In article <KPofk.25150$Uk7.22535@[EMAIL PROTECTED]
>, Jack <jj@[EMAIL PROTECTED]
>
wrote:
[... Typo in Def. 1.1 fixed...]
> > DEFINITION 1.1 For a function t : |N -> |N define a function
> > c_t : |N -> |N by c_t(n) = (1/2)*t(n)*(t(n) - 1).
[...]
> >> I got this further issue. Brian set me up with a definition which
goes
> >> 'We
> >> will find it convenient to define auxilliary functions in the
following
> >> way:
> >> given (g,n) in G there is a unique (s,r) in G', such that
h(g,n)=(s,r),
> >> and
> >> we set h_1(g,n)=s and h_2(g,n)=r'. Can I take this to be a definition
> >> that
> >> holds in my reference to s and r subsequently, or do I have to go
through
> >> the process of saying what they are every time I make a reference to
> >> them?
> >> If so, what about my later use of r to denote memebrs of R?
> >
> > It would appear that you are free to recycle "r" and "s".
> >
>
> I take it, then, that if r is in R, it is invariably tagged such that it
is
> referenced as r \in r. If I don't tag r as such, will the reader know
that I
> mean it to be read in its other sense, i.e. as h_2(s,r)?
As long as h_2 has been suitably defined h_2 : ? -> ??, the reader will
know where the "r" in h_2(s,r) lives. Once you say "r in R" then r is
in R until further notice. It is _probably_ OK to say r in R and then
subsequently refer to h_2(s,r) - since I don't know the domain of h_2,
r may _still_ be R for all I know.
[...]
--
Paul Sperry
Columbia, SC (USA)
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