If the universe is in fact infinite, then there must be infinite matter and space right ? since space is just the measure of the position of matter relative to eachother right? so if there is space there is matter, and if there's infinite matter there is an infinite number of you (as stated before).................this is mindbending shit : D
Gottfried Leibniz would likely agree with the first part of your assessment. Then again, Leibniz's metaphysical scheme was pretty crazy.
Isaac Newton, on the other hand, would have definitely disagreed. For him, space really truly existed, with or without matter.
Now a lot has happened in physics since the time of those two, but this disagreement at least highlights that either view is potentially reasonable to hold, and it isn't immediately obvious which is true. For more info, check out the
Leibniz-Clarke correspondence.
As for the final assumption, that if there is infinite matter, that their is an infinite repetition of everything in existence, I believe I can provide some reasons for why that is not correct.
First, let's start with a simple theoretical universe. It is infinite in both size and matter, and consists entirely of particles that are identical to each other in all but position and movement. Let us further suppose that due to various laws placed on these particles, that there exist only 100 different ways in which the number and arrangement of particles can occur within any given cubic meter of space. We might be tempted to presume that each of these 100 different arrangements must occur an infinite number of times. After all, even if the universe were only 101 cubic meters in size, at least one of the patterns must occur more than once. However, what if only 3 of the 100 different arrangements are repeated, are repeated infinitely, and the other 97 arrangements happen a finite number of times, or maybe even only once? There is no mathematical contradiction here. It is only when we assign
non-infinitesimal probabilities to the occurence of each pattern that they must all occur infinitely often. But there is nothing that rules out the possibility of infinitesimal but greater-than-zero probabilities in a universe that is infinite in space and matter.
If we expand our universe some by allowing an infinite number of arrangements within any finite piece of space, which I think is quite plausible, then it becomes even more difficult to guarantee and infinite reoccurrence of everything. The infinitey of matter must be of a higher cardinality than the infinity of possible arrangements. (For example, consider the quantity of real numbers compared to the quantity of integers. There are infinitely many more real numbers than there are integers, even though there is an infinite quantity of both.) And here is an example of why I consider this possibility to be quite plausible: Within some cubic meters of space, there might be only two particles, and the only relevant relation they have to each other is distance. And if the position of a particle is measured using real numbers, then there will be an infinite number of distances which are possible between two particles. So let us consider a universe where every single cubic meter contains only two particles, but where for each of these cubic meters, a different distance occurs. No relation of particles ever occurs twice, even though there are an infinite number of them, and this is possible primarily because the infinity of possible distances and the infinity of space/matter are of equal magnitude. We'd have to increase the latter magnitude to get away from this possibility, and here my knowledge of mathematics starts to get quite fuzzy. I have a hard time imagining the infinity of space/matter as being larger than the infinity of the real numbers. But regardless, even if that is doable, we still have the same problem we had above, such that some patterns in the universe may occur only once or only a finite number of times, while the rest repeat themselves infinitely in order to fill the infinity of space.
TL;DR: An infinity of space/time does not
guarantee an infinite repetition of every single pattern found in the universe, though such a universe is not logically ruled out either.