The function $f(x) = x+2$ on the given sets $([2,3]$ and $[4,5])$ is bijective which should imply that the cardinality is equal. Now, consider the function $f(x) = x^2$ on the sets of real numbers $[2,3]$ and $[4,9]$. Again this function is bijective. This implies, the cardinality of $[2,3]$ is equal to $[4,9]$.
Since $[4,5]$ is a subset of $[4,9]$, therefore cardinality of $[4,5]$ is less than that of $[4,9]$ and therefore less than $[2,3]$.
But then this is in contradiction to our initial observation. What's the flaw in the above reasoning/comparison?