Prove the following conjecture: Between any two unique Real Numbers, there exists another Real Number.
namely, their average: (a+b)/2
To prove this conjecture, we need to demonstrate that between any two unique real numbers, there exists another real number.
To do this, let's consider two arbitrary real numbers, let's say a and b, where a < b. We need to show that there exists another real number between a and b.
One way to approach this is to use the denseness property of real numbers on the number line. The denseness property states that between any two real numbers, there exists another real number.
To apply the denseness property, consider the number (a + b) / 2. This is the midpoint between a and b. Since a < (a + b) / 2 < b, this number is indeed between a and b.
Therefore, by using the denseness property, we have proven that between any two unique real numbers, there exists another real number.