. Instead think about the definition of "divisibility". Also recall that we proved in class that if is even, then is even.
Problem 3: Most of the errors on this problem would have been avoided by being clearer at the outset about what proof technique is being used, what the assumptions are, and what is going to be proven. If you have to revise that one, this would be an important first step.
Problems 5--8 generally: Please note the fourth bullet above -- do not prove an equation or inequality by starting with the equation or inequality. Instead start with just one side of the proposed equation or inequality and do work to arrive at the other side. Also __clearly state the induction hypothesis when it's time to do so. Without a clearly stated induction hypothesis the proof is incorrect.
Problems 5 and 6: Beware that when you proceed to the induction step that you write down exactly the right statement to be proven. "We will now prove this for k+1" is not precise enough to be correct. Also it involves more than just adding 1 to everything.
Problem 8: There are two variables in the expression but only one of them is used by the predicate, namely . The variable is not used in the induction process.
Now, use the chat feature to ask questions -- this won't be threaded and so you may have to scroll to see other people's questions and responses, but we'll try to maintain order anyway.