Cheuk wrote:

> I am not sure if I am correct but my observation is that in \\(\mathbb{N}(T)\\), even the reflexive property implies that

> $$a_{E}[E]\le a_{E}[E],$$

> but we do not have

> $$a_{E}[E]\le b_{E}[E],$$

> even if \\(a_{E}\le b_{E}\\) in \\(\mathbb{N}\\) because we do not have the condition that \\(0\le [E]\\). \\(0\\) just serves as the identity in \\(\mathbb{N}(T)\\) but it does not mean it is less than the "non-zero" elements.

This is right, because we aren't including any process that lets you throw away eggs!