Let S be equivalence relation defined on $\{x : x ∈ \mathbb{R},\ 0 ≤ x ≤ 5\} $defined by $xSy$ if and only if $[x] = [y]$. What are the equivalence classes of $S$?
Note: $[q]$ is defined to be the smallest integer greater than or equal to $q$. You can think of it as “$q$ rounded up”. You don’t need to prove that $S$ is an equivalence relation.
My answer is as follows but i am not sure if this is what they are looking for:
Equivalence classes of $S$ = $\{[0, 1), [1,2), [2,3), [3,4), [4,5)\}$
You are almost there. The interval should be closed on the right, and you left out $5$. The equivalence classes are: $$S= \left\{ {0}, (0,1], (1,2], (2,3], (3,4], (4,5] \right\}$$