On Saturday, February 1, 2020 at 3:37:57 AM UTC+1, Norman Megill wrote: > > On Friday, January 31, 2020 at 8:23:08 PM UTC-5, Benoit wrote: >> >> Regarding the possible introduction in the main part of semigroups and >> magmas: >> When I look at the page http://us2.metamath.org/mpeuni/df-mnd.html I >> feel a bit dizzy. The abundance of parentheses and conjunctions makes it >> hard to parse. >> > > If you already know about magmas, semigroups, and monoids, of course you'd > feel that way. Look at it from the perspective of someone who's never > heard of these and really doesn't care to learn, because all they came for > was groups. Just the names of these things are somewhat intimidating and > have little or nothing to do with what they really are. >
I think we will not agree on this. I prefer to face difficulties one by one, instead of all three at the same time. I personnally still find the long chain of characters in http://us2.metamath.org/mpeuni/df-mnd.html intimidating. It's always difficult to look from the perspective of someone who's completely new to it. I may be underestimating the difficulty of facing several notions, and you may be underestimating the difficulty of reading such long expressions of formal math. As Groucho Marx said: "Send someone to fetch a child of five." Or actually, fetch at least a thousand, half of them learning one way and half the other way, and see which group does best ! But most probably, each type of learning will suit different people. > As I wrote earlier: > > "The user knows from the description and from the property theorems that > are referenced. But even without that, I do see all of these properties > pretty immediately - they're right there in the definition: ( x p y ) e. b > for closure, ( ( x p y ) p z ) = ( x p ( y p z ) ) for associativity, and > E. e ... ( ( e p x ) = x /\ ( x p e ) = x ) for left and right identity." > You see them immediately because you've been reading expressions like this every day for more than a decade. By the way: you are doing in the above sentence exactly what the intermediate definitions do: you are clearly separating the three properties of closure, associativity and unitality from each other, so that we can digest each of them successively. This is indeed clearer, and that's exactly the point. > I acknowledge that Bourbaki has had a lot influence, and I have no problem >> using its notation and terminology - if it has survived and is still used >> in the mainstream literature after 80+ years. What I think is not a good >> idea is the blind use of Bourbaki as being the "bible" of mathematics. >> > I fully agree: no book should be followed blindly, nor used as a bible. Benoît -- You received this message because you are subscribed to the Google Groups "Metamath" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/metamath/5bcb29d6-8da8-4233-8df4-20740192aab4%40googlegroups.com.
