Adding Strings to NsMutableSets

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If I have two string objects that both have value "hi", and I add them to an NSMutableSet, are they treated as different objects or not? Thanks a bunch!

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Beside the correct comment of @rmaddy, there is a fundamental problem with it: It is simply mostly impossible to guarantee that no objects are equal in a set. (It is easy to guarantee that the are not identical.) This would imply to recheck the equaty of all objects (expensive), when one changes (mostly impossible to detect). This is, because NSSet does not copy its content objects.

Let's have an example:

NSMutableString *first = [@"Amin" mutableCopy];
NSMutableString *second = [@"Amin Negm" mutableCopy];
NSSet *set = [NSSet setWithObjects:first, second];

[first appendString:@" Negm"];

Both objects are equal than, but none is removed. (Which one?)