1. In mathematics, a set A is a proper subset of set B if every element of A is also in B, but A is not equal to B (A ≠ B)
The set {1, 2} is a proper subset of {1, 2, 3} because it contains some but not all elements of the larger set.
O conjunto {1, 2} é um subconjunto próprio de {1, 2, 3} porque contém alguns, mas não todos os elementos do conjunto maior.
2. A subset that is strictly smaller than the original set, excluding the set itself
All proper subsets of {a, b} are: ∅, {a}, {b}
Todos os subconjuntos próprios de {a, b} são: ∅, {a}, {b}
This is a specialized mathematical term used consistently across both Brazilian and Portuguese academic contexts. It is primarily found in mathematics education, set theory courses, and formal mathematical writing. The concept is fundamental to understanding mathematical logic and foundations.