23. In how many ways can the number $n$ be represented as the sum of two positive integers, if representations differing only in the order of the addends are considered the same?



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23. If the number $n$ is represented as the sum of two addends

$$
n=x+y
$$

then one of these addends will not be greater than $\frac{n}{2}$. This addend can take the values $1,2,3, \ldots,\left[\frac{n}{2}\right] ;$ all these cases are distinct, since the second addend in this case will be no less than $\frac{n}{2}$. Therefore, the number of different ways is $\left[\frac{n}{2}\right]$.