∅ Empty Set Symbol
The empty set symbol (∅) is the set with no elements. It is a mathematical symbol, not the letter Ø and not the diameter sign ⌀.
Also known as: empty set symbol, null set symbol, zero with line through it, o with slash.
Codes
| Symbol | ∅ | |
| Unicode | U+2205 | |
| HTML entity (named) | ∅ | |
| HTML entity (decimal) | ∅ | |
| HTML entity (hex) | ∅ | |
| CSS | \2205 | |
| LaTeX | \varnothing | |
| Windows Alt code | Alt + 8709 |
How to type ∅ (Empty Set Symbol)
In Word, type 2205 then press Alt + X. Elsewhere, copy ∅ above or use Character Map (search “empty set”).
⚠️ Option + O gives ø (U+00F8), the Danish letter — not the empty set. There is no keystroke for ∅: copy it above, or use Character Viewer (Control + Cmd + Space) and search “empty set”.
Type 2205, then press Alt + X to convert it to ∅.
Insert → Special characters, then search “empty set”. In an equation, \varnothing followed by a space also works.
\varnothing (amssymb) gives the slashed circle most people want. Plain \emptyset renders as a slashed zero, which is narrower — both are correct, and \varnothing is the more common choice in modern papers.
Usage
- ∅ is the set with no elements. It is not the same as {∅}, which is a set containing one thing — the empty set — and so is not empty.
- The empty set is a subset of every set: ∅ ⊆ A for any A. When two sets share nothing, their intersection is empty: A ∩ B = ∅.
- Which one to use: ∅ (U+2205) is the mathematical empty set. ⌀ (U+2300) is the engineering diameter sign. Ø / ø (U+00D8 / U+00F8) are Danish and Norwegian letters. All four are a circle with a slash, and only the code point tells them apart.
- Watch the Mac keyboard: Option + O hands you ø, which looks close enough to pass a glance and will silently fail any search, sort or comparison against the real ∅.