# function expression!

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• June 17th 2013, 10:06 AM
lawochekel
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
• June 17th 2013, 10:22 AM
emakarov
Re: function expression!
Quote:

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

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.