I am reading Devaney's definition of chaos. Which says:
Let $V$ be a set. $f:V \rightarrow V$ is said to be chaotic on V if
- $f$ has sensitive dependence on initial conditions
- $f$ is topologically transitive
- periodic points are dense in $V$
It seems that conditions 2 and 3 implies 1. Also, condition 2 seems to imply 1. Am I missing something here?