A deficient number is a positive integer that is greater than the sum of its proper divisors, excluding itself. Proper divisors are the numbers that divide the integer evenly, apart from the integer itself. For example, the number 8 has proper divisors 1, 2, 4, and their sum is 7, which is less than 8. Therefore, 8 is a deficient number. In contrast, a perfect number is one where the sum of its proper divisors equals the number itself, like 6, which has proper divisors 1, 2, 3 that sum to 6. Another category is abundant numbers, where the sum of the proper divisors exceeds the number. Understanding these classifications helps in the study of number theory.