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Math Help - validity of convergent sequences with strict inequalities

  1. #1
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    validity of convergent sequences with strict inequalities

    Suppose there are two sequences {xk} and {yk} of reals such that {xk} converges to x, and yk converges to y.

    I know that if xk >= yk for all k>=m, then x>=y.

    However, if xk>yk for all k>=m, would x>y hold true as well?

    I'm rather bad with understanding subtle differences when it comes to strict inequalities, so please provide a reason as well.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by dgmath View Post
    Suppose there are two sequences {xk} and {yk} of reals such that {xk} converges to x, and yk converges to y.

    I know that if xk >= yk for all k>=m, then x>=y.

    However, if xk>yk for all k>=m, would x>y hold true as well?

    I'm rather bad with understanding subtle differences when it comes to strict inequalities, so please provide a reason as well.
    Of course not. 0<\frac{1}{n}
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  3. #3
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    Unhappy

    Quote Originally Posted by Drexel28 View Post
    Of course not. 0<\frac{1}{n}
    um, not sure I understand
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by dgmath View Post
    um, not sure I understand
    Define x_n=0 and y_n=\frac{1}{n} then x_n<y_n but \lim\text{ }x_n=\lim\text{ }y_n=0
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