On Wed, 16 Jul 2008 15:53:37 +0100, Jack <jj@[EMAIL PROTECTED]
>
wrote in <news:KPofk.25150$Uk7.22535@[EMAIL PROTECTED]
> in
alt.algebra.help:
[...]
>> It certainly wouldn't be amiss to make the definition explicit:
>> 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'm just worried that I'm using the lower case 'n' without any prior
> definition.
There isn't anything to define: n is a dummy variable: its
sole function is to provide a tem****ary name for the
argument so that we know what object on the right-hand side
*is* the argument. The definition would say exactly the
same thing if it read as follows:
For a function t : |N --> N define a function
c_t : |N --> |N by c_t(k) = (1/2) * t(k) * (t(k) - 1).
> Incidentally, where you give the second definition,
> << DEFINITION 2. For a set of primes J define t_J : |N -> |N by
> t_J(n) = |{p in J : p divides n}|>>
> I wonder what you think of this. I have defined J as a
> subset of a set of the first m primes, where m is an
> integer, which I denote by P(m). In accordance with your
> advice, I reference the function t_J in the notation
> (x,y,t_J) without comment. Now, if I want to refer to a
> set J comprised of all m primes, I make the reference
> (x,y,t_P(m)), again without comment. Is that acceptable?
Of course.
[...]
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