Empty set (∅) in LaTeX
\emptyset typesets the empty set symbol ∅, the unique set with no elements at all.
LaTeX command
\emptysetNot the symbol you meant? Draw it to find the command →
The empty set has no members whatsoever: for every x, the statement x \in \emptyset is false. It is unique, since any two sets with no elements are equal by definition, and it is a subset of every set, including itself. Writing = \emptyset is the standard way to say two sets are disjoint.
LaTeX offers two glyphs. \emptyset is the default: a narrow, slightly oval zero with a slash through it. \varnothing (from amssymb, built in on KaTeX) is a round circle with a slash, which many style guides in set theory and algebra prefer because it reads clearly as a symbol rather than as a crossed-out zero.
Do not write \{\emptyset\} when you mean \emptyset; the set containing the empty set as its only element has one element, and is not the same as the empty set itself. This distinction matters in constructions that build the natural numbers or ordinals out of nested sets.
Other forms
\varnothingrounder variant (∅)Examples
$A \cap B = \emptyset$A and B are disjoint
$\emptyset \subseteq A$the empty set is a subset of every set
$\{x \in \mathbb{R} : x^2 < 0\} = \emptyset$a set with no real solutions
$A \cup \emptyset = A$the empty set is the identity for union
$\varnothing$the alternative rounder glyph from amssymb
Tips and common mistakes
- Choose one glyph,
\emptysetor\varnothing, and use it consistently through a document; do not mix the two, since they look similar but are not identical. \emptysetis never the same as \{\emptyset\}, the second is a set containing one element (itself the empty set), so it has size 1, not 0.- Do not confuse the empty set
\emptysetwith the number 0 or the empty string; they belong to different kinds of object even though all three mean 'nothing' informally. \emptysetis a subset of every set, including itself, which is a useful base case in inductive proofs about subsets.- State disjointness explicitly as =
\emptysetrather than describing it in words only, it is clearer and easier to chain into further algebra.
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What is the difference between \emptyset and \varnothing?
They typeset two visual variants of the same empty-set symbol. \emptyset is a narrow, oval slashed zero; \varnothing (from amssymb, available by default in KaTeX) is a round slashed circle, often preferred in set theory since it looks less like a crossed-out zero. Either is correct; pick one and stay consistent.
Is the empty set the same as zero?
No. \emptyset is a set with no elements, while 0 is a number. They are different types of mathematical object, even though the empty set is often used to construct the number zero in formal set theory.
Is \emptyset a subset of every set?
Yes. Vacuously, every element of \emptyset (there are none) satisfies any membership condition, so \emptyset \subseteq A holds for every set A, including A = \emptyset itself.
What is \{\emptyset\}?
It is a set containing exactly one element, namely the empty set. It has one member, so \{\emptyset\} \neq \emptyset; do not conflate a container with what it contains.