# Real line

The real line carries a standard topology which can be introduced in two different, equivalent ways. First, since the real numbers are totally ordered, they carry an order topology. With respect to this topology, the real line is a linear continuum. Second, the real numbers can be turned into a metric space by using the metric given by the absolute value: ${\displaystyle d(x,y):=|y-x|}$. This metric induces a topology on R equivalent to the order topology.