🔢 Complete Set Theory Symbols Generator
Master set theory with ∈, ⊂, ∪, ∩, ∅, ℕ, ℤ, ℚ, ℝ, ℂ symbols, mathematical sets, operations, and interactive calculator. Perfect for mathematics students, professors, and researchers with step-by-step explanations.
🧮 Set Theory Calculator
Evaluate set theory expressions, perform set operations, and analyze mathematical sets with step-by-step explanations.
Complete Set Theory Symbol System
∈ Basic Set Relations
⚡ Set Operations
🔢 Number Sets
📊 Cardinality & Size
🔗 Functions & Relations
🎯 Advanced Set Theory
Set Theory Expressions & Examples
🔢 Complete Set Theory Symbols Reference Table
Master the complete set theory symbol system with our comprehensive reference table. Click any set theory symbol to copy it instantly for use in your mathematical proofs, research papers, and educational materials.
| Symbol | Name | HTML Code | Unicode | Category | Usage |
|---|---|---|---|---|---|
| ∈ Basic Set Relations | |||||
| ∈ | Element of | ∈ | U+2208 | Set Relation | x ∈ A |
| ∉ | Not element of | ∉ | U+2209 | Set Relation | x ∉ A |
| ⊂ | Subset | ⊂ | U+2282 | Set Relation | A ⊂ B |
| ⊆ | Subset or equal | ⊆ | U+2286 | Set Relation | A ⊆ B |
| ⊃ | Superset | ⊃ | U+2283 | Set Relation | A ⊃ B |
| ⊇ | Superset or equal | ⊇ | U+2287 | Set Relation | A ⊇ B |
| ∅ | Empty set | ∅ | U+2205 | Set Symbol | ∅ |
| ⚡ Set Operations | |||||
| ∪ | Union | ∪ | U+222A | Set Operation | A ∪ B |
| ∩ | Intersection | ∩ | U+2229 | Set Operation | A ∩ B |
| ∖ | Set difference | ∖ | U+2216 | Set Operation | A ∖ B |
| △ | Symmetric difference | △ | U+2206 | Set Operation | A △ B |
| × | Cartesian product | × | U+00D7 | Set Operation | A × B |
| 🔢 Number Sets | |||||
| ℕ | Natural numbers | ℕ | U+2115 | Number Set | ℕ |
| ℤ | Integers | ℤ | U+2124 | Number Set | ℤ |
| ℚ | Rational numbers | ℚ | U+211A | Number Set | ℚ |
| ℝ | Real numbers | ℝ | U+211D | Number Set | ℝ |
| ℂ | Complex numbers | ℂ | U+2102 | Number Set | ℂ |
| ➕ Additional Set Relations | |||||
| ≡ | Identical to | ≡ | U+2261 | Set Relation | A ≡ B |
| ∋ | Contains as member | ∋ | U+220B | Set Relation | A ∋ x |
| ∌ | Does not contain | ∉ | U+220C | Set Relation | A ∌ x |
| 🔧 Advanced Set Operations | |||||
| ⊕ | Direct sum | ⊕ | U+2295 | Set Operation | A ⊕ B |
| ⊗ | Tensor product | ⊗ | U+2297 | Set Operation | A ⊗ B |
| ⊙ | Hadamard product | ⊙ | U+2299 | Set Operation | A ⊙ B |
| 🔢 Extended Number Sets | |||||
| ℚ⁺ | Positive rationals | ℚ² | U+211A U+207A | Number Set | ℚ⁺ |
| ℝ⁺ | Positive reals | ℝ² | U+211D U+207A | Number Set | ℝ⁺ |
| ℝⁿ | n-dimensional reals | ℝ&supn; | U+211D U+207F | Number Set | ℝⁿ |
| ℤ⁺ | Positive integers | ℤ² | U+2124 U+207A | Number Set | ℤ⁺ |
| 📊 Cardinality Symbols | |||||
| | | Cardinality | | | U+007C | Set Size | |A| |
| ℵ₀ | Aleph null | ℴ&sub0; | U+2135 U+2080 | Cardinality | ℵ₀ |
| 𝔠 | Continuum | 𝕬 | U+1D4B4 | Cardinality | 𝔠 |
| 🔗 Function Symbols | |||||
| ↦ | Maps to | ↦ | U+21A6 | Function | x ↦ f(x) |
| ⟶ | Long right arrow | ⟶ | U+27F6 | Function | f: A ⟶ B |
| ∘ | Function composition | ∁ | U+2218 | Function | (f ∘ g)(x) |
| 🎯 Advanced Set Theory | |||||
| ∀ | For all | ∀ | U+2200 | Quantifier | ∀x |
| ∃ | There exists | ∃ | U+2203 | Quantifier | ∃x |
| ⋂ | Intersection of family | ⋂ | U+22C2 | Set Operation | ⋂Aᵢ |
| ⋃ | Union of family | ⋃ | U+22C3 | Set Operation | ⋃Aᵢ |
| ≅ | Isomorphism | ≅ | U+2245 | Relation | A ≅ B |
🧮 Quick Set Theory Symbols Reference
Basic Relations
∈ Element • ⊂ Subset • ∅ Empty
Operations
∪ Union • ∩ Intersection • △ Symmetric • ⊕ Direct Sum
Number Sets
ℕ Natural • ℤ Integer • ℚ Rational • ℝ Real
Advanced
∀ For all • ∃ Exists • ↦ Maps to • ∘ Composition
Cardinality
| Cardinality • ℵ Aleph • 𝔠 Continuum • ∞ Infinity
Functions
→ Function • ⟶ Long arrow • ⤖ Injection • ⤚ Surjection
Set Theory Expressions and Applications
x is an element of set A – basic set membership
Set A is a subset of set B – proper subset relation
Union of sets A and B – elements in A or B or both
Intersection of sets A and B – elements common to both
For all elements x in set A – universal quantification
Cartesian product of real and complex numbers
Sets A and B are isomorphic – same structure
Power set of A – set of all subsets of A
Cartesian product of sets A and B – ordered pairs
Symmetric difference – elements in exactly one of A or B
Universal quantification – for every element x in set A
Existential quantification – there exists x not in B
Union of positive and negative real numbers
Integers that are also rational numbers
Function f mapping from set A to set B
Intersection of indexed family of sets
Direct sum of sets A and B
Aleph null equals cardinality of natural numbers
Element x maps to f(x) under function f
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