Re: Dedekind versus Cauchy reals

I have enjoyed, without entirely following, the debate on this theme and would like to ask some naive questions. Rather practical toposes are presheaf toposes. Do the Dedekind and Cauchy reals differ in some of those? To be more practical again, one use of the reals is to analyse motion, as Lawvere has said. Motion includes change of data, which is analysed by statistics. But suppose the data to be analysed has structure, such as a directed graph. Then perhaps we need the reals in the topos of directed graphs? I.e. insert the required structure at the very beginning of the study, instead of post facto. Is the law of large numbers valid in the (??) probablity theory based on those reals? And which reals? Idle curiosity I fear! Ronnie