Ralf Hemmecke <address@hidden> writes:
 > The definition you gave is it: least fixed point of
 > X > 1 + T × X × X

 Hmmm, good question. In Aldorcombinat (AC) we deal with combinatorial
 species. They encode actual structures. The corresponding generating
 series G(x) for binary trees given by your X above has to fulfil the
 equation

 G(x) = 1 + x * G(x) * G(x) (+)

 As a quadratic formula it has at most 2 solutions. And only one of
 those solution is a power series with only nonnegative
 coefficients. Since I don't know what it should mean to say "there are
 5 trees with 3 nodes", it is clear which solution I choose for the
 generating series.

 Assuming that I understand a bit of the theory of species, then there
 is only *one* solution to

 X = 1 + T * X * X.

 We are not yet dealing with "virtual species" which would allow
 negative coefficients in the generating series.
I realize my sentence could be ambiguous: I meant "least fixed point
in the category of continuous partial orders (CPO)."