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Math Help - point set, open closed,

  1. #1
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    point set, open closed,

    I am really confused about closed or open set,

    I have options of choosing open, closed, or neither...

    a) all x such that x<1 :I think it's open because tbere is some neighborhood of x0 which belongs entirely to S

    b) All x such that x>= 0 : I think closed, because then 0 cannot have neighborhood?

    c) all x such that either x<0 or x>=1 neither , because one side is open and the other is closed?

    d)all rational numbers: neither?? because both rational irrational can be neighborhood

    e)all irrational number: open

    Are my answers right ??? and am I getting them right????
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by mathsohard View Post
    I am really confused about closed or open set,

    I have options of choosing open, closed, or neither...

    a) all x such that x<1 :I think it's open because tbere is some neighborhood of x0 which belongs entirely to S
    Right, prove it.

    b) All x such that x>= 0 : I think closed, because then 0 cannot have neighborhood?
    The right answer, but an incoherent reason.

    c) all x such that either x<0 or x>=1 neither , because one side is open and the other is closed?
    Right idea, say it a little better.

    d)all rational numbers: neither?? because both rational irrational can be neighborhood
    Right idea, say it a little better.

    e)all irrational number: open
    If this were open then wouldn't it's complement, the rationals, be closed?
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  3. #3
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    I would suggest you start by writing out, so you have it clearly before you, the definitions, in your text book, of "closed" and "open" sets.

    In fact, no one here can tell you how to prove those because different books may have different (though equivalent) definitions and we don't know which you are using.
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  4. #4
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    My book's definition of open is : A point set S is called open if for each point Xo of S there is some neighborhood of Xo which belongs entirely to S and definition of closed is that A set is called closed if its complement is open.
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