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Is it possible without using exponentiation to have a set of numbers that when added together, always give unique sum?
I know it can be done with exponentiation (see first answer): The right way to manage user privileges (user hierarchy)
But I’m wondering if it’s possible without exponentiation.
No, you can only use exponentiation, because the sum of lower values have to be less than the new number to be unique: 1+2=3 < 4, 1+2+4=7 < 8.
[EDIT:]
This is a laymen’s explanation, of course there are other possibilities, but none as efficient as using exponentials of 2.