@cshentrup from Mas-Colell, the preeminent textbook in microeconomic theory (very expensive, but hey there's a pdf just sitting there) http://www.hawkinqian.com/uploads/media/2014/09/Microeconomic_Theory.pdf

@cshentrup "the preference relation associated with a utility function is an ordinal property"

here's another screenshot, same PDF (this PDF appears to be a draft of an edition, since we see Exercise ??), "the special forms of the utility representations in (i) and (ii) are not preserved; they are —it cardinal properties that are simply convenient choices for a utility representation."

@cshentrup when I was taught this stuff, I was taught that utility functions are equivalent across affine transformations, ie given a utility function U(c), any function of the form a(U(c)) + b represents precisely the same preferences.