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Thread: analysis!!

  1. #1
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    analysis!!

    Let $\displaystyle {x_n \ be \ a \ bounded \ sequence \ ,\ for \ m \ \in N , \ let \ y_m = sup \{x_n ; n \geq m \}} $
    $\displaystyle show \ that \ y_m \ is \ convergent $
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  2. #2
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    Quote Originally Posted by flower3 View Post
    Let $\displaystyle (x_n)$ be a bounded sequence. For $\displaystyle m \in N$, let $\displaystyle y_m = \sup \{x_n ; n \geq m \}$.
    Show that $\displaystyle (y_m)$ is convergent.
    Hint: Show that $\displaystyle (y_m)$ is a decreasing sequence that is bounded below.
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