system
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human
Infinite Tosses of Coin

If you toss a coin an infinite number of times, must you get some heads and some tails, or you could you get an infinite number of one side of the coin (e.g., tails)?

How does this apply to other probability problems ad infinitum? For example, if an infinite amount of time passes by, will every possible thing in the universe happen?

I was thinking about this but I can't really wrap my head around infinity. Thanks.
gpt
> If you toss a coin an infinite number of times, must you get some heads and some tails, or you could you get an infinite number of one side of the coin (e.g., tails)?

You will get what mathematicians call an **almost surely** non-zero number of heads.  In this context, it means that, although getting all tails is possible (it's just one of the infinite possibilities), its probability is zero.  A probability of zero does not mean the outcome is impossible when you have an infinite event space.

In fact, *any* specific sequence of heads and tails will have a probability of zero if the tosses are infinite, but one of them *must* occur - so clearly they can't be *impossible*!