Integer Symbol ℤ

Integer Symbol uses ℤ, U+2124 DOUBLE-STRUCK CAPITAL Z, for the set of integers. In standard mathematical writing, ℤ includes negative whole numbers, zero, and positive whole numbers. A typical membership statement is x ∈ ℤ, while a function declaration such as f: ℤ → ℤ states that both the domain and codomain are the integers. The character should not be replaced by an ordinary Latin Z unless the document explicitly defines Z to have the same role. It is also distinct from ℕ for natural numbers, ℚ for rational numbers, and ℝ for real numbers. The statement ℤ ⊂ ℝ describes a subset relation between sets, whereas x ∈ ℤ describes membership of an element; exchanging ⊂ and ∈ changes the mathematical claim. Writers should define any restricted subset. Phrases such as positive integers, nonnegative integers, or ℤ⁺ can follow different conventions about whether zero is included, so the surrounding definition remains essential. Examples including ℤ = {…,-2,-1,0,1,2,…} and f: ℤ → ℤ make the intended set explicit and are useful checks after copy and paste. Keep ℤ as selectable mathematical text or use equation markup when the expression becomes complex. For HTML, the symbol may be written literally, as ℤ, or as ℤ. After export to PDF, slides, or a content-management system, verify U+2124 because some fonts may fall back to a plain Z or another double-struck design. They do not settle every author’s convention for named subsets, so definitions in the surrounding document take precedence.