Browse Definitions:
Definition

proper subset symbol

The proper subset symbol indicates a specific relationship between two set s. The symbol looks like the uppercase letter U in a sans-serif font , rotated 90 degrees clockwise. Proper-subset relations form the foundation of mathematical logic, including Boolean algebra, which is important in the design of computers and signal-processing systems.

Suppose there are two sets A and B. The statement "Set A is a proper subset of set B" is written A B. This means that every element contained in set A is also contained in set B, and there is at least one element in B that is not contained in A. Thus, no set is a proper subset of itself.

Here are some examples of true statements using the proper subset symbol:

{1, 2, 3, 4, 5, ... } {0, 1, 2, 3, 4, ...}
{0, 1, 2, 3, 4} {0, 1, 2, 3, 4, ...}
{-2, -3, 4} {-2,-2.5, -3, -3.5, -4}

The following statements, however, are not true:

{0, 1, 2, 3, 4, ...} {0, 1, 2, 3, 4, ...}
{0, 1, 2, 3, 4, ...} {0, -1, -2, -3, -4, ...}
{0, 1, 2, 3, 4, ...} {0, 1, 2, 3, 4}

Sets can contain things other than numbers. Examples are points on a plane, points on a spherical surface, and points in three-dimensional (3D) space. Proper subset relationships can be expressed in terms of specialized illustrations called Venn diagram s. In the illustration below, A B, and C B. However, it is not true that B A, nor is it true that A C, nor is it true that B C. In addition, the following statements are false: A A, B B, and C C.

Compare subset symbol . Also see set theory and Mathematical Symbols .

This was last updated in September 2005

Start the conversation

Send me notifications when other members comment.

SearchCompliance

• PCAOB (Public Company Accounting Oversight Board)

The Public Company Accounting Oversight Board (PCAOB) is a Congressionally-established nonprofit that assesses audits of public ...

• cyborg anthropologist

A cyborg anthropologist is an individual who studies the interaction between humans and technology, observing how technology can ...

• RegTech

RegTech, or regulatory technology, is a term used to describe technology that is used to help streamline the process of ...

SearchSecurity

• email spam

Email spam, or junk email, is unsolicited bulk messages sent through email with commercial, fraudulent or malicious intent.

• distributed denial of service (DDoS) attack

A distributed denial-of-service attack occurs when an attack originates from multiple computers or devices, usually from multiple...

• application whitelisting

Application whitelisting is the practice of identifying applications that have been deemed safe for execution and restricting all...

SearchHealthIT

• athenahealth Inc.

Based in Watertown, Mass., athenahealth Inc. is a leading vendor of cloud-based EHRs for small to medium-sized physician ...

• Affordable Care Act (ACA or Obamacare)

The Affordable Care Act (ACA) is legislation passed in 2010 that changed how uninsured Americans enroll in and receive healthcare...

• HIPAA Privacy Rule

The Standards for Privacy of Individually Identifiable Health Information, commonly known as the HIPAA Privacy Rule, establishes ...

SearchDisasterRecovery

• disaster recovery as a service (DRaaS)

One approach to a strong disaster recovery plan is DRaaS, where companies offload data replication and restoration ...

• data recovery

Data recovery restores data that has been lost, accidentally deleted, corrupted or made inaccessible. Learn how data recovery ...

• disaster recovery plan (DRP)

A company's disaster recovery policy is enhanced with a documented DR plan that formulates strategies, and outlines preparation ...

SearchStorage

• yottabyte (YB)

A yottabyte is a measure of theoretical storage capacity and is 2 to the 80th power bytes, or, in decimal, approximately 1,000 ...

• Kilo, mega, giga, tera, peta, exa, zetta and all that

Kilo, mega, giga, tera, peta, exa, zetta are among the list of prefixes used to denote the quantity of something, such as a byte ...

• brontobyte

A brontobyte is a measure of memory or data storage that is equal to 10 to the 27th power of bytes.

SearchSolidStateStorage

• SSD caching

SSD caching, also known as flash caching, is the temporary storage of data on NAND flash memory chips in a solid-state drive so ...

• NVDIMM (Non-Volatile Dual In-line Memory Module)

An NVDIMM (non-volatile dual in-line memory module) is hybrid computer memory that retains data during a service outage.

• NAND mirroring

NAND mirroring has been proposed to break the security in certain portable devices that use NAND flash memory for encryption.

SearchCloudStorage

• RESTful API

A RESTful application program interface breaks down a transaction to create a series of small modules, each of which addresses an...

• cloud storage infrastructure

Cloud storage infrastructure is the hardware and software framework that supports the computing requirements of a private or ...