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Thread: Rationalizing An Irrational Number

  1. #1 Rationalizing An Irrational Number 
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    Excuse me ... .

    A set of the rational numbers is denoted as , where is the set of integers ... .

    A set of the irrational numbers consists of the real numbers which cannot be denoted as such that and ... .

    The problem is in following ... .

    For example, in present time, here is which be agreed as an irrational number ... .

    Can the irrational number be rationalized to be a rational number if a person is able to denote the as , where and , in the next time ... ? [Here, the absolute values of and may be the very very huge integers ... .]

    Thank you for the answer ... .


    Last edited by trfrm; April 16th, 2013 at 02:28 AM.
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  3. #2  
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    Quote Originally Posted by trfrm View Post
    Here, the absolute values of and may be the very very huge integers ... .
    It seems to me you've just modify your definition of just in the middle of your question.

    Is it all integers or only small ones ? What is small ? What is huge ?


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  4. #3  
    Brassica oleracea Strange's Avatar
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    I don't actually undrstand what you are trying to do. You define irrational numbers in a way that mean they are ... irrational. What do you mean by"rationalize"? (I can't follow from your notation)

    Here is a simple proof that is irrational: Proof that the square root of 2 is irrational number

    You can do this with most (all?) irrational numbers, for example: Proof that is irrational
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    ei incumbit probatio qui dicit, non qui negat
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  5. #4  
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    Quote Originally Posted by Boing3000 View Post
    Is it all integers or only small ones ? What is small ? What is huge ?
    Oh, I'm sorry ... . The term "small" and "huge" are relative ... .


    Quote Originally Posted by Strange View Post
    I don't actually undrstand what you are trying to do. You define irrational numbers in a way that mean they are ... irrational. What do you mean by"rationalize"? (I can't follow from your notation)
    I just tried to regard an irrational number as a rational number ... .

    Quote Originally Posted by Strange View Post
    Here is a simple proof that is irrational: Proof that the square root of 2 is irrational number

    You can do this with most (all?) irrational numbers, for example: Proof that is irrational
    Thank you very much for the explanation ... . Now, I understand why the square root of 2 and the pi are regarded as the irrational numbers ... .

    All rational numbers and all irrational number can form a set of real numbers ... .

    There are significant differences between character of and character of ... .

    If in example we define the set and the set , then we can see the significant difference ... .

    We can find at least one bijective map , in example and , where is a constant ... .

    But, however, we cannot find at least one bijective map ... .

    How can it ... ? Until now I have not understood ... .
    Last edited by trfrm; April 16th, 2013 at 02:33 PM.
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  6. #5  
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    "But, however, we cannot find at least one bijective map ... .

    How can it ... ? Until now I have not understood ... ."
    We can:
    Since all rationals are countable, and all rationals between -1 and 1 are countable, we can make lists of both sets, and then match them up.
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    Professor of Articulation Zesterer's Avatar
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    pi * infinity = infinity

    1 / pi = 1

    Food for thought.
    Science cannot solve the ultimate mystery of nature. And that is because, in the last analysis, we ourselves are a part of the mystery that we are trying to solve.
    Max Planck
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  8. #7  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by Zesterer View Post
    1 / pi = 1
    Er... no.

    1/pi = 0.31831 (approx.)
    ei incumbit probatio qui dicit, non qui negat
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  9. #8  
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    That is not true. The function maps the set of all rational numbers one-to-one onto the set of rational numbers between -1 and 1.
    1) if x is a rational number then x/(x- 1) is also rational.

    2) For any x, x+1> x so x/x+1 is between -1 and 1.

    3) For any y between -1 and 1, x= y/(y-1) maps to y.
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  10. #9  
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    Quote Originally Posted by HallsofIvy View Post
    That is not true. The function maps the set of all rational numbers one-to-one onto the set of rational numbers between -1 and 1.
    Excuse me ... . The plot of f(x) = x/(x + 1) is in the following site ... .

    x/(x+1) - Wolfram|Alpha

    The domain of the function is ... , and the range (or image) of the is ... . Thus, the function is not bijection from to ... .

    I'm sorry ... .
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  11. #10  
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    Quote Originally Posted by Zesterer View Post
    pi * infinity = infinity

    1 / pi = 1

    Food for thought.
    ... is this some kind of childish joke where you say or window?

    As strange pointed out:...

    That's not food for thought, that's just trash, no offense.
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