[:linear continuum:] • A nonempty set LL with a total order is called a linear continuum if the following hold: • LL has the least upper bound property, i.e. every nonempty subset of LL with an upper bound has a least upper bound • The order is a dense order, i.e. for every a<ca < c exists a bb s.t. a<b<ca < b < c • Intuition: linear continuums are "R\mathbb R-like" without requiring properties of R\mathbb R besides order-related ones