Old Pappus Book of Mathematical Calligraphy (2014) https://loopspace.mathforge.org/CountingOnMyFingers/Calligraphy/"By using a little of this art of letter-forming, a mathematician can ensure that these strange symbols that she uses are clear both to others and, six months later on, to herself. There are many, many books that explain how to do calligraphy and which explain in detail how to form the letters. However, calligraphy for mathematicians is slightly different to calligraphy in general."#mathematics #calligraphy #art #books

@sed good luck.From his dump before this one, it's apparent he conceives of 0.(3) as "(3)/1(0)". But I don't think he means this notation to literally denote transfinite numbers because his mathematical understanding is not sophisticated enough for that; instead judging by his wording "for any given number of digits we can rewrite 1(0) as (9)+1", he doesn't have a well-defined understanding of recurring decimals at all; to him they are, I think, a way of talking about decimals with an *undefined* rather than *infinite* number of decimal places. So he talks a lot like he thinks 0.(9) is 0. followed by an unspecified number of nines.You're unlikely to get any confirmation of this; he seems to be aware this isn't how everyone else treats the notation so won't sign up to it (and he's blocked me so I won't get an answer; I'm still here because I find it all so fascinating).But from that point of view, it *does* make a kind of sense that you "can't do" 0.(9) × 10 because the former doesn't refer to a specific number. Buuut, if you do the obvious thing and treat 0.(9) × 10 as "9. followed by an unspecified number of nines" the normal argument goes through.Enjoy.