On 3/12/2012 20:00, Albert van der Horst wrote:
In article<4f5df4b3$0$1375$4fafb...@reader1.news.tin.it>,
Kiuhnm<kiuhnm03.4t.yahoo.it> wrote:
On 3/12/2012 12:27, Albert van der Horst wrote:
Interestingly in mathematics associative means that it doesn't matter
whether you use (a.b).c or a.(b.c).
Using xxx-associativity to indicate that it *does* matter is
a bit perverse, but the Perl people are not to blame if they use
a term in their usual sense.
You may see it this way:
Def1. An operator +:SxS->S is left-associative iff
a+b+c = (a+b)+c for all a,b,c in S.
Def2. An operator +:SxS->S is right-associative iff
a+b+c = a+(b+c) for all a,b,c in S.
Def3. An operator +:SxS->S is associative iff it is both left and
right-associative.
I know, but what the mathematicians do make so much more sense:
(a+b)+c = a+(b+c) definition of associative.
Henceforth we may leave out the brackets.
That's Def3. I don't see your point.
Don't leave out the brackets if the operators if the operators is
not associative.
(1 - 1) - 1 != 1 - (1 - 1)
and yet we can leave out the parentheses.
P.S. There is no need for the operators to be SxS->S.
For example a b c may be m by n, n by l, l by k matrices respectively.
Ops, you're right.
Kiuhnm
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