The question is a True/False one and reads:

"Every subset of the rational numbers \(\mathbb{Q}\) which is bounded from below has a greatest lower bound \(c \in \mathbb{Q}\)."

and the answer given is false.

My understanding is that, since the Completeness Axiom says every non-empty set which is bounded from below has a greatest lower bound, the \(c\in \mathbb{Q}\) must be the part which makes the statement false but I can't think of why.

Thanks :)

This makes much more sense, thanks so much!