The natural number 15 as a set

For natural numbers, the Von Neumann definition is usually used: A natural number N then is the set of all lower natural numbers, with 0 being the empty set.

N₁ < N₂ is defined as N₁ ∈ N₂.

N + 1 is defined as N ∪ { N }.

N + 0 is defined as N.

N₁ + (N₂ + 1) is defined as (N₁ + N₂) + 1.

15 = { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 }