>>606
アンタね、その無限グラフってやね、もし連結性を仮定しなかったらサ、例えば
assume that the vertex set is fixed to be ${\Bbb Z}$ due to the fact
that you work on the category of infinite graphs. Then the set of all
possible choice of the edges with this fixed vertex set is restricted
in the following simple way as:
\[
\{ (n)\mbox{---}(n+1) : n\in {\Bbb Z} \} \simeq {\Bbb Z}
\]
is clearly a countable set. This is the same as to consider the 1-dimensional
lattice model together with the assumption that you just pay attention to the
nearest neighbors assigned by the edges of the graphs. Then {\bf the
set of all possible configurations corresponds to the power set of such},
namely the cardinality of what you are saying is nothing but:
\[
2^{\Bbb Z}
\]
so that, your statement seems to be quite obvious.
I really do not understand {\bf what is that good for}.
