I am having a bit of confusion about the real numbers and ZF set theory (I asked a question about it a few days ago). I am a bit unsure as to why the real numbers can be in any model of ZF as they seem to contradict the axiom of foundation (regularity) i.e. that for every set $X$ and $Y\subseteq X$ $\exists a\in Y:\forall b\in Y ((b\neq a)\ b
Thanks very much for any help