# Thread: Finding integers between two numbers

1. ## 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.

2. ## 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

$\left \{x: -\dfrac 2 7 < x < \dfrac 7 3 \wedge x \in \mathbb{Z}\right \}$

3. ## Re: Finding integers between two numbers

Or maybe $~\{0~,1~,2\}$, although that might not contribute much to learning set notation.

4. ## Re: Finding integers between two numbers Originally Posted by chels2000 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).

$\displaystyle \left\{ {\left\lfloor {\frac{{ - 2}}{7} + k} \right\rfloor :k = 1,2,3} \right\} = \left\{ {0,1,2} \right\}$

5. ## Re: Finding integers between two numbers

Sorry...but what a silly question: your math teacher on drugs?

6. ## Re: Finding integers between two numbers Originally Posted by DenisB 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

7. ## Re: Finding integers between two numbers Originally Posted by DenisB Sorry...but what a silly question: your math teacher on drugs? Originally Posted by topsquark 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 $-\dfrac{29}{4}~\&~\dfrac{37}{3}~?$