1 \(1\) — Von Neumann Ordinal Numeral One (1 = 0 ∪ {0})
The von Neumann ordinal one 1 = 0 ∪ {0} = {∅}, used as the first-component tag index in Dunaev ordered pairs pr1 (Entries DefNaturalNumberModels (3.50), DefDunaevOrderedPair (3.76)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
1
\(1\)
|
| 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 | 1 |
| How to Understand It | Formal Definition (DefNaturalNumberModels (3.50)): |
| Canonical Law / Usage | 1 = 0 ∪ {0} |
| Related Symbols & Kernel Entries |