Final answer:
A perfect number is one that equals the sum of its proper positive divisors, excluding itself. The function 'isperfect' checks if a number is perfect, and 'main' prompts a user until a perfect number is entered, incorporating appropriate multiplication and division sign rules. Exact numbers, like the integer 12 for inches in a foot, have infinite significance in mathematical expressions.
Step-by-step explanation:
The concept of a perfect number in mathematics is related to the sum of its proper divisors. A perfect number is defined as a number that is equal to the sum of its proper positive divisors, excluding itself. We can write a function isperfect which tests whether a given integer is perfect. Similarly, we can define a function main to repeatedly ask a user to enter an integer until a perfect number is entered.To write these functions in a programming context, we would need to consider the multiplication and division rules that impact the evaluation of factors. For instance, when two positive or two negative numbers are multiplied, the result is positive (2x3 = 6, (-4) x (-3) = 12). When numbers with opposite signs are multiplied, the result is negative ((-3) x 2 = -6, 4 x (-4) = -16).Exact numbers in mathematics are integers that either count objects or come from definitions and have infinitely many significant figures. An example of an exact number is the integer 12, which defines the number of inches in a foot. The use of exact numbers is critical when evaluating mathematical expressions and writing functions for computational purposes.