A new year has begun, and I still have yet to hear from the Mathematics Magazine. This isn’t the subject of this post though. Over this J-Term, I had the privilege of learning about hyperreal numbers, which extends \(\mathbb{R}\) to the hyperreal numbers by including infinitesimal and infinite numbers. I gave a presentation on this topic that follows the first couple sections of Keisler’s very rigorous (maybe unnecessarily so) treatment of something that seems no more than a recreational creation of Conway, despite its vast history in the development of nonstandard analysis. I didn’t have the opportunity to learn much more, but from what I can see, Keisler’s treatment focuses a lot on words, sentences, and other “grammatical” concepts from model theory that I have yet to learn about. Maybe I’ll take a look at some point in the future.

The presentation in all of its pause-heavy glory is linked here.

(30 January, 2025)