sequence multiplied by -1

Paul Rubin at nospam.invalid
Sun Sep 26 12:06:03 CEST 2010

Seebs <usenet-nospam at> writes:
> * It seems clear that, given two sequences x and y, "x + y" ought to
>   be the concatenation of these sequences.
> Helps, perhaps, that I got exposed to group theory early enough to be used
> to redefining + and * to be any two operations which have interesting
> properties*.

But groups have only one of those operators, and when it's written as +
that usually means the group is commutative.  So you wouldn't want + to
denote sequence concatenation.  If + and * are both present, that sounds
like a ring, in which case you'd want "foo"*"bar" to work.  It actually
seems to me that exponentiation makes more sense than multiplication
for turning "a" into "aaa".  We think of aaa as what results from
writing "a" with "3" in the superscript position.

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