a partition of

USAGE SUMMARY

The phrase "a partition of" is correct and usable in written English.
It can be used in mathematical contexts, particularly in set theory or number theory, to describe a way of dividing a set into distinct subsets. Example: "A partition of the set {1, 2, 3, 4} could be {{1, 2}, {3, 4}}."

✓ Grammatically correct

Science

News & Media

Academia

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

An experimental hypothesis is defined as a partition of the sampled flux distribution set.

BMC Systems Biology

The result, he said, could be a "partition of Iraq".

The New York Times

So we're going to draw a partition of the we're going to draw a partition of the object space from a Chinese restaurant process.

Massachusetts Institute of Technology

"We do not want a partition of Ukraine, we do not need this," he said.

The Guardian

A dissection of a plane geometrical figure is a partition of it by straight lines.

Cornell University

The best thing now is to admit defeat, allow a partition of the Yugoslav province along ethnic lines and leave.

The New York Times

This historic decision paved the way for a potential settlement of the conflict based on a partition of the land.

The Guardian

So the prior generates a partition of data, so it doesn't depend on the observed features of the data.

Massachusetts Institute of Technology

Does this foreshadow a partition of the country, and more generally the entire Middle East on ethno-religious criteria?

Columbia University

An extended analysis based on a partition of the statistic into independent components is suggested.

Journal of Statistical Planning and Inference

As a method of increasing the resolution, a partition of unity based extrinsic enrichment is used.

International Journal of Solids and Structures

Expert writing Tips

Best practice

When using "a partition of", ensure that the subsets created are mutually exclusive and collectively exhaustive, meaning that each element belongs to exactly one subset and all elements are accounted for.

Common error

Avoid using "a partition of" when you simply mean a general division or separation. A partition has a specific mathematical meaning: subsets must be disjoint and their union must equal the original set. If these conditions aren't met, use "a division of" or "a separation into" instead.

Linguistic Context

The phrase "a partition of" functions as a noun phrase that often serves as a prepositional complement. It specifies the action of dividing a set or entity into mutually exclusive subsets. As Ludwig AI confirms, its use is grammatically correct and supported by numerous examples.

Expression frequency: Very common

Frequent in

Science

60%

Academia

20%

News & Media

20%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, the phrase "a partition of" is a grammatically correct and frequently used expression, as affirmed by Ludwig AI. It primarily functions as a noun phrase, indicating a structured division into mutually exclusive subsets. Its purpose is to describe such divisions within formal and scientific contexts, frequently appearing in science and academic domains. While alternatives like "a division into" or "a segmentation of" exist, "a partition of" carries a more precise, often mathematical, connotation. Therefore, it is crucial to use the phrase accurately and be mindful of its underlying mathematical implications. Remember, a valid partition requires that all subsets are disjoint and their union forms the original set.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

a division into

This alternative focuses on the act of dividing something into separate parts, similar to creating a partition.

a separation into

Emphasizes the act of separating something into distinct elements, akin to partitioning.

a segmentation of

This term is frequently used when referring to dividing something, like a market or image, into segments.

a dissection of

Implies a more detailed and analytical division, often used in scientific contexts.

a breakdown of

Focuses on breaking down a whole into its constituent parts, which can also represent a partitioning.

a fragmentation of

Suggests breaking something into smaller, often disconnected, pieces.

a compartmentalization of

Highlights the act of dividing into separate compartments or categories.

a categorization of

Focuses on grouping items into distinct categories, effectively partitioning a larger set.

a clustering of

Suggests grouping similar items together, which implicitly creates a partition of a larger dataset.

a decomposition of

Implies breaking down a complex entity into simpler components, representing a form of partitioning.

FAQs

How is "a partition of" used in mathematics?

In mathematics, "a partition of" a set divides the set into non-empty subsets such that every element is in exactly one subset. The subsets are mutually exclusive, and their union is the original set.

What's the difference between "a partition of" and "a division of"?

"A partition of" has a more specific mathematical connotation, requiring disjoint subsets that cover the whole set. "A division of" is a more general term that may not have these strict requirements.

Can "a segmentation of" be used instead of "a partition of"?

While both terms imply division, "a segmentation of" is often used when dividing something into distinct segments or categories, but it doesn't necessarily adhere to the mathematical precision of "a partition of".

How do I ensure I'm using "a partition of" correctly?

Verify that the resulting subsets are non-overlapping (disjoint) and that their combination includes all the original elements. If not, consider alternatives like "a grouping of" or "a separation into".