The natural number 2 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.

2 = { 0 , 1 }

2 is the 4th set in Vω

See also 2 in Linked Open Numbers

(back to √2)