I was reading about Kolmogorov's zero-one law specifying:
a certain type of event, called a tail event, will either almost surely happen or almost surely not happen
I came to this example:
In an infinite sequence of coin-tosses, a sequence of 100 consecutive heads occurring infinitely many times is a tail event.
That can't be true, can it?
In an infinite sequence of coin-tosses, any specific sequence will occur infinite times. A sequence of 100 consecutive heads will always occur infinitely many times, not almost surely.
Saying that a sequence will occur any less than infinite many times actually get absurd. If the 100 consecutive heads occur any finite number of times, if I then get 99 consecutive heads any time after that, the next toss will not be random, but it has to turn up tails.
So, am I missing something fundamental?