Dan Bron wrote: > John, > > I wanted you to know that it was just for you that I wrote: > > JR> decades (years? centuries? millennia?) > > instead my original "centuries". We've had more than one talk about the > modernity of mathematical notation. And now I'm feeling pretty smug tha I > hit it on the money with "decades" :) >
Well thanks, Dan: I rose to the bait. Cajori's book is the reference on such questions. > Seriously though, I bet, even before Peano, people would be inclined to > say "is x is a member of y?" more often than "does y have member x?". > I don't think people really thought about sets the way we do now. You could not make up your own: they were more God-given. Bear in mind the latter half of the 19th century was the time mathematicians were formalizing the notions of real numbers and integers that we use now. It was not until the early 20th century that people realized all of mathematics could be built on sets. My point with bonding is that x&P should be more common than P&y. I agree that x e. y with fixed y is more common than with fixed x. In particular you are more likely to ask "which elements are in this set?" than "in which sets is this element?" Mathematicians do use a backwards epsilon, corresponding to e.~ . > Because J is right-to-left, a primitive P should be designed to make: > > x P y =. thing I'm likely to calculate > > more likely than > > y P ~ x =. thing I'm likely to calculate > > or > (x =. thing I'm likely to calculate) P y > > Dyadic i. follows this design principle. But that doesn't mean it > wasn't a tradeoff. I basically agree with this point. On these grounds, ! is the wrong way round: you are more likely to calculate x ! y for fixed y than fixed x. On the other hand, | is the correct way round. I still think it is a matter of convenience and convention. Naturality arguments and self-evident truths often don't last. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
