Q:

Could "$\infty$" be understood by taking the reciprocals of the Hyperreal numbers?

When learning mathematics we are told that infinity is undefined. (*)
Recently I read about the infinitesimal version of Calculus and how we can in fact treat $dy/dx$ as a fraction under this approach (something we can't do with limits). This is achieved by constructing the Hyperreal numbers $^*\mathbb{R}$, which contain the real numbers and the infinitesimal numbers (all positive numbers greater than zero, yet less than any real number).
Thinking back to (*) I wonder, could sense of infinity be made somehow by including the reciprocal infinitesimal numbers? Presumably these numbers would be defined since the infinitesimal numbers are never zero.

A:

In fact, infinite numbers are a part of the Hyperreal Numbers. Just check this out on Wikipedia.

