Abstract
We discuss convergent sequences, give some examples, and then prove the fundamental result that every bounded sequence has a convergent subsequence. This is then used to prove that every nonconstant complex polynomial has a complex root. Finally, we discuss what is meant by a sequence converging to ∞.
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© 1997 Springer Science+Business Media New York
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Beardon, A.F. (1997). Sequences. In: Limits. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0697-2_7
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DOI: https://doi.org/10.1007/978-1-4612-0697-2_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6872-7
Online ISBN: 978-1-4612-0697-2
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