Final answer:
In mathematics, we count borders when summing up distinct items as in adding numbers of goats or students, and use multiplication for scaling or repeated addition. Counting uses a base-10 system, while borders in geopolitics represent territorial boundaries that affect policy and international relations.
Step-by-step explanation:
The reason we count borders rather than multiply them in mathematics is because counting involves summing discrete quantities. When we add numbers, such as counting goats or students, we are combining individual entities to find a total amount. Multiplication, on the other hand, implies a scaling or repeated addition of the same number, and is used in different contexts, such as determining the area of a rectangle by multiplying its length by its width. Units also play a critical role in mathematics. When manipulating quantities, especially in science and engineering, the associated units must be considered. For instance, when we multiply meters, we treat them like variables, combining them to derive units for area, volume, or other dimensional measures.
Counting typically uses a base-10 or powers-of-ten system, which is intuitive because humans have ten fingers that were historically used for counting. Multiplication applies to counting in certain situations, like unit conversions where you multiply by conversion factors. However, for counting distinct items, addition is the correct method. It's important to respect the accuracy and precision required for the situation, often acknowledging when approximate numbers are appropriate. Additionally, counting transcends cultural, geographical, and temporal boundaries, highlighting the universal nature of mathematics.
In a broader context, borders in fields such as geopolitics and social studies have different meanings, often representing the limits of a nation's territory or influence. Issues like terrorism or climate change transcend these political borders, creating complex challenges for policy and international relations. Both in mathematics and in geopolitical issues, understanding borders is key to identifying and solving problems.