Linearly ordered group

In abstract algebra a linearly ordered or totally ordered group is a group G equipped with a total order "≤", that is translation-invariant. This may have different meanings. Let a, b, c ∈ G, we say that (G, ≤) is a

In analogy with ordinary numbers, we call an element c of an ordered group positive if 0 ≤ c and c ≠ 0, where "0" here denotes the identity element of the group (not necessarily the familiar zero of the real numbers). The set of positive elements in a group is often denoted with G₊.