If the universe goes on in all possible directions, and in an infinite distance, then wouldn't that mean that there would have to be more planets out there (another universe?) If you have an infinite amount of space, then wouldn't there absolutely HAVE to be another universe out there (perhaps an infinite number of them?) And if there are an infinite number of universes, then that would mean that EVENTUALLY there would be another milky way galaxy, and everything that has happened here in 'our' galaxy, would happen the exact same in that galaxy. Also, there would be an infinite number of us, doing an infinite number of things. For example, in other worlds I have won the Nobel Peace Prize, the word 'fish' is a curse word, George Bush is a serial killer. I just want to know if that is possible, and if there is a theory/document that has been published about it, and perhaps where I can read this theory/document.
The universe may be infinite, but we can only see a finite section of it due to the finite speed of light. We can only see those parts from which light has had time to reach us since the beginning of the universe - which means we can (in theory) see a spherical universe with radius of about 47 billion light years. If I gave you some time to think about that I'm sure that you would come up with the following conclusion - "that means that the universe must have expanded faster than the speed of light at some point", which appears to violate special relativity. In fact that is what is thought to have happened, during a period called "inflation", and it does not violate special relativity since it is not a spatial motion, but the expansion of space itself.
Back to your question: if the universe is infinite beyond our horizon, is there an infinite number of "you"s out there? I wonder if you have covered probabilities in school? (If you haven't let me know if you don't understand the following).
If there is a finite probability of something happening (ie. a planet forming around a star, or a galaxy forming), then in an infinite universe there will be an infinite number of that thing. So there would be an infinite number of galaxies and planets in an infinite universe. If however there is an infinitesimal probability of something happening, then in an infinite universe there would only be a finite number (for example 1) of those things. I would argue that the probability of creating a specific person with a specific genetic make-up and way of thinking may only be infinitesimal (it depends on how complex you think humans are) - therefore there is only one of you! People also use this argument against the idea that there must be ET life out there in such a big universe - if the probability of life forming is infinitesimal then there could only be one life bearing planet. I personally think that it's more likely that life forms with a finite probability than it is that a specific person forms.