Use the results of exercises 18 and 19 to prove that given any two rational numbers r and s with r , s, there is another rational number between r and s. An important consequence is that there are infinitely many rational numbers in between any two distinct rational numbers.

Step-by-step explanation:

Let r and s be two rational numbers

Without loss of generality assume that r<s, because one number has to be necessarily less than the other otherwise two would be equal.

Then find mid value of r and s as

So we have atleast one rational number between r and s. Note that t is rational because it is sum of two rational numbers r/2 and s/2

Now using r and t we find one rational number say u between r and t.  

Again with r and u we find another rational number between them

This process can be repeated infinitely

Thus we conclude there are infinitely many rational numbers in between any two distinct rational numbers.

the answer is a reflection across the line m

step-by-step explanation:

on edge

33

step-by-step explanation: g=6