I haven't posted anything here in a while, so let's do something cool... like construct $^*\mathbb{R}$
Swag.
The hyperreals, $^*\mathbb{R}$, (Abraham Robinson's world of nonstandard analysis) are a neat way to rigorously develop the notion of infinitesimal numbers in analysis. Because we want our numbers to form a field, that means we'll
also pick up a new description of 'infinitely large' numbers (quite distinct from the cardinals/ordinals though).
This will be more about the crazy set theory shenanigans that go into building $^*\mathbb{R}$, rather than
actually working in $^*\mathbb{R}$... maybe I'll cover the practical side in another blogpost...
