![]() |
|
Number Theory Number Theory Math Forum |
![]() |
| LinkBack | Thread Tools | Display Modes |
September 11th, 2012, 06:58 PM | #1 |
Senior Member Joined: Feb 2010 Posts: 324 Thanks: 0 | Proof for there does not exist a unique x that is an ...
Proof of: There does not exist a unique x that is an element of the rationals such that x squared equals 3. Would contradiction be the way to do this or trichotomy like how you would for there exists a unique x >0 such that x squared equals 2? |
![]() |
September 11th, 2012, 07:33 PM | #2 |
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs | Re: Proof for there does not exist a unique x that is an ..
Personally, I would use reductio ad absurdum (contradiction) for this.
|
![]() |
September 11th, 2012, 07:44 PM | #3 |
Senior Member Joined: Nov 2011 Posts: 595 Thanks: 16 | Re: Proof for there does not exist a unique x that is an ..
Hi, Ok I have never been very good at this so please don't take this for granted, might be wrong, just an attempts here. So if Since 3 is prime I guess this shows generally (IF it is correct....) that |
![]() |
September 11th, 2012, 08:03 PM | #4 |
Senior Member Joined: Feb 2010 Posts: 324 Thanks: 0 | Re: Proof for there does not exist a unique x that is an ..
Mark, elaborate. I would do x squared does not equal three (he hasnt defined square root so i cant use it in the proof). Then do what? |
![]() |
September 11th, 2012, 09:18 PM | #5 |
Senior Member Joined: Nov 2011 Posts: 595 Thanks: 16 | Re: Proof for there does not exist a unique x that is an ..
So is there something wrong in the proof I wrote? Would be nice to at least acknowledge you saw it, especially when people spend a bit of their time to try to help ![]() I hope it is not just a problem that "he hasnt defined defined square root" because you can of course simply start the proof saying: Let us assume a rational x=p/q such that |
![]() |
September 11th, 2012, 09:20 PM | #6 |
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs | Re: Proof for there does not exist a unique x that is an ..
I would begin by assuming there is a rational number whose square is 3: This implies: which means |
![]() |
September 11th, 2012, 09:34 PM | #7 | |
Senior Member Joined: Nov 2011 Posts: 595 Thanks: 16 | Re: Proof for there does not exist a unique x that is an ..
I think this one also works! Just when you say Quote:
| |
![]() |
September 11th, 2012, 09:46 PM | #8 |
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs | Re: Proof for there does not exist a unique x that is an ..
Yes, you are right, I meant to type a 3, but typed 9 instead! ![]() I'm glad you caught that! ![]() |
![]() |
September 11th, 2012, 10:04 PM | #9 |
Senior Member Joined: Nov 2011 Posts: 595 Thanks: 16 | Re: Proof for there does not exist a unique x that is an ..
No problem ![]() And both proofs would work the same for any prime number instead of three |
![]() |
September 11th, 2012, 10:08 PM | #10 |
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs | Re: Proof for there does not exist a unique x that is an ..
Yes, and hopefully we are not as stricken as the followers of Pythagoras... ![]() |
![]() |
![]() |
|
Tags |
exist, proof, unique |
Thread Tools | |
Display Modes | |
|
![]() | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
unique factorization domain, zero of a polynomial , proof | rayman | Abstract Algebra | 2 | October 19th, 2012 07:38 AM |
0/0 does not exist? | Dart Plegius | Algebra | 4 | June 19th, 2012 01:37 PM |
Prove that lim (x -> 0) (1/x^2) does not exist | scherz0 | Real Analysis | 10 | October 24th, 2009 02:21 PM |
Does the following limit exist? | BUBLIL | Complex Analysis | 1 | December 12th, 2008 09:15 AM |
Does this graph exist? | tinatran2 | Applied Math | 1 | May 9th, 2007 09:16 PM |