In the partition problem one asks whether a given set of numbers can be partitioned into two sets $S_1$, $S_2$, with a property that elements of $S_1$ sum to the same value as elements of $S_2$.
My first question is how do we call a set satisfying such a property, i.e. a set for which the partition problem has a solution?
Let $\vartheta = \{\alpha_1, \dots, \alpha_N\} \subset \mathbb{R}$, and \begin{equation} \delta (\vartheta) \equiv \min_{\varsigma \in \{\pm 1\}^{N}} \left| \sum_{i = 1}^{N} \varsigma_i \alpha_i \right|. \end{equation} Obviously $\delta (\vartheta) = 0$ if, and only if the set $\vartheta$ has this property. Otherwise $\delta (\vartheta) > 0$.
My second question is how do you call this quantity, $\delta (\vartheta)$? Is there a standard notation for it?
Please, note that in the standard partition problem in the complexity theory one considers sets of integers, whereas here I would like to consider sets of real numbers.