# Math Help - function expression!

1. ## 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

2. ## Re: function expression!

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.