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Bijection entre P(N) et [0,1]

f: P(N) -> [0,1]
∅ -> 0
N -> 1
A -> 0,b1b2b3...bn ... ;développement binaire
où
bn = 1 si n ∈A
bn = 0 si non

A={1,4,5,7,8} -> 0,10011011
A={2,4,6,8,...} -> 0,01010101....; infini

g: [0,1] -> P(N)
0 -> ∅
1 -> N
0,b1b2b3...bn ... -> A
n si bn = 1
0,01100101 -> A={2,3,6,8}
0,101010101.... -> A={1,3,5,7,9,....} ; infini

fog = id
gof = id