"Without a way of calculating probabilities,
cosmology is a dead science, it doesn't exist," says Vitaly Vanchurin of Tufts University. "At first, I thought, this is crazy, this is not science. But if we cannot answer
this question, we can't do cosmology." .
Probable cause of a bang, then a Boltzman Brain appearing next to you is close to "infinity", if every concievable permutation of likely "cause" events occuring, has happened, then the likelyhood of brains popping into existence increase's.
The BB is very similar to "egg and chicken" question, you can observe an egg emerging out of a chicken, just as you can observe a chicken emerging out of an egg, both occur and both have "probable cuase" ?
Now, Infinity for say counting of numbers cannot happen in a finite time, and thus anything that has a beginning, must have an end, example there is only one way to count to/for infinity, and it has a starting number, 1 and a following number 2, there happens a consecutive ordering process, 3 follows 2, and 4 follows 3.
Even a computer operating at the speed of light, and is in countinueous counting operative mode, will eventually fail in some way, a glitch in software or hardware, or the environment degrades to an extent the computer no longer functions, thus Infinity ( to keep on going forever ) cannot or will not be a probable outcome?..you really do need a glitch free supercomputer, that can operate for at least an eternity, and probably longer !
Nature has a functioning reset button, if something has a start point, then it probable has an end point, thus is infinity free, for the Universe, this may be effectively "continuous", or "cyclic" for a percieved eternity?
If there is an infinity of time and space, then there cannot have been a start point to time and a beginning to space? The Big-Bang model is actually infinity free, because it has, by its very implicated nature, had a starting point and it will evolve into a infinty free end point?