The costs form a partial order.
Perfect. The next time I'm asked about this, I'll just make the analogy to partial ordering and all confusion will instantly evaporate.
It was said in the other thread, but consider the cost of a card to be an element of
N_0x{0,1}, where
N_0 is the natural numbers plus {0}. The first coordinate is the cost in coins and the second coordinate is the cost in potions. (You could expand {0,1} to all of
N_0, but it isn't necessary as long as the highest potion cost is one potion.) So Possession's cost would be (6,1), Village's cost would be (3,0), Vineyard's cost would be (0,1), etc.
The partial ordering in question is the product order:
(x,y) <= (a,b) if x<=a and y <=b.
The ordering has the corresponding strict ordering: (x,y) < (a,b) if (x,y)<=(a,b) and (x,y)!=(a,b)
So in the example from before 3p costs more than 2p is saying (2,1) < (3,1) (since 2<=3, 1<=1 and (2,1)!=(3,1)). 3P costs more than 3 corresponds to (3,0)<(3,1).
2P and 3 aren't related in the ordering since neither (2,1) <=(3,0) nor (3,0) <=(2,1) are true.
There are other partial orderings (lexicographical, for example), so you may not instantly evaporate the confusion by just saying it's a partial ordering