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Math Help - sequence convergence

  1. #1
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    sequence convergence

    show that if x is a real number then there is a sequence of irrational numbers converging to x
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  2. #2
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    Quote Originally Posted by spikedpunch View Post
    show that if x is a real number then there is a sequence of irrational numbers converging to x
    If x is irrational take \,\,a_n=x\frac{n+1}{n} , and if x is rational take \,\, x\frac{\pi n+1}{\pi n}

    Tonio
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  3. #3
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    I'm really shaky with my understanding of this stuff, so could you elaborate on what I would do with those sequences?
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    Quote Originally Posted by spikedpunch View Post
    I'm really shaky with my understanding of this stuff, so could you elaborate on what I would do with those sequences?
    What "to do" with them? Well, just convince yourself that indeed both of them are irrational sequences and that both converge to x...what else?

    Tonio
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