I just read in a textbook that "An infinite set may not have a maximum or minimum, but it will always have a supremum and infimum."
Is this true? What, for example, is the supremum of the real numbers, or the infimum of the real numbers?
I can imagine that any bounded infinite set has a supremum/infimum, but if a set is unbounded (e.g. $\mathbb{R}$), then how can it have a greatest lower bound or least upper bound?