If we have $n$ coin tosses and we want to prove that the coin will eventually land heads, will this proof be considered a proof of a.s convergence?
Let's consider a contracting sequence of events $A_1, A_2,\ldots A_n$ where A is an event that heads don't fall on the current iteration (T, TT, TTT, ...), then the probability $P(A_1 \cap A_2\cap \ldots A_n= \lim_{n\to\infty}P(A_n)=0$ and then take the complement. I am trying to understand what would count as an a.s proof and, for now, I am just confused.