Re: Playing the boardgame "go"

In article <1128345097.117744.260590@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<pauldepstein@xxxxxxx> wrote:
>David,
>
>Yes, my comment is irrelevant to your central point. In fact, I
>commented on a peripheral point -- I hope that's o.k. Actually, you
>did say otherwise. Assuming that you are a mathematician (and there is
>a mathematician with your name), it might be worth pointing out that
>mathematical English has different conventions to ordinary prose.
>
>In ordinary prose, to say "X is a property shared by all but Y" means
>that Y does not have property X but the complement of Y does have
>property X. By contrast in mathematical English, the quoted statement
>asserts only that the complement of Y has property X, and makes no
>claim about Y.

I don't follow this on several grounds.

I take the statements to mean:

given a set S containing an element Y and possibly some other
elements.

The first statement says that for every e such that e is an element of S, then
e has property X if and only if x != y, for some definition of
equality. It doesn't say anything at all about complement(Y), since
complement(Y) may not exist or may not be a member of S

The statement makes assertations about members of S which are not
element Y and it makes a statement about Y, it conveys no information
about complement(Y)

As an example, take the set of all rational numbers (numbers which can
be represented in the form x/y where x and y are integers). Every
member of this set with the exception of 0 has it's multiplicative
inverse (1/x) in the set of rational numbers. 0 does not have a well
defined multiplicative inverse and if such an inverse existed, it
might or might not be considered a member of the set of rationals.





--
Jim Segrave (jes@xxxxxxxxxxxxxx)

.

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