well-ordered

USAGE SUMMARY

The phrase "well-ordered" is correct and usable in written English.
It can be used to describe something that is organized, structured, or arranged in a systematic way. Example: "The well-ordered files made it easy to find the necessary documents quickly."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

44 human-written examples

(The real numbers are not well-ordered in their usual order: just consider an open interval. Meanwhile, N is the simplest infinite well-ordered set).

SEP

Generally, English teams are less well-ordered.

The Guardian - Sport

His Masada pieces are often tidy, well-ordered, alluring.

The New York Times - Arts

She recalls the bliss of visiting a well-ordered home.

Independent

Does any of this suggest a well-ordered universe?

The New York Times

Then was the world of such folk well-ordered".

The Economist

Human-verified similar examples from authoritative sources

Similar Expressions

16 human-written examples

Note that the ordered set ( X, ⪯ ) is not well ordered.

Fixed Point Theory and Applications

Layered spaces seem at once well ordered and dynamically jumbled.

The New York Times - Arts

It's meant to be very well ordered, like a shop.

The New York Times - Magazine

Also, let Θ be well ordered.

Mathematical Sciences

Then it is clear that A is not well ordered but it is g-well ordered.

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When describing abstract concepts like data structures or systems, use "well-ordered" to highlight a clear and logical arrangement. For example, "a well-ordered database" implies easy navigation and retrieval.

Common error

Avoid using "well-ordered" when you simply mean 'tidy' or 'neat'. "Well-ordered" implies a deeper, structural arrangement, not just a superficial cleanness. Use "neatly arranged" or "tidily organized" in those cases.

Linguistic Context

The phrase "well-ordered" primarily functions as a descriptive adjective, modifying nouns to indicate a state of organized arrangement or structured order. As Ludwig AI shows, it describes anything from social lives to crystal structures.

Expression frequency: Common

Frequent in

Science

50%

News & Media

44%

Wiki

6%

Less common in

Formal & Business

0%

Encyclopedias

0%

Reference

0%

Ludwig's WRAP-UP

In summary, the term "well-ordered" is a grammatically correct adjective phrase primarily used to describe something possessing a clear, logical, and systematic arrangement. Ludwig AI confirms its correct usage and applicability across various domains, especially in science and news media. While synonyms like "systematically arranged" or "methodically organized" can be used, "well-ordered" often implies a more profound structural arrangement than simple tidiness. It's crucial to use the hyphenated form when using it as an adjective before a noun. In mathematical contexts, "well-ordered" carries a very specific technical meaning.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

orderly

A simpler, one-word alternative emphasizing order.

structured

A shorter alternative focusing on the presence of structure.

systematically arranged

Replaces "well-ordered" with a more descriptive term focusing on arrangement.

methodically organized

Focuses on the method of organization instead of the result.

precisely structured

Emphasizes the precision of the structure.

neatly arranged

Highlights the tidiness and orderliness.

logically organized

Emphasizes the logical aspect of the organization.

carefully planned

Shifts the focus to the planning process.

in good order

Expresses the idea of being in a state of orderliness.

well-regulated

Focuses on the control and regulation aspect of the order.

FAQs

How can I use "well-ordered" in a sentence?

You can use "well-ordered" to describe systems, sets, or structures that have a clear and logical arrangement, for instance: "The professor presented a well-ordered argument" or "The data was stored in a well-ordered database".

What is a good substitute for "well-ordered"?

Depending on the context, you can use alternatives such as "systematically arranged", "methodically organized", or simply "orderly".

Is it correct to say something is "well ordered"?

Yes, "well ordered" is a correct and commonly used phrase. However, ensure that the hyphen is included ("well-ordered") when using it as an adjective before a noun, as in "a well-ordered system".

What does "well-ordered" mean in mathematical contexts?

In mathematics, especially set theory, "well-ordered" has a specific meaning: a set is well-ordered if every non-empty subset has a least element. This is a stricter condition than simply being ordered.