analysis

Question 1

how do we prove a set S is bounded

Answer 1

if |x| ≤ H for all x ∈ S

Question 2

what is the definition for boundedeness above

Answer 2

∃M ∈ R such that ∀x ∈ S one has x ≤ M

Question 3

now negate that definition, now its the definition for unboundedness above

Answer 3

∀M ∈ R ∃x ∈ S such that x > M