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