Classic Fallacies

Classic Fallacies
Our mathematical correspondent has just announced some startling
discoveries, claiming to have found conclusive proof that
1 is equal to 2, that every person in Canada is the same
age, that a ladder will fall infinitely fast if you pull on it, and many
other results that threaten the very fabric of common sense.

Of course, you know these things cannot be true. And yet, our
correspondent has come up with some quite convincing “proofs” of these
facts. Can you discover what is wrong with each of them?