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Question 523337: show that between any two rational numbers there exist infenite number of rational numbers
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Many ways to do it, but one way to do it is to show that for any two rational numbers a and b, (a+b)/2 is a rational number. This is quite simple, since we can let a = m/n, b = p/q, (a+b)/2 = (mq+pn)/(2pq) = rational.
Hence we have shown that for any two rational numbers, their average/midpoint is rational. We can iterate this process indefinitely to produce infinitely many rational numbers.
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