Abstract
As we have seen, we can represent any rational number, for instance \(\sqrt 2 \), by its successive approximations with rational numbers, q1, q2, .... According to Greek mathematicians the process which generates the approximations q1, q2, ... never ends; for us, instead, such a process is the realization of \(\sqrt 2 \) as the limit of the sequence {q n }. In this chapter we shall discuss the notions of sequence and of limit of a sequence.
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© 2004 Springer Science+Business Media New York
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Giaquinta, M., Modica, G. (2004). Sequences of Real Numbers. In: Mathematical Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4414-7_2
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DOI: https://doi.org/10.1007/978-0-8176-4414-7_2
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4337-9
Online ISBN: 978-0-8176-4414-7
eBook Packages: Springer Book Archive