It is not that the Pope is infallible in his own personal strength and power, or make decision on his own personal authority
When and which pope ever said something ex cathedra,and what was it?
Catholics debate this quite a bit... most will tell you that infallibility has been invoked by popes only twice: by Pius IX, in defining the Immaculate Conception of the Blessed Virgin in 1854 (16 years before papal infallibility itself was actually defined at Vatican I), and by Pius XII, in defining the dogma of the Assumption of the Blessed Virgin in 1950.
Some will say that papal canonizations of saints are infallible (I don't agree) and some will assert that just about everything the Pope says (from the Wed. audiences to his lunch menu) is infallible.
If you read a modern document (post-Vat I) and read the words “we define