Why must std::sort compare function return false when arguments are equal?

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The compare function simply models a “less than” operator. Consider how the < operator works for primitive types like int:

int a = 1, b = 2;     a < b == true      a is less than b
int a = 2, b = 1;     a < b == false     a is not less than b, because a is greater than b
int a = 1, b = 1;     a < b == false     a is not less than b, because a equals b

Returning true means you want a to be ordered before b. So return false if that is not the case, either because you want b to be ordered before a, or because their order doesn’t matter.

If you return true when the arguments are equal, then you are saying that you want a to come before b and you want b to come before a, which is a contradiction.

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