In math, the adjective proper usually denotes something as being less than or equal to another thing. For example, we have:
Proper subsets: A is a proper subset of B iff every element in A is an element in B, but A is not equal to B. A then has less elements than B.
- Proper divisors: a is a proper divisor of b if a*k = b, for some natural number k != 1. That is, a divides b and a !=b, so a < b
- Proper fractions: Think way back to elementary school... a proper fraction has a numerator which is smaller than its denominator. 5/3 is an improper fraction, which everyone (I, anyway) had to write as 1 2/3 up until the beginning of Algebra 1.