It's completely wrong within ZF set theory the cardinality of the integers is stricly smaller than the cardinality of the real numbers. The continuum hypothesis states that there is no set with a cardinality strictly larger than the natural numbers (or integers) and strictly smaller than the real numbers.

It accidentally kind of comes to the right conclusion, but even the conclusion isn't really correct, you don't need to be concerned with finite time since integers are a smaller cardinality.

Let's say people can be placed on a point on the track indexed by the real numbers, given any two seperate, finite, points, there would be more people packed between those two points than the entire integer track.