wp/Constructions based on set theory
| 0 := { } | = { } |
| 1 := { 0 } | ≡ {{ }} |
| 2 := { 1 } | ≡ {{{ }}} |
| 3 := { 2 } | ≡ {{{{ }}}} |
| n := { n-1 } | ≡ |
Set 0 = { }, and Successor(a) = {a}.
Each natural number equal to the set containing just the natural number preceding it.
| 0 := { } | ≡ ∅ |
| 1 := { 0 } | ≡ {∅} |
| 2 := { 0, 1 } | ≡ { ∅, {∅} } |
| 3 := { 0, 1, 2 } | ≡ { ∅, {∅} , {∅, {∅}} } |
| 4 := { 0, 1, 2, 3 } | ≡ { ∅, {∅} , {∅, {∅}}, {∅, {∅}, {∅, {∅}}} } |
With this definition, a natural number n is a particular set with n elements.
E' la definizione adottata dalla teoria standard.