Question

{ x : x belongs to r and 1 < x < 2 } is finite or infinite?

Answer 1

the set is infinite because there are infinitely many rational numbers between 1 and 2

Answer 2

If you are considering that x belongs to Z(Integers) then,

yes it is finite

and acutually a null set

but, if you consider thar x belongs to R (Which is in this case) then It is infinte as it will contain all the real numbers between 1 and 2

Ex. 1.1, 1.01, 1.001 and so on...