I am not sure I understand your question: We're talking about math notation, here, not machine programming language. And, math notation has had a history of being made up on the spot, by people with the inclination to do so. (I remember one math book where the author was careful to use a different character set for every section of the book -- I wish I could remember the author.) For example: https://en.wikipedia.org/wiki/Einstein_notation is a fairly well-known example of author-specific notation.
Anyways, the rules tend to be informal and tend to rely on analogies to other subjects. (And this particular concept tends to be difficult to search on, because "space" tends to be used to describe math concepts which have little relation to typography.) That said, it's still possible to find hints of people acting on this concept in math contexts. For example, consider the current final entry at https://www.reddit.com/r/grammar/comments/48nbqp/math_symbols_and_space/ "EveRedux 1 point · 3 years ago I'm a journal editor and we publish a fair bit of complex math, using MathType from Design Science. The rule of thumb is to add space around math operators that function as verbs (add, subtract, divide, multiply) between two numbers but close up those functioning as modifiers (greater than, less than, etc.) of a number." But if we were talking about programming languages, I could bring up numerous examples where spaces were significant to parsers or were not significant to parsers. (In Forth, for example, the typically machine tokens are any sequence of printable characters separated by whitespace. In Fortran, in contrast, for example, spaces typically are irrelevant to the language. (Some details differ from implementation to implementation, and both have exceptions when dealing with character strings.)) Anyways... I can't find it now, but I do remember a book where the convention was to use minimal spaces between factors but significant space between terms of an expression. Thanks, -- Raul On Fri, Sep 27, 2019 at 3:53 PM Devon McCormick <[email protected]> wrote: > > Are you serious? I attended a talk by Bjarne Stroustrop one memorable > April 1st where he started talking about potential extensions to C++, > including one that would make a space an operator. He was joking, of > course. > > On Fri, Sep 27, 2019 at 3:50 PM Raul Miller <[email protected]> wrote: > > > Spaces. > > > > Generally speaking, spaces indicate lower priority operations. They > > are not as strict as parenthesis, but they are still a hint. > > > > Thanks, > > > > -- > > Raul > > > > On Fri, Sep 27, 2019 at 3:47 PM Devon McCormick <[email protected]> > > wrote: > > > Why do you think the thing to right of "8÷" is anything other than "2"? > > > What rule says multiplication comes before division? > > > > > > On Fri, Sep 27, 2019 at 3:36 AM Bernie Eckhart < > > [email protected]> > > > wrote: > > > > > > > BEDMAS a.k.a. PEDMAS gives 1 imho. > > > > > > > > Surprisingly, given that Ken is in both live and, sadly after life, > > > > Canadian, my expectation is BEDMAS. > > > > > > > > Brackets (properly called "parentheses") > > > > > > > > (2+2) i.e. (4) > > > > > > > > Giving 8 ÷ 2( 4) > > > > > > > > again, this post is being written by a non-mathematician. > > > > > > > > .......... > > > > A mathematician walked into a bar. > > > > An order was pondered. > > > > An order was never placed. > > > > > > > > .......... > > > > A mathematician walked into a bar. > > > > The bartender was also a mathematician. > > > > A fight broke out. > > > > > > > > .......... > > > > BEDMAS is left to right. > > > > > > > > so what is to the right of the ÷ sign? > > > > > > > > I suggest it's an expression that evaluates to 8 > > > > > > > > Big question is what rule was broken. > > > > > > > > Answer imho round brackets were not used. > > > > > > > > To my eyes, in 2(4) > > > > 2 modifies (4) > > > > yielding 8 > > > > > > > > 8÷8 is 1 > > > > > > > > OTOH > > > > 8 ÷ 2 x (2+2) > > > > becomes > > > > 8 ÷ 2 x (4) > > > > which becomes > > > > 4 x (4) > > > > yielding 16 > > > > > > > > Rule learned in elementary school: > > > > confusion must be avoided with round brackets. > > > > > > > > non authouritative reference: > > > > en.wikipedia.org/wiki/order_of_operations > > > > > > > > On Sep 26, 2019 10:23, "'Mike Day' via Chat" <[email protected]> > > wrote: > > > > > > > > Hardly worth commenting as it's a matter of convention, but > > > > I did this check with my Silverfrost/Plato Fortran 95, albeit in > > > > Fortran as I wrote it mid-20th C: > > > > > > > > Program: > > > > " > > > > print *, 8 / 2 * (2 + 2) > > > > end > > > > " > > > > Output: > > > > " > > > > 16 > > > > > > > > Press RETURN to close window... > > > > " > > > > > > > > Also, 8 / 2 * 2 + 2 is of course 10 as far as my Fortran is concerned. > > > > > > > > How different from J and APL ... and K (mine needs updating though!): > > > > "K 2.8t 2000-08-23 Copyright (C) 1993-2000 Kx Systems > > > > Evaluation. Not for commercial use. > > > > \ for help. \\ to exit. > > > > > > > > 8 % 2 * (2 + 2) > > > > 1.0 > > > > 8 % 2 * 2 + 2 > > > > 1.0 > > > > " > > > > > > > > Only chatting/cheating! > > > > > > > > Mike > > > > > > > > > > > > > > > > On 26/09/2019 06:07, Bernie Eckhart wrote: > > > > > as a non-mathemation, > > > > > seems obvious to me, > > > > > > > > > > reading left to right, > > > > > we have > > > > > > > > > > thing divided by an expression > > > > > > > > > > expanding the expression give 8; > > > > > > > > > > except for zero divided by zero, > > > > > > > > > > value divided by same value is AFAIK > > > > > always ONE, > > > > > > > > > > if this were a sentence, > > > > > 8 is the subject > > > > > divided by is the verb, and > > > > > 2(2+2) is the object. > > > > > > > > > > On Sep 25, 2019 04:28, "R.E. Boss" <[email protected]> wrote: > > > > > > > > > > From > > > > > > > > > > > > > > > https://www.quantamagazine.org/the-math-behind-a-faster-multiplication-algorithm-20190923/ > > > > > “This summer, battle lines< > > > > > > > > > > > > > > > https://twitter.com/pjmdolI/status/1155598050959745026?ref_src=twsrc%5Etfw%7Ctwcamp%5Etweetembed%7Ctwterm%5E1155598050959745026&ref_url=https%3A%2F%2Fwww.nytimes.com%2F2019%2F08%2F02%2Fscience%2Fmath-equation-pedmas-bemdas-bedmas.html > > > > > > > > > > were drawn over a simple math problem: 8 ÷ 2(2 + 2) = ? If you > > divide 8 > > > > by > > > > > 2 first, you get 16, but if you multiply 2 by (2 + 2) first, you get > > 1. > > > > So, > > > > > which answer is right? The conflict grew so heated that it made the > > pages > > > > > of The New York Times< > > > > > > > > > > > > > > > https://www.nytimes.com/2019/08/02/science/math-equation-pedmas-bemdas-bedmas.html > > > > >. > > > > > And as the comments section shows, even a professional mathematician > > > > > weighing in on the matter wasn’t enough to bring the two sides > > together.” > > > > > > > > > > > > > > > > > > > > R.E. Boss > > > > > > > ---------------------------------------------------------------------- > > > > > For information about J forums see > > http://www.jsoftware.com/forums.htm > > > > > > > ---------------------------------------------------------------------- > > > > > For information about J forums see > > http://www.jsoftware.com/forums.htm > > > > > > > > > > > > -- > > > > This email has been checked for viruses by Avast antivirus software. > > > > https://www.avast.com/antivirus > > > > > > > > > > > > ---------------------------------------------------------------------- > > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > ---------------------------------------------------------------------- > > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > > > > > > > > > -- > > > > > > Devon McCormick, CFA > > > > > > Quantitative Consultant > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > -- > > Devon McCormick, CFA > > Quantitative Consultant > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
