 An important point is that there is a relativity of viewpoint here: the NFU world can be understood to be a nonstandard initial segment of the world of ZFC (which could be arranged to include its entire standard part!) with an automorphism and the ZFC world (or an initial segment of it) can be interpreted in NFU as the theory of isomorphism classes of well-founded extensional relations with top (often restricted to its strongly cantorian part); these two theories are mutually interpretable, so the corresponding views of the world admit mutual translation.