Editing Collatz conjecture (section)

===Iterating on all integers===
An extension to the Collatz conjecture is to include all integers, not just positive integers. Leaving aside the cycle 0 → 0 which cannot be entered from outside, there are a total of four known cycles, which all nonzero integers seem to eventually fall into under iteration of {{mvar|f}}. These cycles are listed here, starting with the well-known cycle for positive&nbsp;{{mvar|n}}:

Odd values are listed in large bold. Each cycle is listed with its member of least absolute value (which is always odd) first.

{| class="wikitable" style="text-align: center;"
! Cycle !! Odd-value cycle length !! Full cycle length
|-
|style="text-align: left;"| <big>'''1'''</big> → 4 → 2 → <big>'''1'''</big> '''...''' || 1 || 3
|-
|style="text-align: left;"| <big>'''−1'''</big> → −2 → <big>'''−1'''</big> '''...''' || 1 || 2
|-
|style="text-align: left;"| <big>'''−5'''</big> → −14 → <big>'''−7'''</big> → −20 → −10 → <big>'''−5'''</big> '''...''' || 2 || 5
|-
|style="text-align: left;"| <big>'''−17'''</big> → −50 → <big>'''−25'''</big> → −74 → <big>'''−37'''</big> → −110 → <big>'''−55'''</big> → −164 → −82 → <big>'''−41'''</big> → −122 → <big>'''−61'''</big> → −182 → <big>'''−91'''</big> → −272 → −136 → −68 → −34 → <big>'''−17'''</big> '''...''' || 7 || 18
|}

The generalized Collatz conjecture is the assertion that every integer, under iteration by {{mvar|f}}, eventually falls into one of the four cycles above or the cycle 0 → 0.