I've somewhat recently discovered hyperreal numbers, but I haven't gotten the chance to thoroughly research them.

What resources do you all recommend for undergrad level study of the hyperreal number line and hyperreal numbers? The "undergrad" criterion includes resources that cover hyperreals from both an undergrad and postgrad level. Please note that I wish to learn both the infinitesimals and hyperreal infinities (as opposed to Cantor's transfinites, the infinity on the Riemann sphere, and any other types of infinities), so resources only concerning infinitesimal calculus do not suffice.


  • $\begingroup$ The place where it all began is ostensibly Robinson's Non-standard Analysis. That might be where you want to start as well. $\endgroup$ – InequalitiesEverywhere Jan 1 at 12:20
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    $\begingroup$ also consider the textbook Lectures on the Hyperreals: An Introduction to Nonstandard Analysis of Robert Goldblatt. I didnt read it. $\endgroup$ – Masacroso Jan 1 at 12:22
  • $\begingroup$ Keisler's "Elementary Calculus" is not fully rigorous, but gives some intuition at a basic level about the applications of Robinson's hyperreals to Calculus. It doesn't "only concern infinitesimal calculus" since you need infinities for things like integrals, etc. $\endgroup$ – Mark S. Jan 1 at 14:03

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