In my excercise book of math , I have found one problem . In that problem I have been asked to detect whether the number $2.1234....$ is rational or irrational?
My concept is : "$2.1234....$ is irrational." But the answer of book says that the number is rational. I want to argue the answer. Is this answer right?
Can you guys help me to clarify my misconcepts?
I am supposing that $2.1234\dots$ means that the digits continue: $2.12345678901234\dots$. Note also that a continuation could be $2.123456789101112\dots$, it is unclear exactly whether single digits continue, or if it counts ten, eleven, etc.
Note that in the first case, that means that the portion $1234567890$ is repeating.