The natural number 0 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.

0 = { }

0 is the 1st set in Vω

See also 0 in Linked Open Numbers

(back to √2)