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Math Help - Analysis Countinuity Problem

  1. #1
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    Analysis Countinuity Problem

    Was wondering if someone could outline the following problem:

    Let g: R to R by defining g(x) as 2x for x rational and as x+3 for x irrational. Find all the points where g is continuous and prove your assertion.

    Thanks for any help.
    Jack
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  2. #2
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    Do you know how to solve 2x=x+3?
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  3. #3
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    Well how would I prove the assertion?
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  4. #4
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    Well prove that it is continuous only at 3.
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  5. #5
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    Basically the Dirchelet function.

    When we approach a number (limit at the point) by rationals we get one value and when we approach a number (limit at the point) by irrationals we might get a different value. Well, approaching a number (limit) by rationals is anagolous with the irrationals because the irrationals are contrsucted by a Cauchy sequence of rationals. Thus, what Plato said is to solve the equation, for it says the rationals and irrationals produce the same limit (which must be if it exists).
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