is that whose aliquot parts, taken all together, do not make a sum that is equal to the number itself, but either exceed it, or fall short of it; being an abundant number in the former case, and a defective number in the latter. Thus, $12$ is an abundant imperfect number, because the sum of all its aliquot parts, $1, 2, 3, 4, 6$, makes $16$, which exceeds the number $12$. And so is a defective imperfect number, because its aliquot parts, $1, 2, 5$, taken all together, make only $8$, which is less than the number $10$ itself.