Writing Proofs Discussion

(The following is/are the initial prompt(s) for an online discussion; students may have posted responses, and prompts for further discussion may have been added, but these things are not shown.)

So far, we have written proofs pretty informally. This discussion is an opportunity to start writing them more formally.

See if you can post as replies in this discussion formally written proofs of some of the conjectures from the direct proofs discussion or introduction to direct proofs class:

• If x and y are even integers, then xy is even.
• If x and y are odd integers, then x + y is an even integer.
• If x is an even integer and y is an odd integer, then x - y is odd.
• If q is a rational number and n is an integer, then q + n is rational.

It’s likely to be somewhat painful to write formal proofs in Canvas, so don’t feel that any one person has to do all of them, or even do more than contribute a couple of lines to one of them.

To explore a hopefully easier setting for writing formal proofs, try writing some of the proofs for this discussion using LaTeX or your favorite other word processor or typesetter. Comment here on your experiences — what, if anything, was easier or harder with that tool, what interesting things did you learn about the tool (if anything), ask questions you ran into, etc.