Knowing that the set $[0,1]$of real numbers between $0$and $1$is uncountable. That means the set is infinite and there is no bijection between $[0,1]$and $($ this set of natural numbers $).$ How can I use this fact to show that $[1,1.001]($the set of real numbers between $1$and $1.001,$inclusive $)$ is also uncountable?