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Math Help - Interior points subsets of R

  1. #1
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    Interior points subsets of R

    Find the set of interior points for each of these subsets of R (real #s).
    (a) (-1, 1)
    (b) (-1, 1]
    (c) Q (rational #s)
    (d) R - Q (irrational #s)

    attempted answers:
    (a) (-1, 1)
    (b) (-1, 1)
    (c) R - Q
    (d) R - Q

    I was just wondering whether or not these answers where correct or not.
    Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by tbyou87 View Post
    Find the set of interior points for each of these subsets of R (real #s).
    (a) (-1, 1)
    (b) (-1, 1]
    (c) Q (rational #s)
    (d) R - Q (irrational #s)

    attempted answers:
    (a) (-1, 1)
    (b) (-1, 1)
    (c) R - Q
    (d) R - Q

    I was just wondering whether or not these answers where correct or not.
    Thanks
    (a) and (b) are OK.

    (c) is the empty set (there are no interior points of Q, as every open interval
    containing a rational also contains an irrational)

    (d) same as (c) (there are no interior points of R-Q, as every open interval
    containing an irrational also contains an rational)

    RonL
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