Academic life has given me a lesson for the second time, and it was harsh this time.
The first lesson had a happy ending, and it can be described by the following words:
Beware of the paper bin!
This happened on 2008. I was experimenting with a really wonderful software, the bundle Prover9-Mace4, by the late Bill McCune. My aim was to obtain a family of examples of equational classes where some formula grows unboundedly in complexity (this formula was related to direct product representations). Continue reading
Assume you want to prove a Theorem X. If you’re a fan of reductio ad absurdum (RAA), you start by saying “Assume that Theorem X is false. Hence…” and after some reasoning, you reach a contradiction. You write as a closing sentence, “This contradiction shows that Theorem X must be true.”
I want to argue about the following questions: Do we need only one use of the rule of contradiction? Can we start a proof as above and not use an argument by contradiction but at the end? Continue reading
This is my very first post.
Plans for the next few months: expository posts on 6 or 7 results (hope interesting enough), and maintain some discussion on basic set theory, aiming to develop this area in the neighboring region of my university (this will probably be in Spanish, and if times permits, also in English).