Double-Struck Capital Z

ℤ means all integer values. That includes …, −2, −1, 0, 1, 2, … . In x ∈ ℤ, x must be an integer.

The Z comes from the German word Zahlen, meaning “numbers.” ℤ is also called blackboard-bold Z or double-struck Z; its style marks a number set rather than an isolated variable. Its relatives ℕ, ℚ, ℝ, and ℂ use the same convention for other number systems.

Why is Z written double struck?

Double strokes make mathematical sets distinct from ordinary letters. Printed mathematics could use bold type, but heavy letters were harder to distinguish on chalkboards and typewriters; doubling the strokes offered another way to mark them.

Blackboard-bold Z history is usually dated to around 1930 and linked to Edmund Landau. As of 2026, accounts still do not settle on one inventor; broader teaching and publishing use took hold by the early 1960s.

Why does ℤ look different in different fonts?

The font changes the drawing, not the character. Unicode encodes ℤ, while each font chooses its serifed or sans-serif strokes and their weight. That design variation does not change the notation. ℨ is black-letter capital Z, a different character from the standard integer symbol.