In the realm of mathematics, a set is essentially a collection of unique objects, which is itself considered as a single entity. For instance, the collection of English alphabet vowels can be represented as a set $\{a, e, i, o, u\}$.

The act of determining the number of elements in a set involves counting each distinct item within the set. This numerical count is referred to as the “cardinality” of the set.

Let’s consider an example. Assume we have a set $A = \{2, 4, 6, 8\}$. To ascertain the number of elements in set $A$, we enumerate each unique number: $2$, $4$, $6$, and $8$. With four distinct numbers, the cardinality of set $A$ is $4$.

Remember, if a set includes duplicate elements, we only count each distinct element once. For example, in the set $B = \{1, 2, 2, 3, 3, 3\}$, we would count $1$, $2$, and $3$, disregarding the repetitions. Hence, the cardinality of set $B$ is $3$.

In certain situations, sets can be defined using a rule or an equation. For instance, the set of all even numbers less than $10$ can be denoted as $\{x | x \text{ is an even number, } x < 10\}$. To determine the cardinality, list out the even numbers less than $10$: $2$, $4$, $6$, and $8$. This set thus contains four elements.

In summary, the key to determining the cardinality of a set is to count each unique item within it. This technique is applicable regardless of whether the set is finite or infinite, although the process of counting elements in an infinite set incorporates more complex mathematical principles.