In an infinite universe, if each person has an infinite amount of space to move around in, it would still not necessarily mean that an infinite number of people would have an individually infinite amount of space.
Infinity is a concept that can lead to counterintuitive and paradoxical situations. While it may seem intuitive that if one person has an infinite amount of space, an infinite number of people would also have an infinite amount of space, it is not necessarily the case.
In mathematics, different sizes of infinity exist. For example, the set of natural numbers (1, 2, 3, ...) is infinite, but it is a countable infinity. However, the set of real numbers between 0 and 1 is also infinite, but it is an uncountable infinity and larger than the set of natural numbers. So, even though both sets are infinite, they have different sizes.
Similarly, in the scenario you described, each person having an infinite amount of space would mean that there is an uncountable infinity of space available. However, even if an infinite number of people were present, they would still be sharing the same uncountable infinity of space.
This concept can be challenging to grasp, as it defies our everyday experiences and intuition. Infinity and its implications often lead to paradoxes and unexpected outcomes. Therefore, reasoning about infinite quantities can be complex and may not always conform to our intuitions based on finite experiences.