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subseteq

Denotes a subset relationship where one set can be equal to another, commonly used in set theory and mathematical proofs.

Overview

Essential for expressing mathematical relationships between sets, particularly when showing hierarchical containment or proving set equivalence.

  • Frequently used in abstract algebra and topology to demonstrate subset relationships
  • Critical in formal mathematical writing to distinguish from strict subset notation
  • Common in discrete mathematics and computer science when describing set hierarchies
  • Appears regularly in proofs involving power sets and set operations

Examples

Showing a subset relationship between number sets.

N⊆Z⊆Q⊆R\mathbb{N} \subseteq \mathbb{Z} \subseteq \mathbb{Q} \subseteq \mathbb{R} 
\mathbb{N} \subseteq \mathbb{Z} \subseteq \mathbb{Q} \subseteq \mathbb{R}

Defining a power set relationship.

A⊆B  ⟹  P(A)⊆P(B)A \subseteq B \implies \mathcal{P}(A) \subseteq \mathcal{P}(B) 
A \subseteq B \implies \mathcal{P}(A) \subseteq \mathcal{P}(B)

Expressing interval containment.

[0,1]⊆[−1,2]⊆R[0,1] \subseteq [-1,2] \subseteq \mathbb{R} 
[0,1] \subseteq [-1,2] \subseteq \mathbb{R}