Well, we've already proven it's impossible to have all heads infinitely. The same would be true of any non-uniform sequence. Any sequence that favours heads by

Well, we've already proven it's impossible to have all heads infinitely. The same would be true of any non-uniform sequence. Any sequence that favours heads by any margin at all, taken to infinity, would necessarily contain an infinite sub-sequence that contains all heads, which we've proven is impossible by the limit to infinity. Have we? We only said that the probability of having an infinite sequence of all heads is zero but not that it is impossible to obtain that result. After all the probability of any infinite sequence is zero and therefore if we would equate probability zero with impossible to obtain, then we could obtain no infinite sequence at all. The second part is obviously wrong, H H T H H T... ad infinitum obviously favors heads over tails but does not contain an infinite subsequence of all heads.