A good point. So the real numbers exist in the same sense that anything else they might describe does. My original point was really a comment on the way that t

A good point. So the real numbers exist in the same sense that anything else they might describe does. My original point was really a comment on the way that the subject is often taught: the real number system is not introduced as some arbitrary set of rules that is as good as any other (though of course it is); it is introduced as if it were as incontrovertible an idea as, say… integer addition. I don’t think it is. It can perfectly well be argued that it makes sense and is useful, but its naturality is another matter. I personally find the leap from R to C less controversial than that from Q to R.