Hi Jonathan, I have a question about how you are thinking about the relationships in \\(\mathbb N[S]\\) and \\(\mathbb N[T]\\). You say:

> For any particular \\(T\\)-complex \\(y\\), the set of \\(T\\)-complexes less than it are all those with no more \\(T\\)-resources than \\(y\\).

Does this mean that you are defining \\(\leq\\) according to the amount of resources in each complex? I thought that we were using \\(\leq\\) to represent possible reactions. Remember, \\(y \leq y'\\) means that we can get \\(y\\) from \\(y'\\) not that there are fewer resources in \\(y\\) than in \\(y'\\). As an example:

\\[ [\textrm{yolk}] + [\textrm{white}] \leq [\textrm{egg}] \\] because you can get a yolk and a white from a whole egg. However \\[ [\textrm{egg}] \nleq 2[\textrm{egg}] \\] because you can't get exactly one egg from two eggs.

Maybe I'm misunderstanding your explanation or the definition of \\(\le\\)?

> For any particular \\(T\\)-complex \\(y\\), the set of \\(T\\)-complexes less than it are all those with no more \\(T\\)-resources than \\(y\\).

Does this mean that you are defining \\(\leq\\) according to the amount of resources in each complex? I thought that we were using \\(\leq\\) to represent possible reactions. Remember, \\(y \leq y'\\) means that we can get \\(y\\) from \\(y'\\) not that there are fewer resources in \\(y\\) than in \\(y'\\). As an example:

\\[ [\textrm{yolk}] + [\textrm{white}] \leq [\textrm{egg}] \\] because you can get a yolk and a white from a whole egg. However \\[ [\textrm{egg}] \nleq 2[\textrm{egg}] \\] because you can't get exactly one egg from two eggs.

Maybe I'm misunderstanding your explanation or the definition of \\(\le\\)?