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Math Help - Corollary on Irrational Number

  1. #1
    Member aldrincabrera's Avatar
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    Cool Corollary on Irrational Number

    ,.hello everyone,.,i need ur help agen with this,.,


    Let epsilon>0 be an irrational number and let z>0. then there exists a natural number m such that the irrational number epsilon/m satisfies 0<(epsilon/m)<z.


    ,.i somehow understand the proof on the book but i was having a hard time proving that

    epsilon/m is an irrational number,.,can anyone give me a hand with this???any hint will do,.,.thnx a lot[IMG]file:///C:/Users/User/AppData/Local/Temp/msohtmlclip1/01/clip_image010.gif[/IMG]
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  2. #2
    MHF Contributor

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    Re: Corollary on Irrational Number

    Your image did not load. However, given any irrational number, \epsilon> 0, there exist a real number, r, greater than \epsilon, \epsilon+ 1, for example. Given that, let z= r/m where m is any natural number. Then 0< \epsilon< r= mz and so 0< \epsilon/m< z.
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