I have 2 statements that I need to say whether they are True or False. I do not need a proof. I would like some confirmation whether my answers are correct.
Every ordered field has the least upper bound property: False. I believe that if Q is an ordered field, then since Q does not have the least upper bound property, then every ordered field cannot have the least upper bound property.
Every ordered set that is bounded has a greatest lower bound. False. I think this is False due to basically the same reasoning as above. Q is an ordered set. For every subset, it can be bounded, but it does not have a greatest lower bound.