# Between a rational and a irrational

• Nov 3rd 2008, 12:48 PM
nerdy_time
Between a rational and a irrational
Hello.
Between a rational and a irrational is there a rational? and a irrational? and vice-versa?
I know that between 2 rationals there is a rational and a irrational and that between 2 irrationals there is a rational and a irrational, but i cannot figure this out... please help.
Thanks.
• Nov 3rd 2008, 12:52 PM
Mathstud28
Quote:

Originally Posted by nerdy_time
Hello.
Between a rational and a irrational is there a rational? and a irrational? and vice-versa?
I know that between 2 rationals there is a rational and a irrational and that between 2 irrationals there is a rational and a irrational, but i cannot figure this out... please help.
Thanks.

If I remember this proof is best done assuming that it is false and finding a contradiction. Why don't you try it and report back.
• Nov 3rd 2008, 01:10 PM
nerdy_time
Quote:

Originally Posted by Mathstud28
If I remember this proof is best done assuming that it is false and finding a contradiction. Why don't you try it and report back.

So...it is true? Right? I am not worried about the proof for now.
• Nov 3rd 2008, 01:18 PM
Moo
Hello,
Quote:

Originally Posted by nerdy_time
So...it is true? Right? I am not worried about the proof for now.

Yes it is true, though the most common proof is about "there is a rational between two irrationals" or "there is an irrational between two rationals"