## Abstract

A *sequence* is a function whose domain is a set of the form {*n* ∈ ℤ : *n ⩾ m*}; *m* is usually 1 or 0. Thus a sequence is a function that has a specified value for each integer *n ⩾ m*. It is customary to denote a sequence by a letter such as *s* and to denote its value at *n* as *s* _{ n } rather than *s(n)*. It is often convenient to write the sequence as \( ({S_n})_{n = m}^\infty or({S_m},{S_{m + 1}},{S_{m + 2}},...) \). If *m* = 1 we may write *(s* _{ n })_{ n } ∈ ℕ or of course (*s* _{1},*s* _{2},*s* _{3},...). Sometimes we will write (*s* _{ n }) when the domain is understood or when the results under discussion do not depend on the specific value of *m*. In this chapter we will be interested in sequences whose range values are real numbers, i.e., each *s* _{ n } represents a real number.

## Keywords

Rational Number Cauchy Sequence Formal Proof Convergent Sequence Convergent Series## Preview

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