The Hyperreal Line

The aim of this article is to explain that the hyperreal line is, what it looks like, and what it is good for. Near the beginning of the article we shall draw pictures of the hyperreal line and sketch its construction as an ultrapower of the real line. In the middle part of the article, we shall survey mathematical results about the structure of the hyperreal line. Near the end, we shall discuss philosophical issues concerning the nature and significance of the hyperreal line.

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