Why does an infinite universe imply that everything that can happen will happen? Why can’t an infinite universe be boring and uneventful?

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Let’s say you have some event with probability *p*, where *p* is the percentage chance this event might happen in a given second.

The odds of it not happening in a given second are (1 – p).

The odds of it not happening for two seconds in a row are (1 – p)^(2)

For three seconds it would be (1 – p)^(3)

For *n* seconds it is (1 – p)^(n)

Discounting impossibilities (p = 0) and certainties (p = 1) then p is between 0 and 1 (exclusive) and therefore (1 – p) is also between o and 1 (exclusive). As n gets larger and larger (1 – p) gets smaller and smaller. The limit of (1 – p) as n approaches infinity is 0.

This means the odds of this event never happening are 0 which means the odds of it happening at least once over all of infinity is 1.

Simple probability.

Let’s say that we are throwing a fair coin, it has a *50/50* chance of landing on either tails(T) or heads(H), and we want it to land on **heads at least once.**

With 1 throw you have two possible outcomes – T or H, so the chance to get it is 50% (1 of 2).

With 2 consecutive throws, you have 4 possible results – TT, HH, TH, and HT, your chances of scoring rise to 75%(3 of 4).

With 3 throws we have 8 possible results – TTT, TTH, THT, HTT, HHH, HHT, HTH, THH, which means 87.5% of scoring(7/8).

And so on. The closer your number of throws is to infinity the closer your chance of scoring is to 100%, culminating at guaranteed if you perform infinitely many throws because even if you did X out of infinity throws without getting your desired result you will still have an X+1 throw that can still result with what you expect.

The same logic can be applied to our universe – if we cut a box of space of some size and define the specific spatial combination of atoms inside of that box as “something happening” then it’s pretty unlikely that any other randomly taken box of that size from any other place in the universe will be the exact “something” we are looking for, but the more boxes you cut and check the more likely you are that at least one of them has an exact same combination of atoms inside and in an infinite universe you can cut an infinite amount of such boxes, meaning that as long as a given “something” has a non-zero chance of happening you will eventually arrive at a box where it happened because even if you did X boxes where it didn’t the next X+1 box might be the one where it does, thus “everything that can happen will happen”.

I think, and please correct me if not, that the going theory speaks of the possibility of infinite universes, each one finite. Each one bound by the laws of physics. Essentially infinite sandboxes.

Okay, an infinite universe doesn’t necessarily imply that everything can happen (it could be infinite in size but finite in mass and energy)

Now, let’s look at something truly infinite in its own dimension: Pi decimals. Pi goes on and on and on and on. That means that at some point in Pi there’s the number 12345678901234567890, and we are absolutely certain about that, because Pi is infinite and irrational (which means that it is random). That also means that at some point in Pi there’s something like one quintillion 7s one after another. That also means that, if we take digits in pairs and substitute them with letters (like 00=A, 01=B, 02=C…) at some point we will find all the books that have ever been written along with the whole biography of every person in the world and the movements of each atom in the entirety of time (after an unsurmountable amount of noise and nonsense ofc, it kinda works like the milion monkeys with typewriters thing)

To sum up: With an infinite number of possibilities (as long as they aren’t periodical) any outcome will happen at some point

I’m pretty sure that if you subscribe to the theory of infinite universes, that there is a universe where everything is boring and uneventful. There’s also the universe where dinosaurs haven’t died and Fred Flintstone is yabba dabba doing his yabba do life.