Consider the following standard definition of mutual independence of (discrete) random variables:
"A set of random variables is mutually independent iff for any finite subset $X_1, ..., X_n$ and any finite set of numbers $a_1, ..., a_n$, the events $\{X_1 \le a_1\}, ..., \{X_n \le a_n\}$ are independent events (as defined above)." Taken from Wikipedia.
My question is: Shouldn't we also have specified that we have to have $n>1$ ? Since otherwise for $n=1$ it is not defined what it mean for just one random variable to be independent. As far as I can see, we need at least two random variables (even if they are the same).