John wrote:

> $5 ≤ $10

At the same time, \\(F \le T\\) and \\(\\{1, 2\\} \le \\{1, 2, 3\\}\\), where \\(\le\\) is \\(\vdash\\) and \\(\subseteq\\) appropriately. These are the two instances I lean on more. :/

I tend to remember \\(x \le y\\) as \\(y\\) being "more" than \\(x\\) with an appropriate notion of "more". With propositions it's "more permissive", and with sets it's just plain "more". In the case of resources, I expected "more" to be "more processed" or "later". I do see what you're saying about 10 being _literally_ more than 5, so \\(5 \le 10\\) might model a "spending" action in a resource theory. It is a bit confusing, though, since the reactions are written analogously to \\(10 \to 5\\), i.e. the other way around.

> $5 ≤ $10

At the same time, \\(F \le T\\) and \\(\\{1, 2\\} \le \\{1, 2, 3\\}\\), where \\(\le\\) is \\(\vdash\\) and \\(\subseteq\\) appropriately. These are the two instances I lean on more. :/

I tend to remember \\(x \le y\\) as \\(y\\) being "more" than \\(x\\) with an appropriate notion of "more". With propositions it's "more permissive", and with sets it's just plain "more". In the case of resources, I expected "more" to be "more processed" or "later". I do see what you're saying about 10 being _literally_ more than 5, so \\(5 \le 10\\) might model a "spending" action in a resource theory. It is a bit confusing, though, since the reactions are written analogously to \\(10 \to 5\\), i.e. the other way around.