total order
[/ˈtoʊtəl ˈɔrdər/]
nounpl: total orders
ordem total
1. In mathematics and computer science, a binary relation on a set where every pair of distinct elements is comparable, meaning for any two elements a and b, either a ≤ b or b ≤ a (or both if they are equal)
The set of real numbers with the standard less-than-or-equal relation forms a total order.
O conjunto dos números reais com a relação padrão de menor-ou-igual forma uma ordem total.
2. A relation that is reflexive, antisymmetric, transitive, and total (connected), establishing a complete ordering of elements
A total order allows us to arrange all elements in a linear sequence without ambiguity.
Uma ordem total nos permite arranjar todos os elementos em uma sequência linear sem ambiguidade.
This is specialized mathematical terminology used primarily in academic and technical contexts in both English and Portuguese-speaking countries. It is fundamental to computer science, mathematics, and formal logic courses. The term is relatively recent in origin (20th century) and is not part of everyday colloquial speech in either culture.
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