Final answer:
To show that a set a is bounded above and below, we must identify lower and upper bounds for the set. The supremum (sup) and infimum (inf) are the least upper and greatest lower bounds respectively. Without specifics of set a, we cannot find exact values, but we can understand the concept with an example set containing numbers 1 to 10.
Step-by-step explanation:
To demonstrate that a is bounded above and below, we must find two numbers, say M and m, such that m ≤ a ≤ M for all elements within the set a. The supremum (sup) of a is the least upper bound, meaning it is the smallest number M such that all elements of the set are less than or equal to M. Similarly, the infimum (inf) of a is the greatest lower bound, which is the largest number m such that all elements of the set are greater than or equal to m. Without the specific definition of the set a, we cannot compute the exact values of sup a and inf a, but the process involves finding the least and greatest bounds that satisfy these conditions.
For example, if the set a contains all numbers from 1 to 10 inclusive, then inf a is 1 and sup a is 10, because there are no numbers less than 1 or more than 10 in the set.