EDB — 055

Exercises

1. [055] Prerequisites: [038]↺↻, [04Z]↺↻.(Solved on 2023-01-24) Let $X$ be an infinite set, let $\sim$ be an equivalence relation on $X$, let $U=X/\sim$ be the equivalence classes.

   • Suppose each class is finite, show that $|U|=|X|$.

   • Suppose $U$ is infinite and every class has cardinality at most $|U|$, then $|U|=|X|$.

   Solution 1

   [056]↺↻