Empty Set ∅ vs Ø vs 0: How to Tell Them Apart

∅, Ø, and 0 can look surprisingly similar, especially in small fonts. But they’re three different Unicode characters with three very different jobs.

∅ is the mathematical empty-set symbol. Ø is a Latin letter. 0 is the digit zero.

If you’re working with math, copied text, code, or exact character matching, choosing the right one matters.

∅ vs Ø vs 0 at a Glance

The first character belongs naturally in the wider family of math symbols. The other two may resemble it in some fonts, but Unicode encodes them separately because they represent different things.

What Does ∅ Mean?

U+2205 EMPTY SET represents a set containing no elements.

For example:

A = ∅

means that the set A is empty.

You may also see the empty set written with braces:

{}

In ordinary mathematical notation, ∅ is a set symbol. It isn’t the digit zero and it isn’t the letter Ø.

Is the Empty Set the Same as Zero?

No—not in ordinary notation.

∅ denotes the empty set, while 0 denotes the number zero.

For example:

|∅| = 0

says that the empty set has zero elements. The two symbols clearly play different roles in the same statement.

There’s a deeper mathematical nuance: in some formal constructions of the natural numbers, zero can be represented using the empty set. That still doesn’t make the characters ∅ and 0 interchangeable in normal mathematical writing.

What Is Ø?

Ø is U+00D8 LATIN CAPITAL LETTER O WITH STROKE.

It’s a letter, not the Unicode empty-set character.

The confusion is easy to understand. Both Ø and ∅ can be drawn as rounded shapes crossed by diagonal strokes, and some fonts make them look extremely close.

But Unicode keeps them separate because their identities and uses are different.

Why Can ∅ Look Like a Slashed Zero?

The exact glyph used for U+2205 depends on the font and mathematical typesetting style.

Unicode also defines the standardized variation sequence:

U+2205 + U+FE00 (VS1)

for an empty-set glyph variant with a long diagonal stroke overlay.

The sequence contains two code points—the U+2205 base character followed by VS1. It requests a particular glyph variant; it doesn’t turn the empty-set character into the digit zero.

What About a Slashed Zero?

A slashed zero is often a glyph style used to make the digit 0 easier to distinguish from the letter O.

Unicode separately defines:

U+0030 + U+FE00 (VS1)

for a digit-zero variant with a short diagonal stroke.

So Unicode deliberately keeps these ideas separate:

• U+2205 + VS1 requests the standardized long-diagonal variant of EMPTY SET;
• U+0030 + VS1 requests the standardized short-diagonal variant of DIGIT ZERO.

A slash through a round shape isn’t enough to identify the character.

How Can You Tell ∅, Ø, and 0 Apart?

If you have digital text, check the code point instead of relying on the font:

• U+2205 → ∅ EMPTY SET;
• U+00D8 → Ø LATIN CAPITAL LETTER O WITH STROKE;
• U+0030 → 0 DIGIT ZERO.

This is far more reliable than comparing the angle of the slash or the shape of the oval.

Can Ø Be Used Instead of ∅?

If someone substitutes Ø because it looks similar, the encoded result is still U+00D8—the Latin letter—not U+2205 EMPTY SET.

That may be visually understandable in an informal context, but it isn’t the same Unicode character.

If you’re preparing mathematical text, searchable content, data, or anything where character identity matters, use U+2205 for the empty set.

Can 0 Be Used Instead of ∅?

Not as a character substitute.

The fact that an empty set contains zero elements doesn’t make the symbols equivalent.

Compare:

A = ∅

with:

x = 0

The first assigns an empty set. The second assigns the numerical value zero.

Why Does Copy and Paste Make This More Confusing?

Copy and paste preserves encoded characters, not just what they look like.

A copied Ø stays U+00D8 even if it appears inside a mathematical formula. A copied ∅ stays U+2205 even if the font makes it look like a slashed zero.

That difference can matter in search, databases, formulas stored as text, and exact string comparisons.

Which Character Should You Use?

Use ∅ when you mean the empty set.

Use Ø when you mean the Latin letter O with stroke.

Use 0 when you mean the digit zero.

If the font makes them hard to distinguish, check the Unicode value. The code point tells you what the character actually is.