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Re: I think Omitting the multiplication sign is a big mistake

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  Re: I think Omitting the multiplication sign is a big mistake Murray Eisenberg <murray@math.umass.edu> - 2011-07-14 09:21 +0000
    Re: I think Omitting the multiplication sign is a big mistake David Bailey <dave@removedbailey.co.uk> - 2011-07-15 01:21 +0000

#3702 — Re: I think Omitting the multiplication sign is a big mistake

That's a wonderful example illustrating the difficulties of traditional 
mathematical notation, the sort of thing that makes one appreciate why 
so many students don't understand it. The fact that traditional math 
notation was designed to handle single-letter variables with aplomb 
makes thing even more confusing when students have to deal with 
multi-character variables.

A couple of programming languages have built on, among other things, the 
principle that every operation must be explicitly indicated with a 
symbol (so no space and no juxtaposition to denote multiplication). Such 
of those languages that I know (APL and J) also abandon any hierarchy of 
operators of the same kind, e.g., no precedence of multiplication over 
addition (but they impose a different kind of precedence among 
"functions" and "operators" or, as Ken Iverson later preferred to call 
them, "verbs" and "adverbs" and "conjunctions").


On 7/13/11 3:11 AM, a boy wrote:
> In philosophical sense, to omit the multiplication sign is incorrect.
> Space-key or null is always describe the place of objects.
> A little student may think a(b+c)=ab+ac ==>  2(3+4)=23+24 ?
> In Mathematica, array[[n]]  puzzled almost all of new ones who never
> used the software.
>

-- 
Murray Eisenberg                     murray@math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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#3723

On 14/07/2011 10:21, Murray Eisenberg wrote:
> That's a wonderful example illustrating the difficulties of traditional
> mathematical notation, the sort of thing that makes one appreciate why
> so many students don't understand it. The fact that traditional math
> notation was designed to handle single-letter variables with aplomb
> makes thing even more confusing when students have to deal with
> multi-character variables.
>
> A couple of programming languages have built on, among other things, the
> principle that every operation must be explicitly indicated with a
> symbol (so no space and no juxtaposition to denote multiplication). Such
> of those languages that I know (APL and J) also abandon any hierarchy of
> operators of the same kind, e.g., no precedence of multiplication over
> addition (but they impose a different kind of precedence among
> "functions" and "operators" or, as Ken Iverson later preferred to call
> them, "verbs" and "adverbs" and "conjunctions").
>
>
> On 7/13/11 3:11 AM, a boy wrote:
>> In philosophical sense, to omit the multiplication sign is incorrect.
>> Space-key or null is always describe the place of objects.
>> A little student may think a(b+c)=ab+ac ==>   2(3+4)=23+24 ?
>> In Mathematica, array[[n]]  puzzled almost all of new ones who never
>> used the software.
>>
>
Of course, you have to work quite hard using HoldForm to actually output 
the expression 2 3 + 2 4,so the problem is with input where two numbers 
are adjacent. I think an optional syntax restriction to require a "*" 
between two numbers, or else an error, might be quite useful.

David Bailey
http://www.dbaileyconsultancy.co.uk

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