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Math Help - Proof Dealing with real and rational numbers

  1. #1
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    Proof Dealing with real and rational numbers

    I'm having trouble understanding how to prove this problem. I need some help.

    Let a ∈ ℚ, a ≠ 0 and b ∈ ℝ \ ℚ. Prove the following:
    a) a + b ∈ ℝ \ ℚ
    b) ab ∈ ℝ \ ℚ
    c)1/b ∈ ℝ \ ℚ

    Thanks for any help provided
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  2. #2
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    Quote Originally Posted by tuyt6444 View Post
    I'm having trouble understanding how to prove this problem. I need some help.

    Let a ∈ ℚ, a ≠ 0 and b ∈ ℝ \ ℚ. Prove the following:
    a) a + b ∈ ℝ \ ℚ
    b) ab ∈ ℝ \ ℚ
    c)1/b ∈ ℝ \ ℚ

    Thanks for any help provided


    All you have to know is that the rational numbers \mathbb{Q} is a field: closed under sum, multiplication and inverses (for elements different from zero, of course).

    Tonio
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