The hyperreal number system is a way of treating infinities and infinitesimals in a rigorous way that is consistent with the way that we treat ordinary numbers. I recently posted a short video introducing the concept in a simple way. I thought some of you might be interested. I find the hyperreals interesting for a number of reasons. First of all, I think that infinities and infinitesimals are somewhat of the equivalent of Intelligent Design for mathematics. Infinitesimals were essentially banned from mathematics in the 1800s because it was said that they were inconsistent and non-rigorous (this is why calculus switched from infinitesimals to limits). This move was largely philosophically motivated, with Hilbert and others trying to naturalize mathematics. However, Read More ›