On Fri, 11 Jul 2008, Paul Sperry wrote:
> > That's what I had thought. But then Brian said, "Do you need to
discuss
> > *simultaneously* a function t_J : N --> N that is defined in terms of
> > divisibility by members of a set J of primes *and* a completely
arbitrary
> > function t : N --> N? If not, then of course you can call
> > them both 't'; whyever not?!"
>
> What Brian is saying and what I am saying is that you cannot have two
> _concurrent_ definitions of t.
>
No. However, there are not one, but two functions, t and T_J.
To define two functions simultaneously or concurrently is common.
For example:
f(0) = g(0) = 1
f(n+1) = g(n) - f(n)
g(n+1) = g(n) + f(n)
f(1) = 0; g(1) = 2
f(2) = 2; g(2) = 2
f(3) = 0; g(3) = 4
etc.
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