Irrational Numbers

Answers and Replies

  • #2
shmoe
Science Advisor
Homework Helper
1,992
1
the link for me says

"You do not have the permission to view this blog"

I guess you have to register to see it?

Can you type the problem here?
 
  • #3
1,235
1
you should be able to see it now. changed the settings
 
  • #4
shmoe
Science Advisor
Homework Helper
1,992
1
I'm getting a page that says it's your blog, but it also says "total entries: 0" and there's not much tehre besides a calender.

Is it that long of a problem that you couldn't just type it in here?
 
  • #5
1,235
1
yeah, now it should work.
 
Last edited:
  • #7
shmoe
Science Advisor
Homework Helper
1,992
1
Alright. You get to p^2=n*q^2 and then assume that n=2*t? That's completely unjustified.

If n is not a perfect square then you can write it as n=r*m^2 where r has the property that if s is a prime and s divides r then s^2 does not divide r, r>1 obviously as well (you should prove this). Proceed from p^2=n*q^2 and see what happens.

You could also just look at the prime factorization of n if you have unique factorization at this point.
 
  • #8
1,235
1
Ok, so [tex] p^{2} = rm^{2}q^{2} [/tex] and [tex] p^{2} [/tex] is divisible by [tex] rm^{2} [/tex]. So then I have to show that [tex] q^{2} [/tex] is also divisible by [tex] rm^{2} [/tex]. Is [tex] m [/tex] just any positive number?

Thanks
 
  • #9
shmoe
Science Advisor
Homework Helper
1,992
1
courtrigrad said:
Ok, so [tex] p^{2} = rm^{2}q^{2} [/tex] and [tex] p^{2} [/tex] is divisible by [tex] rm^{2} [/tex]. So then I have to show that [tex] q^{2} [/tex] is also divisible by [tex] rm^{2} [/tex]. Is [tex] m [/tex] just any positive number?

Thanks
It's probably easiest at this point to focus on some prime that divides r, say s. Then it will look very much like the usual proof sqrt(2) is irrational.

However we have a little snag. You are looking at p^2=r*(mq)^2 and you don't necessarily have mq and p relatively prime, but you should be able to fix this without much trouble.
 

Related Threads on Irrational Numbers

  • Last Post
Replies
15
Views
4K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
3
Views
959
Replies
26
Views
17K
  • Last Post
Replies
18
Views
12K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
3
Views
1K
Replies
2
Views
1K
Replies
2
Views
3K
Top