transgalactic said:
MAX[a,b] refers to the maximum value between two numbers, a and b. It is the larger of the two numbers. MIN[a,b] refers to the minimum value between two numbers, a and b. It is the smaller of the two numbers.
We can prove this by using the axioms and properties of real numbers. For example, we can show that the maximum value between two numbers can be found by comparing their decimal representations and choosing the larger one. Similarly, the minimum value can be found by comparing decimal representations and choosing the smaller one.
Yes, there are a few different methods that can be used to prove this. One method is by using the definition of maximum and minimum values and showing that they can be represented using real numbers. Another method is by using algebraic manipulations and properties of real numbers to show that the maximum and minimum values can be expressed using real numbers.
No, we cannot prove MAX[a,b] and MIN[a,b] using only integers or rational numbers. This is because the set of integers and rational numbers is not closed under maximum and minimum operations. In other words, there may be cases where the maximum or minimum value between two numbers is not an integer or a rational number.
Proving MAX[a,b] and MIN[a,b] using real numbers is important because real numbers are widely used in mathematics and in real-world applications. Real numbers have specific properties and axioms that make them useful for representing and manipulating quantities. By proving that MAX[a,b] and MIN[a,b] can be represented using real numbers, we can confidently use them in various mathematical equations and problems.