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    • CommentRowNumber1.
    • CommentAuthorTobyBartels
    • CommentTimeNov 25th 2009

    I mentioned the intermediate value theorem at pentagon decagon hexagon identity and then began an article on it.

    • CommentRowNumber2.
    • CommentAuthorColin Tan
    • CommentTimeDec 26th 2013
    I notice that Theorem 2 already implies that there some c of the unit interval such that f(c) is strictly between -1 and 1. Although we may not be able to construct all values between -1 and 1 to lie in the image of f, at least we can construct one value.
    • CommentRowNumber3.
    • CommentAuthorTobyBartels
    • CommentTimeDec 28th 2013

    Right, and more specifically we can construct a cc whose value is as close as we like (within ε\epsilon) of our desired value.

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