0 \(0\) — Von Neumann Ordinal Numeral Zero (0 = ∅)
The von Neumann ordinal zero 0 = ∅, base element of ω and initial index in Dunaev class-list marking (Entry DefNaturalNumberModels (3.50)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
0
\(0\)
|
| Category | Functional Symbol (0-ary Ordinal Numeral Constant) |
| SML AST Constructor | Kernel AST Symbol / Sort Constructor in typetheory.ML (Class_p / Truth_p / EXP / UCol) |
| Constructor Arguments | Typed arguments as specified by the Signature / Sort field above |
| Metatype / Signature | Class |
| Binder Status | See Category & Signature above |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | 0 |
| How to Understand It | Formal Definition (DefNaturalNumberModels (3.50)): |
| Canonical Law / Usage | 0 = ∅ |
| Related Symbols & Kernel Entries |