Quiz 5

Question 1

perfect set

Answer 1

A set P ⊆ R is perfect if it is closed and contains no isolated points.

Question 2

separated sets

Answer 2

Two nonempty sets A,B ⊆ R are seperated in Aclosure∩B and A∩Bclosure are both empty

Question 3

disconnected set

Answer 3

A set E ⊆ R is disconnected if it can be written as E = A∪B, where A and B are nonempty separated sets

Question 4

connected set

Answer 4

It is not disconnected

Question 5

epsilon-delta definition of the limit of a function

Answer 5

limf(x)=L if and only if for every ϵ>0, ∃δ>0 such that |x−c|<δ ⟹ |f(x)−L|<ϵ.

Question 6

epsilon-delta definition of continuity

Answer 6

A function 𝑓(𝑥) is continuous at x=c if, for every ϵ>0, there exists a δ>0 such that: |x−c|<δ ⟹ |f(x)−f(c)|<ϵ