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Math Help - Irrational numbers

  1. #1
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    Thumbs down Irrational numbers

    Say whether the following are true or false, backing up with examples, if \alpha \in R is rational, and \beta \in R is irrational:

    \alpha + \beta is irrational
    \alpha \beta is irrational
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  2. #2
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    With having fifty postings, you should understand that this is not a homework service nor is it a tutorial service. Please either post some of your own work on these problems or explain what you do not understand about the question.
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  3. #3
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    Sorry dude but I am posting the aspects of the course I am having trouble with before the exam (tomorrow).


    These are exam questions from the Further discrete maths exam past papers.

    The question is I dont know how to work out the answer?

    You have to show whether or not they are irrational.

    i know rational means it can be expressed as m/n, both integers. I think both are true that both are irrational? but I dont know how to prove it?

    I had a little think about the first one using my brain and I think its a proof by contradiction, by writing m/n + b = p/q, so b= p/q - m/n = pn - mq/qn which is rational so if a + b is rational b is rational too. but the product i am not too sure?
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Irrational numbers

    Quote Originally Posted by TeaWithoutMussolini View Post
    Say whether the following are true or false, backing up with examples, if \alpha \in R is rational, and \beta \in R is irrational:

    \alpha + \beta is irrational
    \alpha \beta is irrational
    Plato, he called you a dude...

    \alpha + \beta

    \alpha =\frac{a}{b}

    Now assume that \frac{a}{b}+\beta=\frac{c}{d}, why this is a contradiction?

    Try the second one alone?
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  5. #5
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    Re: Irrational numbers

    Quote Originally Posted by TeaWithoutMussolini View Post
    I had a little think about the first one using my brain and I think its a proof by contradiction, by writing m/n + b = p/q, so b= p/q - m/n = (pn - mq)/qn which is rational so if a + b is rational b is rational too.
    Correct.

    but the product i am not too sure?
    Similarly, assume that \alpha=m/n and \alpha\beta=p/q for some integer m, n, p, q and isolate \beta.
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  6. #6
    MHF Contributor Amer's Avatar
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    Re: Irrational numbers

    suppose that a+b rational

    thats mean a+b = n/m
    so b = n/m - a and you that the rational numbers is closed under addition so b is rational contradiction
    the other is same
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