Empty set symbol ∅

• Set theory: ∅ = {}. The empty set has no elements, so its size is 0.
• No solutions: over the real numbers, the solution set of x² = −1 is ∅.
• Disjoint sets: A ∩ B = ∅ means A and B share no elements.
• Subsets: ∅ is a subset of every set.

A common trap: {∅} is not empty. It is a set with one element, and that element is the empty set. Likewise, ∅ is not the number 0 and not “null” in a database; it is a set.

The symbol is usually credited to André Weil, who borrowed the shape of the Scandinavian letter Ø for the Bourbaki group’s notation in the late 1930s.

• Ø and ø are Latin letters used in Danish, Norwegian and Faroese, as in the Danish word ø, “island.” They are easy to type on some keyboards and often used by mistake for the empty set.
• ⌀ (diameter sign) is a technical drawing symbol: ⌀10 mm.
• ⦰ (reversed empty set) is a rare math variant.
• Slashed zero in coding fonts is just a zero styled so it doesn’t look like the letter O.

Fonts disagree on how ∅ should look. Some draw a tall oval with a slash, close to a slashed zero; others draw a round circle. In LaTeX, \emptyset gives the slashed-zero style and \varnothing (from amssymb) gives the rounder style. Both mean the same thing.

• Word: in an equation (Alt+=), type \emptyset and press space. Outside equations, use the Alt+X code from the table above.
• Google Docs: Insert > Special characters and search “empty set,” or Insert > Equation and type \emptyset followed by a space.
• Mac: open the Character Viewer with Control+Command+Space and search “empty set.” Note that Option+Shift+O gives the letter Ø, not the math symbol.
• iPhone and Android: no default key; copy it here or set up a text replacement.
• Plain text: {} is a widely understood fallback.