Abstract
The fixing of a reference point or origin, and a unit point on a line constitutes the establishment of a coordinate system on that line. For each choice of a coordinate system on a line there is determined the set of rational points; those measurable using ℚ, and the set of irrational points such as \(\sqrt {2.} 2\). We have mentioned the idea of using the fact that ℚ is dense, to “approximate” irrationals by rationals, a notion that we must make more precise.
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© 1994 Springer Science+Business Media New York
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Pedrick, G. (1994). Approximation: The Real Numbers. In: A First Course in Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8554-5_2
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DOI: https://doi.org/10.1007/978-1-4419-8554-5_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6435-4
Online ISBN: 978-1-4419-8554-5
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