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 September 1st, 2012, 03:36 AM #1 Newbie   Joined: Sep 2012 Posts: 11 Thanks: 0 How to prove that "i-(ioota)" is irrational? How to prove that "i-(ioota)" is irrational by means of contradiction method?
September 1st, 2012, 03:39 AM   #2
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Re: How to prove that "i-(ioota)" is irrational?

Quote:
 Originally Posted by muhammadmasood How to prove that "i-(ioota)" is irrational by means of contradiction method?
What is "ioota" ?

 September 1st, 2012, 03:46 AM #3 Newbie   Joined: Sep 2012 Posts: 11 Thanks: 0 Re: How to prove that "i-(ioota)" is irrational? ?-1 or sqrt(-1)
 September 1st, 2012, 03:49 AM #4 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: How to prove that "i-(ioota)" is irrational? Oh, you're talking about imaginary unit then. But, i is neither rational nor irrational. In some sense, it can be even called rational since the absolute value of i is 1, which is rational. But i is never irrational.
 September 1st, 2012, 03:53 AM #5 Newbie   Joined: Sep 2012 Posts: 11 Thanks: 0 Re: How to prove that "i-(ioota)" is irrational? but i need to prove it as irrational by using contradiction method.
September 1st, 2012, 03:55 AM   #6
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Re: How to prove that "i-(ioota)" is irrational?

Quote:
 Originally Posted by muhammadmasood but i need to prove it as irrational by using contradiction method.
How would you prove a statement which is not true?

i is neither rational nor irrational I told you that.

From where did you got this problem?

 September 1st, 2012, 04:03 AM #7 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,163 Thanks: 472 Math Focus: Calculus/ODEs Re: How to prove that "i-(ioota)" is irrational? I suppose you could begin be assuming i is rational: $\frac{p}{q}=i$ where $p,q\in\mathbb{Z}$ $p=qi$ $p^2=q^2i^2=-q^2$ Since we must have $p^2>0$ and $q^2>0$, we have a contradiction.
September 1st, 2012, 04:05 AM   #8
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Re: How to prove that "i-(ioota)" is irrational?

Quote:
 Originally Posted by MarkFL I suppose you could begin be assuming i is rational
I don't think you could prove a false statement by using contradiction!

 September 1st, 2012, 04:08 AM #9 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,163 Thanks: 472 Math Focus: Calculus/ODEs Re: How to prove that "i-(ioota)" is irrational? Well, we have really only shown that i is not real, but as it's not real, then it's also not rational!
September 1st, 2012, 04:10 AM   #10
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Re: How to prove that "i-(ioota)" is irrational?

Quote:
 Originally Posted by MarkFL Well, we have really only shown that i is not real, but as it's not real, then it's also not rational!
Right, as I said : i is neither irrational nor rational.

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