Here is a link to Dana Ernst talk on the Futurama theorem of Ken Keeler. In this version, products are just as we treat them (left to right). Also, in this version, there is the “try it yourself” exercise we did not do, but you may want to practice a few examples on your own anyway to make sure you understand the argument.
Finally, the questions mentioned at the end of Ernst’s talk (see here) are all interesting, and if you figure one or several of them out, please turn them in for extra credit.
(By the way, the same applies to all problems we have been discussing. For example, if through the term you figure a way of producing a really long sequence giving us a better bound for than what you obtained when the homework was due, please turn it in as well.)