Question

How did we initially impose structure on an arbitrary set S in Chapter 4? What 'distance measuring' function did we define?

a) Metric space
b) Topological space
c) Vector space
d) Euclidean space

Answer 1

A 'distance measuring' function in a metric space was defined to impose structure on set S in Chapter 4. Displacement is a vector due to its magnitude and direction, whereas distance is a scalar showing only magnitude.

Step-by-step explanation:

The initial structure imposed on an arbitrary set S in Chapter 4 is that of a metric space. In a metric space, a 'distance measuring' function is defined, which is commonly referred to as a metric. This function determines the distance between any two elements within the set, meeting specific criteria such as non-negativity, identity of indiscernibles, symmetry, and triangle inequality.

The difference between distance and displacement is fundamental in the context of this topic. Distance is the total length of the path traveled, while displacement is the straight line distance from the starting point to the ending point, taking into account the direction. Therefore, displacement is a vector quantity because it encompasses both magnitude and direction, unlike distance, which is a scalar and only measures magnitude.