2.48 Find all sets of distinct positive integers (at least 2) such that the sum of the numbers equals their product.
[Solution] Clearly, 1 plays a role in keeping the product unchanged while increasing the sum in the set, and it is the only positive integer with this property.

First, assume that the $n$ numbers in the set do not contain 1 and $1j, j=1,2, \cdots, n$. Since $n \geqslant 2$, we have
$$
\begin{array}{c}
a_{n} a_{n-1}-a_{n}-a_{n-1}=\left(a_{n}-1\right)\left(a_{n-1}-1\right)-1 \geqslant 1, \\
a_{n} a_{n-1} \geqslant a_{n}+a_{n-1}+1 .
\end{array}
$$

Equality holds if and only if $a_{n}=3, a_{n-1}=2$. Therefore, when $n \geqslant 3$,
$$
a_{n} a_{n-1} a_{n-2} \geqslant a_{n} a_{n-1} 2>a_{n}+a_{n-1}+a_{n-2}+1 .
$$

By similar reasoning, we get
$$
a_{n} a_{n-1} \cdots a_{1} \geqslant a_{n}+a_{n-1}+\cdots+a_{1}+1 .
$$
Combining (1) and (2) shows that any set not containing 1 does not meet the requirements, and (2) also implies that even adding 1 to the set does not satisfy the requirements when $n \geqslant 3$.

From (1), we know that when $n=2$, only $a_{0}=1, a_{1}=2, a_{2}=3$ meet the requirements in the problem. Also, when $n=1$, $a_{1} \cdot 1<a_{1}+1$, so any $\left\{1, a_{1}\right\}$ does not meet the requirements in the problem. In summary, the only set that meets the requirements in the problem is $\{1,2,3\}$.