a total order

USAGE SUMMARY

The phrase "a total order" is correct and usable in written English.
It is typically used in mathematics and computer science to describe a binary relation that is reflexive, antisymmetric, transitive, and total. Example: "In this set, we can define a total order based on the numerical values of the elements."

✓ Grammatically correct

Science

Encyclopedias

News & Media

Human-verified examples from authoritative sources

Exact Expressions

46 human-written examples

A set S is well-ordered by a relation < iff < is a total order and every subset of S has a least element in the <-ordering.

SEP

For the class of rooted multi-trees, a canonical form of a rooted multi-tree T is given by an "ordered tree" τ of it (i.e., determination of a total order among children of each vertex).

Journal of Cheminformatics

Even with scenes that require a total order, fully scalable submission and rendering are demonstrated.

Stanford University

The cosmic order is a total order; it comprises not only all natural things but also social and ethical rules.

Encyclopedia Britannica

It did not explain the observable fact that, notwithstanding continual changes, a total order of specific forms continued to exist.

Encyclopedia Britannica

However, state machine replication requires replicas to run deterministically and to process requests sequentially according to a total order.

Journal of Systems and Software

Human-verified similar examples from authoritative sources

Similar Expressions

14 human-written examples

We are focusing on two prominent types of contracts, a total order-delivery commitment and an incentive-based operational just-in-time coordination.

International Journal of Production Economics

The outcome of requirements prioritization is a total ordering of requirements that best accommodates the various kinds of constraints and priorities.

Information and Software Technology

Preserving DE semantics at runtime can be challenging, since the global, consistent notion of time may lead to a total ordering of execution in a distributed system, an unnecessary waste of resources.

University of California, Berkeley

That each (le _{ab}) is a total ordering is obvious from the proof of Proposition 5.0.4.

Bulletin of Mathematical Sciences

Comparatives like John is happier than Mary finally, are according to the received view, such that they refer to abstract objects that form a total ordering (so-called degrees).

SEP

Expert writing Tips

Best practice

Use "a total order" when you need to specify that all pairs of elements in a set are comparable.

Common error

Avoid using "a total order" when a partial order is more appropriate. A partial order allows for elements to be incomparable, whereas a total order requires all elements to be comparable.

Linguistic Context

The phrase "a total order" functions as a noun phrase, typically acting as a subject or object in a sentence. Ludwig AI confirms its usage in technical and formal contexts.

Expression frequency: Very common

Frequent in

Science

76%

Academia

11%

Encyclopedias

6%

Less common in

News & Media

4%

Wiki

2%

Formal & Business

1%

Ludwig's WRAP-UP

In summary, "a total order" is a grammatically correct and frequently used phrase, particularly in scientific and academic contexts. It defines a binary relation where every pair of elements is comparable. Ludwig AI underscores its prevalence in formal writing, especially within mathematics and computer science. When using this phrase, remember its specific definition and avoid confusing it with partial orders. To enhance clarity, be precise and specify the set and properties of the ordering relation. While alternatives like "complete ordering" and "linear order" exist, the choice depends on the specific context and nuances you want to convey.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

complete ordering

Replaces "total" with "complete", emphasizing the comprehensive nature of the order.

linear order

Synonymous with "total order", commonly used in mathematics and computer science.

strict total order

Adds the qualifier "strict" to emphasize that no two distinct elements are equivalent.

full ordering

Similar to "complete ordering", focusing on the entirety of the order.

complete sequence

Shifts the focus to a sequence instead of a general order.

entire arrangement

Uses "arrangement" to denote a structured order, but is less formal.

unconditional sequence

Focuses on sequence without any condition.

absolute arrangement

Substitutes "absolute" to imply that the arrangement is definitive.

finished sequence

Emphasis on a sequence that is finished.

definite arrangement

Definite puts emphasis on an arrangement that is clear and precise.

FAQs

How is "a total order" used in mathematics?

In mathematics, "a total order" refers to a binary relation on a set where every pair of distinct elements is comparable. This means for any two elements a and b, either a ≤ b or b ≤ a.

What's the difference between "a total order" and a partial order?

While "a partial order" allows elements to be incomparable, "a total order" requires all elements to be comparable. Every pair of elements must be related.

Where can I find "a total order" applied in computer science?

"A total order" is crucial in algorithms that require sorting or ranking, ensuring that items are processed in a definite sequence. It is also used in database management to uniquely identify records.

What are some synonyms for "a total order"?

Alternatives include "complete ordering" and "linear order". The choice depends on the specific context.