Question

There are ______ rational numbers between two given numbers.
(a) two
(b) can't say
(c) finitely many
(d) infinitely many

Answer 1

I understand how to explain but can't put it down on paper.

abab and cdcd are rational numbers. For there to be any rational between two numbers I assume ab<cdab<cd.

I let x=abx=ab and y=cdy=cd so x<yx<y. the number in the middle of xx and yy is definitely a rational number so x<x+y2<yx<x+y2<y. I know that there is another middle between xx and x+y2x+y2 and it keeps on going.

hope it helps....^_^