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Math Help - closed interval

  1. #1
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    Chile
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    closed interval

    Hello : I have a problem whit this exercise

    Decide which of the following are subrings of the ring of all functions from the closed interval [0,1] to
    \mathbb{R}:

    1)the set of all rational linear combinations of the functions sin (nx) and cos (x) where m, n
    \in{} {0,1,2,...}

    2)
    the set of all polynomial functions

    3)the set of all functions that have an infinite number of zeros


    2 is a subring but not 1 and 3, but I can not establish the conclusion good, I hope some help


    Thanks
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  2. #2
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    Re: closed interval

    What conditions have be satisfied to be a subring?
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  3. #3
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    Re: closed interval

    a subring S of a ring R is a subset that is closed under addition and multiplication in the ring, and obviously must be different from the empty set
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  4. #4
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    Re: closed interval

    for 3) can you think of a function with an infinite amount of 0's, and another one with an infinite amount of 0's then when added give a function with a finite amount of 0's?
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