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.
$-1 < -\dfrac 2 7 < 0 < 2 < \dfrac 7 3$
can you figure it out from there?
maybe what they are after though is something like this
$\left \{x: -\dfrac 2 7 < x < \dfrac 7 3 \wedge x \in \mathbb{Z}\right \}$
Look at this table.
It uses the floor function (greatest integer).
$\displaystyle \left\{ {\left\lfloor {\frac{{ - 2}}{7} + k} \right\rfloor :k = 1,2,3} \right\} = \left\{ {0,1,2} \right\}$
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 $-\dfrac{29}{4}~\&~\dfrac{37}{3}~?$