The natural number 9 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.

9 = { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }

See also 9 in Linked Open Numbers

(back to √2)