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Math Help - analysis!!

  1. #1
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    analysis!!

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