$\displaystyle sup_{x \epsilon E} |f(x) - f(c)| < \varepsilon $ same as $\displaystyle |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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Originally Posted by lawochekel $\displaystyle sup_{x \epsilon E} |f(x) - f(c)| < \varepsilon $ same as $\displaystyle |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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