# Reelle Zahlen/Folgen/Quetschkriterium/Fakt/Beweis/Aufgabe/en

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Let ${\displaystyle {}{\left(x_{n}\right)}_{n\in \mathbb {N} },\,{\left(y_{n}\right)}_{n\in \mathbb {N} }}$ and ${\displaystyle {}{\left(z_{n}\right)}_{n\in \mathbb {N} }}$ be three real sequences. Let ${\displaystyle {}x_{n}\leq y_{n}\leq z_{n}{\text{ for all }}n\in \mathbb {N} }$ and ${\displaystyle {}{\left(x_{n}\right)}_{n\in \mathbb {N} }}$ and ${\displaystyle {}{\left(z_{n}\right)}_{n\in \mathbb {N} }}$ be convergent to the same limit ${\displaystyle {}a}$. Prove that also ${\displaystyle {}{\left(y_{n}\right)}_{n\in \mathbb {N} }}$ converges to the same limit ${\displaystyle {}a}$.