Given a real number a, we define the half-infinite intervals

Given a real number a, we define the half-infinite intervals

Given a real number a, we define the half-infinite intervals [a,∞) and(a,∞) by

[a, ∞) = {x ∈ R | x ≥ a},(a,∞) = {x ∈ R | x > a}.

Prove that following.

(1) [a,∞) ⊂ (b, ∞) if and only if a > b.

(2) (a, ∞) ⊂ [b, ∞) if and only if a ≥ b.1