What is the difference between element of (∈) and subset (⊂ / ⊆)?

Element of (∈) relates an individual object to a set (e.g. 3 ∈ ℕ). Subset (⊂ or ⊆) relates two sets together where all elements of the first set are contained in the second (e.g. {1, 2} ⊂ ℕ). Using ∈ between two sets is a common mathematical syntax error.

What does the empty set symbol (∅) mean, and how is it written in LaTeX?

The empty set (∅ or ∅) represents a set containing no elements, with cardinality |∅| = 0. In LaTeX, use \emptyset or \varnothing (from the amssymb package).

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Set Theory Symbols

Explore our complete math symbols list and interactive keyboard to lookup meanings, LaTeX codes, and UTF-8 characters for set theory symbols. Symbols representing membership, subsets, unions, intersections, empty set, complement, and cardinality.

Set Theory Symbols Reference Table

Catalog of Set Theory Symbols with LaTeX and Unicode Codes
Symbol	Name	Meaning	Example	LaTeX	Unicode
∈	Element Of (Membership)	Specifies that an object or element belongs to a given set.	5 ∈ ℕ	`\in`	`U+2208`
∉	Not an Element Of	Indicates that an element does NOT belong to a set.	−3 ∉ ℕ	`\notin`	`U+2209`
⊂	Proper Subset Of	Set A is contained in set B, and A is not strictly equal to B.	{1, 2} ⊂ {1, 2, 3}	`\subset`	`U+2282`
⊆	Subset Of or Equal To	Every element of set A is also in set B (A may equal B).	A ⊆ A	`\subseteq`	`U+2286`
∪	Union	Combines all elements that belong to set A, set B, or both.	{1, 2} ∪ {2, 3} = {1, 2, 3}	`\cup`	`U+222A`
∩	Intersection	Set containing only elements common to both sets.	{1, 2, 3} ∩ {2, 3, 4} = {2, 3}	`\cap`	`U+2229`
∅	Empty Set (Null Set)	The unique set containing zero elements.	{x ∈ ℝ \| x² = −1} = ∅	`\emptyset \text{ or } \varnothing`	`U+2205`
\	Set Difference (Relative Complement)	Elements present in set A that are not in set B.	{1, 2, 3} \ {2} = {1, 3}	`\setminus`	`U+2216`
℘(A)	Power Set	Set of all subsets of A, including the empty set and A itself.	\|℘(A)\| = 2^\|A\|	`\mathcal{P}(A)`	`U+2118`
\|A\|	Set Cardinality	Number of elements in set A.	\|{a, b, c}\| = 3	`\|A\| \text{ or } \#A`	`U+007C`
⊇	Superset of or Equal To	Contains all elements of the second set, or is identical.	{1, 2, 3} ⊇ {2, 3}	`\supseteq`	`U+2287`
⊃	Proper Superset	Strictly contains all elements of the second set with at least one more.	{1, 2, 3} ⊃ {1, 2}	`\supset`	`U+2283`
⊄	Not a Subset	First set contains at least one element not present in the second set.	{1, 4} ⊄ {1, 2, 3}	`\not\subset`	`U+2284`