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September 1st, 2012, 03:36 AM   #1
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How to prove that "i-(ioota)" is irrational?

How to prove that "i-(ioota)" is irrational by means of contradiction method?
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September 1st, 2012, 03:39 AM   #2
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Re: How to prove that "i-(ioota)" is irrational?

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How to prove that "i-(ioota)" is irrational by means of contradiction method?
What is "ioota" ?
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September 1st, 2012, 03:46 AM   #3
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Re: How to prove that "i-(ioota)" is irrational?

?-1 or sqrt(-1)
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September 1st, 2012, 03:49 AM   #4
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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.
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September 1st, 2012, 03:53 AM   #5
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Re: How to prove that "i-(ioota)" is irrational?

but i need to prove it as irrational by using contradiction method.
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September 1st, 2012, 03:55 AM   #6
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Re: How to prove that "i-(ioota)" is irrational?

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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?
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September 1st, 2012, 04:03 AM   #7
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Re: How to prove that "i-(ioota)" is irrational?

I suppose you could begin be assuming i is rational:

where





Since we must have and , we have a contradiction.
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September 1st, 2012, 04:05 AM   #8
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Re: How to prove that "i-(ioota)" is irrational?

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I suppose you could begin be assuming i is rational
I don't think you could prove a false statement by using contradiction!
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September 1st, 2012, 04:08 AM   #9
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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!
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September 1st, 2012, 04:10 AM   #10
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Re: How to prove that "i-(ioota)" is irrational?

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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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