Chapter 4 - Functional limits and continuous functions

Question 1

Definition continuous

Answer 1

We say f is continuous at c if for every ε>0 there exists a δ>0 such that for all x∈ A we have |x-c| <δ
|f(x) - f(c)| < ε

Question 2

intermediate value theorem

Answer 2

let a,b∈ R such that a<b and f :[ a,b] converges to R be continuous
if y is real satisfying f(a) < y< f(b)
then there exists x∈ [a,b] such that f(x) = y

Question 3

limit point

Answer 3

let empty set = A (subset of R) be a set
we say c is a subset of R is a limit point of A if for every ε>0 there exists a point a∈ A such that |a-c| < ε