disjoint sets

USAGE SUMMARY

The phrase "disjoint sets" is correct and usable in written English.
It is typically used in mathematics and computer science to describe two or more sets that have no elements in common. Example: "In set theory, disjoint sets are important because they help in understanding the relationships between different groups of data."

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

A and B are hardly disjoint sets.

University of California, Berkeley

- Construction of Almost Disjoint Sets (section 16.1.1).

Princeton University

The important condition is that the problem can be made into disjoint sets.

Joe Celko's Analytics and OLAP in SQL

We maintain for each term two postings lists consisting of disjoint sets of documents, each sorted by values.

Stanford University

The components of this ensemble are trained locally on subsets of features for disjoint sets of data.

Procedia Computer Science

It also permits disjoint sets of adjacent slices to be composited together to form intermediate images, which are then composited together to form a final image.

Stanford University

Mathematically, we partition into three disjoint sets.

EURASIP Journal on Wireless Communications and Networking

This means that (W_{k}) are compact pairwise disjoint sets.

Journal of Inequalities and Applications

Suppose that A and B are convex and disjoint sets.

Advances in Difference Equations

Recall that pilot subcarriers are transmitted over disjoint sets of subcarriers at different antennas.

EURASIP Journal on Wireless Communications and Networking

Remark: In [16], disjoint sets of subcarriers were considered to reduce the MMSE channel estimation error.

EURASIP Journal on Advances in Signal Processing

Expert writing Tips

Best practice

When using "disjoint sets", clearly define the universal set from which these sets are drawn to provide context and prevent ambiguity. For example, specify that you're referring to "disjoint sets of data points" within a particular dataset.

Common error

Avoid assuming that "disjoint sets" implies statistical independence. While disjoint sets have no elements in common, independence refers to the lack of influence between events. Ensure you're using the correct term for your intended meaning.

Linguistic Context

The phrase "disjoint sets" functions as a noun phrase often used as a mathematical or logical term. It describes sets that have no elements in common. Ludwig AI provides examples of this usage in diverse scientific and academic contexts.

Expression frequency: Very common

Frequent in

Science

76%

Academia

22%

Wiki

2%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "disjoint sets" is a grammatically correct noun phrase primarily used in scientific and academic writing to describe sets with no common elements. Ludwig AI confirms its correctness and frequent usage in these contexts. The phrase serves to categorize, classify, or partition information to avoid overlap and ensure clarity. While it's a common term, consider using alternatives like "mutually exclusive sets" or "non-overlapping sets" to add variety to your writing. When using "disjoint sets", ensure that you clearly define the broader context to prevent any potential ambiguity.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

mutually exclusive sets

Changes the phrasing to emphasize the exclusivity between the sets.

non-overlapping sets

Uses more common terminology to describe the absence of overlap.

non-intersecting sets

Specifies that the sets do not have any intersection.

separate sets

Simplifies the wording to indicate that the sets are distinct and not connected.

exclusive sets

Highlights the fact that the elements of these sets are exclusive to them.

independent sets

Highlights the statistical independence, implying no shared elements or influence.

distinct sets

Focuses on the uniqueness and separateness of each set.

unconnected sets

Emphasizes the lack of any relationship or shared elements between the sets.

partitioned sets

Indicates that the sets form a partition of a larger set, with no overlap.

discrete sets

Stresses the individuality and isolated nature of each set.

FAQs

How do I use "disjoint sets" in a sentence?

You can use "disjoint sets" to describe groups that have no elements in common. For example, "The data was divided into two "disjoint sets" for training and testing purposes".

What is the significance of "disjoint sets" in mathematics?

In mathematics, "disjoint sets" are important because they simplify calculations and proofs by ensuring that there is no overlap between sets being considered. This is especially useful in probability theory and set theory.

Are "disjoint sets" the same as mutually exclusive sets?

Yes, the terms "disjoint sets" and "mutually exclusive sets" are often used interchangeably, especially in probability and statistics. Both terms refer to sets that have no elements in common.

What are some examples of "disjoint sets" in real-world applications?

Examples of "disjoint sets" include dividing a population into age groups with no overlap, categorizing species in a habitat where no species belong to multiple categories simultaneously, or partitioning network traffic into separate and distinct flows.