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Math Help - A simple question on multivalued relations

  1. #1
    Forum Admin topsquark's Avatar
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    A simple question on multivalued relations

    I have a quick question about single/multi-valued functions.

    Given the function f: \mathbb{R} \to \mathbb{Z} where f(x) = the digit in the "tenths" position of x in its decimal representation. An example is \sqrt{2} \approx 1.4142 means that f( \sqrt{2} ) = 4. It is obvious that this function is single-valued. But I can't find an argument to prove that.

    It may well be that I'm over-thinking this.

    -Dan
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    Re: A simple question on multivalued relations

    But what is f(1.0) = f(0.999...): 0 or 9?
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    Forum Admin topsquark's Avatar
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    Re: A simple question on multivalued relations

    Quote Originally Posted by emakarov View Post
    But what is f(1.0) = f(0.999...): 0 or 9?
    Nice counter-example! (I'd give you an extra thanks for it, but the Forum won't allow that. So I'll just give you a wet sloppy kiss the next time we have dinner together.)

    I can't seem to get my head away from the graph. I'm suspecting a graph is not the way the text wants me to prove multi-valued-ness. Either way, I guess I've got the idea well enough.

    (So cool!)

    -Dan
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    Re: A simple question on multivalued relations

    Decimal representation is unique, except for infiniteley repeating nines which take the next highest integer by convention, so that they are also unique.

    A sloppy proof of uniqueness is if a has two decimal representations, a-a = 0 is a contradiction.
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