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)