bo198214 Wrote:Sorry, but I dont see any meaning for hyper operations in defining a fucked up function that is so crude that you can not define them on the reals.
Well I found a popular citation that expresses my thoughts rather well and perhaps is more authoritative. From my point of view, given the fast divergent nature of hyperoperations, there can not be a better place to use smaller infinitesimals than used in normal calculus than hyperoperations.
Quote:According to Kruskal, these problems could disappear if
theorists use infinitesimals, numbers smaller than any imaginable
positive real numbers. A series that involves such numbers can
be prevented from diverging essentially because infinitesimals
are so small that they "mop up" any tendency a series might
have to zoom off to infinity. "The surreals give us a way of
working with infinitesimals, and thus perhaps of working with
divergent series," says Kruskal. Divergent integrals, another
common bugbear in theoretical physics, may also bow to the
surreal approach.
Ivars