Question

Is there any rational numbers between 5/7 and 6/7 and why?

Answer 1

I know there is, but I don't know why.

Answer 2

Yes ....

5/7 can be rewritten as 10/14
6/7 can be rewritten as 12/14

and there is clearly a number between 10 and 12 ....

but I do not know if this explains why?

Answer 3

A rational number is defined as the ratio of two integers.

Answer 4

So what meverett04 says is enough for me.

Answer 5

There's a theorem which states: For every \(x,y\in\mathbb{R}\) such that \(x<y\), there exists a rational number \(r\) such that \(x<r<y\).\[\]

Answer 6

Therefore, \(\mathbb{Q}\) is dense in \(\mathbb{R}\).\[\]

Answer 7

Where can I find that kind of theorems @across?

Answer 8

i suppose there is one because difference between 6/7 and 5/7 can be exactly split into 2
12/14 - 10/ 14 / 2 = 1/14

Answer 9

I mean books.

Answer 10

can there be 11/14 between?

Answer 11

@No-data: Analysis books.

Answer 12

yes there can be 11/14