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Section: Theorems Regarding Limits of Functions
We observe that every real sequence $(x_n)_{n\in\mathbb N}$ can be interpreted as a function $f:\mathbb N\to\mathbb R.$ With this observation in mind, all theorems we can prove about the limits of functions will also apply to the limits of sequences. In this section, we present some of these theorems.
Table of Contents
 Proposition: Limit of a Function is Unique If It Exists
 Proposition: Arithmetic of Functions with Limits  Sums
 Proposition: Arithmetic of Functions with Limits  Difference
 Proposition: Arithmetic of Functions with Limits  Division
 Proposition: Preservation of Inequalities for Limits of Functions
 Proposition: Convergence Behavior of the Inverse of Sequence Members Tending to Infinity
 Theorem: Squeezing Theorem for Functions
 Proposition: Arithmetic of Functions with Limits  Product
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
 Modler, F.; Kreh, M.: "Tutorium Analysis 1 und Lineare Algebra 1", Springer Spektrum, 2018, 4th Edition