# Why did Wegman-Carter call their class of hash functions as universal on their seminal paper

Wegman-Carter on their seminal Universal classes of hash functions uses the term universal for their definition. They gave this definition as:

Let $$H$$ be a class of functions from $$A$$ to $$B$$. We say that $$H$$ is $$universal_2$$ if for all $$x,y$$ in $$A$$, $$\delta_h(x,y) \leq \frac{\vert H\vert}{\vert B\vert}.$$ That is, $$H$$ is $$universal_2$$ if no pair of distinct keys are mapped into the same index by more than one $$\vert B\vert^{\text{th}}$$ of the functions.

Is there a rational reason for the naming of this hash functions as universal?