Final answer:
The concept that for any two real numbers there exists a number that lies between them is referred to as the Density of Real Numbers. It highlights the property that the set of real numbers is dense, meaning there are infinitely many numbers between any two real numbers.
Step-by-step explanation:
For any two real numbers a and b, there is a real number n between a and b such that a < n < b. This is known as the Density of Real Numbers. The density property of real numbers states that for any two distinct real numbers, there is always another real number between them.
The options given for the question are:
- Density of Real Numbers: This is the correct answer. It means there are infinitely many real numbers between any two real numbers.
- Intermediate Value Theorem: This theorem is used in calculus and states that for any function that is continuous on a closed interval, if the function takes two values at either end of the interval, it also takes any value between those two values at some point within the interval.
- Archimedean Property: This deals with the sizes of numbers, asserting that for any two positive numbers, there are multiples of the smaller that can exceed the larger.
- Cauchy Sequence: A sequence whose elements become arbitrarily close to each other as the sequence progresses.