It's sloppy practice, but that is one of the strengths of the notation -- the integral sign and the differential element can act as effective delimiters as a backup to overcome sloppy practice. Of course, it can also be argued that it encourages that same sloppy practice, but at least the sloppy practice is rendered immaterial.Hello again,
Well the way i understood it was that if it doesnt make any sense then it cant be that way. So that leaves the only interpretation of:
integral a+b*x dx
as:
integral (a+b*x) dx
I thought that was standard practice. The 'integral' symbol and the 'dx' enclose the integrand just like parens would. I think that is standard practice.
The problem here is that it encourages sloppy practice that does not have an effective backup to offset it. Most of the time people will write their integrals without any parens because, most of the time, the integral is the last (or often only) thing on the line. Now you go and add a term, which we are used to just doing by simply adding the '+' operator and then the term since the operator is low precedence and right associative and we want it executed after everything to the left (i.e., the original expression) is evaluated first. But, with this notation, we have to remember to go back and modify the original expression, which we shouldn't have to do since it is higher precedence to begin with.As for the second form we invoke lex parsimoniae so the only interpretation of:
integral dx a+b*x
is:
integral (a+b*x) dx
or else we would have used parens like:
integral (dx a) +b*x
or:
(integral dx a) +b*x
And since we know that people WILL be sloppy -- just look at how often people write R1·R2/R1+R2 -- a notation that has that build-in backup has considerable merit.
So? I don't care who proposes something -- be it a Nobel laureate or a tenth grader -- I care only about the merits of the proposal.I realize some people wont like this, and it immediately invokes students questions about the form, but the 'inventor' of this form was none other than the same Stanford physicist that proved Steven Hawking wrong about one of the properties of a black hole