Let's say there is a set containing all finite decimal expansions of $\pi$:
$$A = \{3, 3.1, 3.14, 3.141, 3.1415, 3.14159, ... \}$$
Does this set contains $\pi$?
I see that it is probably not true because then it would may mean that $\pi$ is a rational number. But, since it's an infinite set, there is no "last" element of this set. Therefore I am confused. Someone please guide on the same.