Example $1.1$ n players participate in a table tennis singles elimination tournament, how many matches need to be played to produce a champion?
Let $\boldsymbol{A}$ denote the set of all matches, and $B$ denote the set of all players except the champion, then $|B|=n-1$.
Define a mapping $f$ from $A$ to $B$ as follows:
Let $a \in A$, if player $b$ is eliminated in match $a$, then $f(a)=b$. It is evident that $f$ is a one-to-one correspondence from $A$ to $B$.

By the principle of equality, $|A|=|B|=n-1$, so it takes $n-1$ matches to determine the champion.