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Mar 1 at 12:01 comment added Dave L Renfro In case the link I gave to Mark Neyrinck’s May 1995 undergraduate thesis An Investigation of Arithmetic Operations goes dead, I've saved it at the Internet Archive here. To keep from bumping my answer to the top of the queue, I'm putting this new link in a comment. However, if at some later time I happen to notice that my original link is dead, then I'll incorporate the Internet Archive link into the main body of my answer.
Aug 10, 2022 at 10:11 comment added Dave L Renfro Regarding the discussion above about strong and weak tetration, see also the comments to this answer, in particular the up arrow and down arrow operations, which I apparently wasn't aware of until now (or more likely, I had seen it earlier and forgotten about it).
Apr 12, 2022 at 17:52 history answered Dave L Renfro CC BY-SA 4.0