In message <o19e391hgcgk4fv7bd126p7lsle5g9j89o@4ax.com>, dullrich@sprynet.com writes >>> f:X -> Y is an order embedding when >>> for all x,y, (x <= y iff f(x) <= f(y)). >> >>Yes. > >I think no. Surely an embedding is required to be injective.

f(x) = f(y) => f(x) <= f(y) and f(y) <= f(x) => x <= y and y <= x => x = y