find interior points, boundary points and closure

Question

For the following cases, determine the interior points, boundary points and closure

S₁ = {1} ∪ [2, 3] ∪ (4, 5) ⊆ R

Here's what I have so far:

int(S₁) = all points in (4,5) ∪ (2,3)

bd(S₁) = {1,2,3}

cl(S₁) = int(S) ∪ bd(S) = {1,2,3} ∪ (4,5) ∪ (2,3)

Does that seem right? Is there some way we can define the closure to be more concise?

Answer 1

Boundary is $\{1,2,3,4,5\}$ and closure is $\{1\} \cup [2,3] \cup [4,5]$.