Abstract
On the historical scale, analysis is a modern discipline with ancient roots. The machinery of analysis—the calculus—is a fusion of arithmetic with geometry that has been in existence for only a few hundred years, but the problem of achieving such a fusion is much older. The problem of combining arithmetic and geometry occurs in Euclid’s Elements, around 300 BCE, and indeed Euclid includes several of the ideas that we use to solve this problem today.
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Notes
- 1.
In this book we use ⟨ and ⟩ to bracket ordered pairs, triples, and so on. This is to avoid confusion with the notation (a, b), which will later be used for the open interval of points x such that a < x < b.
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Stillwell, J. (2013). The Fundamental Questions. In: The Real Numbers. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-01577-4_1
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