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).
1 thought on “Update of BML”
I leave this comment with a sense of nervousness and excitement.
I am a teacher in the computer science and technology school at Heilongjiang University in China. Last year, I was about to teach Mathematical logic at my college, and I found I knew really little about it. So, I started to search for materials on the internet, and found a link to the main page here in ZhiHu (an APP in China).
I clicked the link, and found all these you have built here was really awesome. I read “An Introduction to Formal Logic”, and decided to use it as my main reference book immediately.
The new term is about to begin, I come back here to see if there is any update and see “A friendly request to the reader!” at the front of IFL, which encouraged me in leaving this comment.
I think the whole book is great. I like those historical or philosophical asides want know more of them. I enjoy reading the “informal logic” parts at the outset, and believe they are very important. I take this course not only teaching some knowledge of Formal Logic to students, but also inspire the students how to think properly and to be reasonable. The “informal” part was really helpful.
Thank you, for all these you make and share.