From: <juanrgonzaleza@canonicalscience.com>

Date: Mon, 20 Nov 2006 01:39:25 -0800 (PST)

Message-ID: <3151.217.124.69.196.1164015565.squirrel@webmail.canonicalscience.com>

To: <www-math@w3.org>

Date: Mon, 20 Nov 2006 01:39:25 -0800 (PST)

Message-ID: <3151.217.124.69.196.1164015565.squirrel@webmail.canonicalscience.com>

To: <www-math@w3.org>

> Comparing a+b+c with (a+b)+c is more interesting, because the order of > operations in the same. This is actually a slight discrepancy between > content MathML (where plus is an n-ary operator) and and the standard > approach for studying groups in mathematics (because the usual > definition of a group makes the operator a binary operator). In rigor c-MathML arises from LISP (plus a b c) and the plus is a function, not a binary operator. Therein the <apply>: "Apply the function plus to the arguments a, b, and c". People becoming from C languages often do not notice that the LISP form (+ a b) means +(a, b) in C-like notation because in LISP (contrary to C) there is no restriction in naming functions and + is a valid name for a function. Note that in rigor the + in (a + b + c) are not binary because the structure is not binary. This is a notation for recursive binary! > I am not > aware of any document which defines how the n-ary operators on a > variable in content MathML map onto the binary operator plus. Basically you follow the same steps that when defining the notation (a + b + c) in mathematics. In CanonML we mimic math: E.g. [a + b + c] => [a + [b + c]] > In this case, the value of the expression is not changed between a+b+c > and (a+b)+c, and therefore, the meaning shouldn't be changed (the only If and only if + is associative, wich may the case in CellML for all practical cases. However, note that is not the case in more general languages. Example, in canonical science [A + B + C] is not the same than [[A + B] + C]. The first maps to one Keizer law, whereas later maps to a sequence of two. In chemical calculus (a variation of Boole algebra: X + Y = XY), in general (A + B) + C is different than A + (B + C), therein than A + B + C has not the same meaning than usual algebra in math.Received on Monday, 20 November 2006 09:39:37 UTC

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