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Permutation of the integers
From OeisWiki
ℤ: {..., –7, –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, 7, ...}) 
A001057 is a very simple example of such a permutation, which gives a singly infinite sequence:

{0, 1, –1, 2, –2, 3, –3, 4, –4, 5, –5, 6, –6, 7, –7, 8, –8, 9, –9, 10, –10, 11, –11, 12, –12, 13, –13, 14, –14, 15, –15, 16, –16, 17, –17, 18, –18, 19, –19, 20, –20, 21, –21, 22, –22, 23, –23, 24, –24, ...}
Sequences like these are known to be permutations because they were so defined. Certain sequences arise in other problems and are proved to be permutations. Others are conjectured to be permutations, until a repeated or absent term can be found.
One may want to distinguish between two kinds of permutations of doubly infinite sequences:
 a permutation giving another doubly infinite sequence (not admissible in the OEIS, since not wellordered)
 a permutation giving a singly infinite sequence (admissible in the OEIS, since wellordered)
Contents
Permutation of the integers
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Permutation of the integers (conjectured)
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Permutation of the integers (open problem)
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