1. A mathematical field equipped with a total order that is compatible with the field operations, meaning the order respects addition and multiplication
The real numbers form a totally ordered field under the standard ordering and arithmetic operations.
Os números reais formam um corpo totalmente ordenado sob a ordenação padrão e as operações aritméticas.
2. An algebraic structure where every two elements are comparable and the ordering is preserved under field operations
In a totally ordered field, if a < b and c > 0, then ac < bc.
Em um corpo totalmente ordenado, se a < b e c > 0, então ac < bc.