Strict order-preserving function
= Strict order-preserving function
{title2=$x<y\Longrightarrow f(x)<f(y)$}
= Strict order-preserving
{synonym}
A <strict order-preserving function> preserves strict comparisons. Between <strict partial orders> it may identify incomparable elements. Between <strict total orders> it is necessarily injective, and in a finite chain it is exactly an increasing injection. It need not reflect comparisons between incomparable elements of general partial orders.