Abstract
In Definition 6.1.5 we defined what it meant for a sequence \((x_n)_{n=m}^\infty \) of real numbers to converge to another real number x; indeed, this meant that for every \({\varepsilon }> 0\), there exists an \(N \ge m\) such that \(|x-x_n| \le {\varepsilon }\) for all \(n \ge N\). When this is the case, we write \(\lim _{n \rightarrow \infty } x_n = x\).
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Tao, T. (2022). Metric Spaces. In: Analysis II. Texts and Readings in Mathematics, vol 38. Springer, Singapore. https://doi.org/10.1007/978-981-19-7284-3_1
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DOI: https://doi.org/10.1007/978-981-19-7284-3_1
Publisher Name: Springer, Singapore
Online ISBN: 978-981-19-7284-3
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