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Sequence Limit (abstract math)

  1. Dec 3, 2008 #1
    1. The problem statement, all variables and given/known data

    If x_n[tex]\rightarrow[/tex] L and y_n [tex]\rightarrow[/tex] M

    prove that

    x_n - y_n [tex]\rightarrow[/tex] L-M

    2. Relevant equations

    Definition of Limit

    3. The attempt at a solution

    I followed and stayed within the definition of limit of a sequence, but I got 0 for x_n - y_n.
  2. jcsd
  3. Dec 3, 2008 #2


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    Can you show us what you did then? Probably your approach is correct but you made a small mistake somewhere.
  4. Dec 3, 2008 #3


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    [itex]|(x_n- y_n)- (L- M)|= |(x_n- L)+ (-y_n+ M)|\le |x_n-L|+ |-y_n+ M|[/itex]
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