As a definition of " similarity mapping" I read in Lipschutz, Set Theory :
the mapping f from A to B ( A and B being ordered sets) is a similarity mapping iff, (a) f is a bijection and (b) for any elements a and a' belonging to A :
a < a' iff f(a) < f(a')
The definition is expressed in terms of < : "strictly precedes".
Would f also be a similarity mapping in case < were replaced by " precedes or is equal to" ?
What I do not understand is that (1) the author has defined ordered sets in terms of " precedes or is equal to " and (2) defines an " order preserving function" in terms of " strictly precedes".