Question:Assume $A$ is the only uncountable set that we currently know of, where

$A= { xin (0,1): x text{ is a decimal fraction consisting only of combinations of 0 and 1} }$From this fact, show that $[2,infty)$ is uncountable.

How do I go about showing this? Any hints will be much appreciated 🙂

## Answer

**HINT:** Find an injection from $A$ into $[2,infty)$. And remember that a superset of an uncountable set is uncountable.