Thread: Rational Number - Question

Let p be a rational number.


Find another rational number q, such that AND

[I am stuck on Rudin pg 1 . I am struggling to find an explanation as how would anyone get (2p+2)/(p+2). It works but I couldn't have imagined it - so is there a way we can do it systematically?]

Thanks

Originally Posted by aman_cc

Let p be a rational number.
Find another rational number q, such that AND
I am struggling to find an explanation as how would anyone get (2p+2)/(p+2). It works but I couldn't have imagined it - so is there a way we can do it systematically?]

I answered this very question several times.
The truth is: there is no satisfactory answer. In general, it is a ‘reverse engineering’ job.
Someone, most likely before Rudin, found that one simply worked.
I have seen several others. Bevin Youse uses which also works.

Originally Posted by Plato

I answered this very question several times.
The truth is: there is no satisfactory answer. In general, it is a ‘reverse engineering’ job.
Someone, most likely before Rudin, found that one simply worked.
I have seen several others. Bevin Youse uses which also works.

Thanks. Good to know people have struggled before me as well. I was like little disappointed - It was pg 1 of Rudin after all !!

Originally Posted by Plato

I answered this very question several times.
The truth is: there is no satisfactory answer. In general, it is a ‘reverse engineering’ job.
Someone, most likely before Rudin, found that one simply worked.
I have seen several others. Bevin Youse uses which also works.

@Plato - I seem to have hit on a way it can be 'worked' out. This is based on a proof in Bartle book.

We know
we need another rational x>0 such that

Note x<2 => Any will do.