# Math Help - Continuity

1. ## Continuity

Definition: a function f is very continuous if for every epsilon>0 there exists a delta>0 s.t. whenever x and t are in the domain of f and absolute value(x-t)<delta, we get absolute value(f(x)-f(t))<epsilon.

Prove: Let f and g be very continuous where f and g have the same domain. What can be said about f+g?

2. Originally Posted by spikedpunch
Definition: a function f is very continuous if for every epsilon>0 there exists a delta>0 s.t. whenever x and t are in the domain of f and absolute value(x-t)<delta, we get absolute value(f(x)-f(t))<epsilon.

Prove: Let f and g be very continuous where f and g have the same domain. What can be said about f+g?
Hint: Triangle inequality.