Prove directly that between any two rational numbers there exists a rational number.



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Posted on (Answer #1)

Let  a and b are two rational numbers such that a<b .

`a,b in Q`  , Q is set of rational numbers.


`a=p/q and b=r/s`

by def of rational numbers .



`=(1/2)((ps+rq)/(qs)) in Q`

`a<(a+b)/2<b`  , this proves there exist at least one rational number between a and b.

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