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Math Help - function expression!

  1. #1
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    function expression!

     sup_{x \epsilon E} |f(x) - f(c)| < \varepsilon

    same as

     |f(x) - f(c)| < \varepsilon  \forall x \epsilon E

    can i write any of the above as same thing? just want to be cleared about something.

    thanks
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  2. #2
    MHF Contributor
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    Re: function expression!

    Quote Originally Posted by lawochekel View Post
     sup_{x \epsilon E} |f(x) - f(c)| < \varepsilon

    same as

     |f(x) - f(c)| < \varepsilon  \forall x \epsilon E
    These are not exactly the same. Consider f(x) = x, c = 0, E = {x | 0 ≤ x < 1} and ε = 1.
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