I'm having some trouble with the definition of "Bounded Set". I have a pretty good idea of what "Limited" means: a Set with a Upper and a Lower bounds. Now i have a quiz in which I must choose the right answer and I have absolutely no idea what to chose:
With A ⊆ R and M ∈ R+, A is Limited if: (a) ∀M ∈ R+ : ∃a ∈ A : |a| > M (b) ∃a ∈ A : |a| > M, ∀M ∈ R+ : (c) ∃M ∈ R+ : |a| ≥ M, ∀a ∈ A (d) ∃M ∈ R+ : ∃a ∈ A : |a| > M (e) ∀M ∈ R+ : |a| ≥ M, ∀a ∈ A
In the same way:
With A ⊆ R and M ∈ R+, A is Unlimited if: (a) ∀M ∈ R+ : ∃a ∈ A : |a| > M (b) ∃M ∈ R : ∃a ∈ A :|a| > M (c) ∀a ∈ A : ∃M ∈ R+ :|a| ≥ M (d) ∃M ∈ R+ : |a| ≥ M, ∀a ∈ A (e) ∀M ∈ R+ : |a| ≥ M, ∀a ∈ A
Can you chose the right answer? ( I have the solutions of course but i want a clear explanation of what an limited and unlimited set is). Thanks
Edit: the right answers: (c) and (a)