Thread: clarification

i was just wondering which is correct:

a function f is defined on an interval I is contonuous if lim as x->c for f(x) is f(c) for all x in I or for all c in I.

i thought it should be the former but the book that im reading states that its the latter.

thanks

It is the latter.


Fernando Revilla

thanks for the clarification..but may i know why, if for this case, it is the latter then for this case:
a function f is cont at c if every seq of points x_n in I such that lim as n->infinity for x_n is c if the lim n->inifinity f(x_n) is f(c).
in this case, we are talking about x_n in I and not for all c in I.

i hope im making sense

Originally Posted by alexandrabel90

thanks for the clarification..but may i know why, if for this case, it is the latter then for this case:
a function f is cont at c if every seq of points x_n in I such that lim as n->infinity for x_n is c if the lim n->inifinity f(x_n) is f(c).
in this case, we are talking about x_n in I and not for all c in I.

i hope im making sense

Think about what you're saying in a simpler sense. This is a "dummy" variable, in the same sense as the in . What's really fixed is the . Think about your definition you gave in terms of sequences. A function is continuous on if at every that's true. No?