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Math Help - surjective function

  1. #1
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    surjective function

    How would I prove that f(x) = [x] is surjective, where [x] denotes the bracket function
    I know how to prove that something is surjective, but I'm stuck on this particular example
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  2. #2
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    Re: surjective function

    What is the bracket function?
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  3. #3
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    Re: surjective function

    Quote Originally Posted by emakarov View Post
    What is the bracket function?
    Also known as the floor function, gauss brackets?
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  4. #4
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    Re: surjective function

    In proofs of surjection, knowing the domain and codomain is essential. For example, f(x) = [x] is not surjective if f is considered from \mathbb{R} to \mathbb{R}, nor when it is considered from \{x\in \mathbb{R}\mid x>0\} to \mathbb{Z}. So I'll assume that f:\mathbb{R}\to\mathbb{Z}.

    We need to prove that for every n\in\mathbb{Z} there is an x\in\mathbb{R} such that [x] = n. Can you find several such x for n = 3?
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