[nonameiguess]

This isn't even close to true. In addition to what the other comment points out about eventually losing causal contact with all parts of the observable universe that aren't already gravitionally bound to the same supercluster as the Milky Way, even something like breadth-first search of the entire local supercluster at near the speed of light would take more time than the local supercluster will still exist. The universe will run out of hydrogen and stars won't exist any more long before you can cover all of even the tiniest portions of infinite space.