# Differential Privacy: why $\delta$ negligible on the row numbers?

The definition of differential privacy says that an algorithm $M$ is $(\epsilon,\delta)$-differentially private if

$$P(M(x \in D) \in S)\leq e^\epsilon P(M(x \in D')\in S) + \delta$$

where $D,D'$ differ by one row and $\delta$ is $\text{negligible}$ in the number of database rows, so $\delta< \frac{1}{p(n)}$ with $n$ being the number of database rows; why do we take $n$ as parameter for this negligible function?

The definition of ($\epsilon$, $\delta$)-differential privacy does not (nor should not) discuss how one should set $\delta$ as a function of the number of records in the input dataset. If you put a period just after ".. differ by one row" you would have the proper definition (by my judgement).
Importantly, differential privacy definitions are universally quantified over all input datasets they must accept as input, and the number of rows is not a parameter on which they can depend. The $\delta$ in ($\epsilon$, $\delta$) is a constant, not a function of $|D|$.