Suppose $\mathcal{A}$ is a set of functions with a common property. Does this mean that the property is shared pairwise or that the property is shared amongst all elements of $\mathcal{A}$?
For example, what does it mean that a set of polynomials do not have a common zero?
Generally, this means that all elements of a set share that property, but it depends on the context a bit. For the polynomial zero question, it is assumed that this means that there is no value $x$ for which $f(x) = 0$ for all $f$ in set $A$