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Thread: Find a function (ideals)

  1. #1
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    Find a function (ideals)

    Hl! I do not understand this exercise

    Recall that $\displaystyle \mathbb{R}^\mathbb{R}$ , the set of all real valued funtions of a real variable, is a commutative ring under pointwise addition and multiplication.
    Let $\displaystyle n\geq{0}$ be an integer, and let $\displaystyle I_n$ be the set of all functions in $\displaystyle \mathbb{R}^\mathbb{R}$ vanishing on integer multiples of $\displaystyle n$


    Find a function that is in $\displaystyle I_8$ but not in $\displaystyle I_4$



    I do not understand why $\displaystyle I_n$ is an ideal and I can not find the function


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  2. #2
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    Re: Find a function (ideals)

    $f(x) = \sin \left( \dfrac{\pi}{8} x \right)$

    $f(8n)=0, f(8n+4)=(-1)^n$
    Last edited by SlipEternal; Aug 29th 2017 at 07:02 PM.
    Thanks from cristianoceli
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  3. #3
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    Re: Find a function (ideals)

    Ok thanks
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