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Consider the set N {\displaystyle \mathbb {N} } of natural numbers. A virtual permutation of N {\displaystyle \mathbb {N} } is a sequence σ n , n ∈ N {\displaystyle \sigma _{n},n\in \mathbb {N} } where each σ n {\displaystyle \sigma _{n}} is a permutation on { 1 , 2 , … , n } {\displaystyle \{1,2,\dots ,n\}} and σ n − 1 {\displaystyle \sigma _{n-1}} is the derived permutation of σ n {\displaystyle \sigma _{n}} .
