You should read 'non negative' where I wrote 'nonzero'.
R.E. Boss > -----Oorspronkelijk bericht----- > Van: [email protected] [mailto:programming- > [email protected]] Namens R.E. Boss > Verzonden: zondag 1 augustus 2010 12:46 > Aan: 'Programming forum' > Onderwerp: Re: [Jprogramming] Order of operations > > Perhaps it has something to do with the following. > Multiplication (by a nonzero integer) is repeated addition and > exponentiation (by a nonzero integer) is repeated multiplication. > So it is more natural to expand * first and interpret a*b+c as a+...+a +b > where there are b a's. > Same with ^ and * . > > If a↑↑b is interpreted as a↑....↑a = a^....^a with b a's, cf. http://en. > wikipedia.org/wiki/Knuth's_up-arrow_notation than that would have > precedence > over ^ as well. > In general, more up-arrows have precedence over fewer for the very same > reason: they need to be expanded first. > > NB. ↑ is right associative, ie. a↑b↑c = a↑(b↑c) and is not equal to (a > ↑b)↑c, which seems natural for J users. > > (I you really want a mind dazzling notation, look at > http://en.wikipedia.org/wiki/Conway_chained_arrow_notation ) > > > R.E. Boss > > > > -----Oorspronkelijk bericht----- > > Van: [email protected] [mailto:programming- > > [email protected]] Namens Dan Bron > > Verzonden: zaterdag 31 juli 2010 17:22 > > Aan: 'Programming forum' > > Onderwerp: [Jprogramming] Order of operations > > > > How did the current mathematical order of operations (PEMDAS) arise? > > > > > > > > Why does it always seem that the more powerful operators also have the > > higher precedence? Is it so that expressions don't explode by default > > (e.g. > > 3*4^5*6 would have a very different value if * was higher precedence > than > > ^). If we introduce a new operator in the chain + * ^, would it > > necessarily > > also have the highest precedence? > > > > > > > > -Dan > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
