Suppose a coin is flipped infinitely many times and we take as our sample space $S$ all possible infinite length sequences of heads and tails. For $n\geq1$, let $A_n$ be the event that in the first $n$ flips the proportion of heads is at least $1/2$.
(a) Express in terms of the events $A_n$ using set operations the event $A$, which is defined as the set of all sequences in $S$ with the property that for some $k$, the proportion of heads in the first $n$ flips is at least $1/2$ for all $n\geq k$.
Could someone help me parse this out a bit. I don't have trouble calculating actual probabilities but the set operation language and notation is a bit confusing for me. Any help would be appreciated.