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Math Help - list the elements in sets.

  1. #1
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    list the elements in sets.

    hey guys having problems with this question.

    List the elements in the following sets:

    1. \{ x \epsilon \mathbb{N} : x^2 < 23\}

    My Answer:
    Elements x = 1,2,3,4


    2. \{ x \epsilon \mathbb{Z} : x^2 < 23\}

    My Answer:
    Elements x = -4,-3,-2,0,1,2,3,4



    3. \{ x \epsilon \mathbb{R} : x^3 + 5x\}

    My Answer:
     \Rightarrow x^3 + 5x = 0
     \Rightarrow x(x^2 + 5) = 0

    so I know x = 0, but dont know how to find x from x^2 + 5 = 0

    4. \{ x \epsilon \mathbb{Q} : x^2 + 4 = 7\}

    My Answer:
    I know Q is rational numbers but dont know how to find this one.

    5. \{ \}

    My Answer:
    This is just an empty set so would it be elements:
    \emptyset ?

    Any help with these 5 questions would be much appreciated.
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  2. #2
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    Quote Originally Posted by jvignacio View Post
    hey guys having problems with this question.

    List the elements in the following sets:

    1. \{ x \epsilon \mathbb{N} : x^2 < 23\}

    My Answer:
    Elements x = 1,2,3,4 what about 0 ?


    2. \{ x \epsilon \mathbb{Z} : x^2 < 23\}

    My Answer:
    Elements x = -4,-3,-2,0,1,2,3,4



    3. \{ x \epsilon \mathbb{R} : x^3 + 5x\} \color{blue}x^3+5x=0\ ?

    My Answer:
     \Rightarrow x^3 + 5x = 0
     \Rightarrow x(x^2 + 5) = 0 \color{blue}x^2=-5 is not real, x=0 is the only solution

    so I know x = 0, but dont know how to find x from x^2 + 5 = 0

    4. \{ x \epsilon \mathbb{Q} : x^2 + 4 = 7\} \color{blue} x^2=7-4=3,\ x=\sqrt{3}\ is\ not\ rational,\ no\ solution

    My Answer:
    I know Q is rational numbers but dont know how to find this one.

    5. \{ \}

    My Answer: no elements
    This is just an empty set so would it be elements:
    \emptyset ?

    Any help with these 5 questions would be much appreciated.
    .
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  3. #3
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    Quote Originally Posted by Archie Meade View Post
    .
    thanks for the help Archie! understood
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  4. #4
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    Quote Originally Posted by jvignacio View Post
    thanks for the help Archie! understood
    One comment: some textbooks include 0 in \mathbb{N}, but others do not.
    So check your textbook to see which definition it uses.
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  5. #5
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    Quote Originally Posted by Plato View Post
    One comment: some textbooks include 0 in \mathbb{N}, but others do not.
    So check your textbook to see which definition it uses.
    Yeah our lecturers include 0 as a natural, just forgot to put it thanks for the comment and reminder!
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