Kurs:Mathematik für Anwender (Osnabrück 2019-2020)/Teil I/Repetitorium/10/Folgenstetigkeit - Logic and Process/Studentenfrage/Antwort

We want to prove the equivalence of two statements. The logic of the proof is thus, that first we assume the first statement (1) and deduce the second statement (2). After we have done that we assume the second statement (2) and deduce the first statement (1).

For the direction (1) ${}\Rightarrow$ (2) we directly prove the convergence of the image sequence using the definitions.

For the other direction we assume the negation of (1) and prove the negation of (2) (i.e. we use proof by contraposition) by explicitly constructing a sequence as a counterexample.

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