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DuplicateFreeQ

Tests whether a list has no duplicated elements.

$ wo 'DuplicateFreeQ[{1, 7, 8, 4, 3, 4, 1, 9, 9, 2}]'
False

No duplicates:

$ wo 'DuplicateFreeQ[{1, 2, 3, 4}]'
True

An empty list is duplicate-free:

$ wo 'DuplicateFreeQ[{}]'
True

A custom test decides which elements count as duplicates:

$ wo 'DuplicateFreeQ[{1, -1, 2, -3}, (Abs[#1] == Abs[#2]) &]'
False