Concept explainers
To Prove:
Between any two rational numbers , there are infinitely many rational numbers.
Explanation of Solution
Given:
That is , the average of two rational numbers is between them.
Calculation:
x and y are rational numbers.
Let
Hence, the arithmetic mean / average of two rational numbers is also a rational number and lies between them.
So,
If we continue in this manner, we will have infinite number of rational numbers between any two rational numbers.
So, between any two rational numbers, there are infinitely many rational numbers.
Hence proved.
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Algebra and Trigonometry: Structure and Method, Book 2
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