Suppose A is the collection of all intervals [i, i 1). Besides the midpoint function f given in Example 1.2.32, what other 'selecting' function g could we formally define on A.

Example 1.2.32. Let A be the collection of the intervals (1, 2), (2, 3), (4, 5), (5, 6)...... More formally, once we recall that the set of natural numbers N is the collection { 1, 2, 3, 4, .....} we see that A = {(i, i+1) : iEN} Now, AC guarantees the existence of a set z that contains precisely one element from each (i, i + 1) in A. We could even make the 'selection' of elements in z precise by defining a 'selecting' function f. For example, we could define f to output the midpoint of each set: f((i, i + 1)) = 14(i+1) How else might you define a 'selecting' function? Exercise 1.2.33 Homework . Unanswered Suppose A is now the collection of all intervals (2, i + 1). Besides the midpoint function f given in example 1.2.32, what other 'selecting' function g could we formally define on A