Can a regular expression be infinite?
If regular expressions were allowed to be infinite, then any language would have been regular.

Given the language $L=\{w_1, w_2, \ldots\}$, we can always define the regular expression $R = w_1 + w_2 + \cdots$, which exactly defines $L$.
(Example: the regular expression $R_1 = \epsilon+0+1+00+01+10+11+\cdots$ defines $L_1=\{0,1\}^*$.)

We know that some languages are not regular, so this shows that infinite regular expressions describe a larger class of languages than finite regular expressions.