Linear (Total) Order (線形順序・全順序) (Definition I.3.3)
- Linear (Total) Order (線形順序・全順序) (Definition I.3.3) #Card
- An order $\leq$ on $X$ is linear (or total) if for any two elements either $x_0 \leq x_1$ or $x_1 \leq x_0$. A linearly ordered set is also called a chain.
An order $\leq$ on $X$ is called linear or total if for any two elements of $X$ either $x_0 \leq x_1$ or $x_1 \leq x_0$（比較不能な対がない）. A linearly ordered set is also called a chain（鎖）.
- $\mathbb{R}$ の標準順序は線形；$(2^{{0,1}}, \subset)$ は線形でない（${0}$ と ${1}$ が比較不能、Example I.3.1）。
- 「linear」の名は実数直線 (real line) に由来。
LinearOrder X（le_total）