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Thread: Finding integers between two numbers

  1. #1
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    Finding integers between two numbers

    Write a set representing the following statement. The integers greater than -2/7 and less than 7/3. Can someone help me understand how you get those numbers.
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  2. #2
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    Re: Finding integers between two numbers

    $-1 < -\dfrac 2 7 < 0 < 2 < \dfrac 7 3$

    can you figure it out from there?

    maybe what they are after though is something like this

    $\left \{x: -\dfrac 2 7 < x < \dfrac 7 3 \wedge x \in \mathbb{Z}\right \}$
    Last edited by romsek; Sep 1st 2018 at 01:43 PM.
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    Re: Finding integers between two numbers

    Or maybe $~\{0~,1~,2\}$, although that might not contribute much to learning set notation.
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    Re: Finding integers between two numbers

    Quote Originally Posted by chels2000 View Post
    Write a set representing the following statement. The integers greater than -2/7 and less than 7/3. Can someone help me understand how you get those numbers.
    Look at this table.
    It uses the floor function (greatest integer).

    $\displaystyle \left\{ {\left\lfloor {\frac{{ - 2}}{7} + k} \right\rfloor :k = 1,2,3} \right\} = \left\{ {0,1,2} \right\}$
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    Re: Finding integers between two numbers

    Sorry...but what a silly question: your math teacher on drugs?
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    Forum Admin topsquark's Avatar
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    Re: Finding integers between two numbers

    Quote Originally Posted by DenisB View Post
    Sorry...but what a silly question: your math teacher on drugs?
    Whether it's silly or not depends on the student's abilities. What if the OP is a Freshman in HS? Then it might be a good question.

    -Dan
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    Re: Finding integers between two numbers

    Quote Originally Posted by DenisB View Post
    Sorry...but what a silly question: your math teacher on drugs?
    Quote Originally Posted by topsquark View Post
    Whether it's silly or not depends on the student's abilities. What if the OP is a Freshman in HS? Then it might be a good question.
    Denis shame on you. I challenge you to prove that if $x-y>1$ then there is an integer between $x~\&~y$ using only the axioms. That ain't easy.
    So $-\frac{2}{7}$ to $\frac{7}{3}$ makes a great classroom discussion on why each of $0,~1,~\&~2$ is between those two and only those three integers.
    Then ask exactly what integers are between $-\dfrac{29}{4}~\&~\dfrac{37}{3}~?$
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