Oh dear. That’s very embarrassing. I spotted a horrid thinko at the top of p. 77 of printed version of Beginning Mathematical Logic. I can hardly believe that I wrote, concerning infinite binary strings and real numbers between 0 and 1, that “different strings represent different reals”. Ouch. So replace the para numbered “2.” by
Note too that a real number between 0 and 1 can be represented in binary by an infinite string. And, by the same argument as before, for any countable list of reals-in-binary between 0 and 1, there will be another such real not on the list. Hence the set of real numbers between 0 and 1 is again not countably infinite. Hence neither is the set of all the reals.
I’ve updated the online PDF, and uploaded a corrected file to Amazon which will take a couple of days to work through the system). And I’ll start a corrections page for those who have the first printings of the book.
I’m not going to fret about every minor typo. But I will correct major mistakes that could mislead the reader (and then, when I do, I’ll take the opportunity to correct any smaller errors I know about). I won’t add new content though: that can wait until a second edition …!
Update Amazon reports that changes are now live: so a book ordered from now on should be the very-slightly-revised version (dated 18 Feb on the verso of the title page).