... unfortunately, there is a flaw in the reasoning. ... [T]o say that each of two numbers cannot be bigger than the other is to repeat the statement that is to be proved. It is not correct in logic to prove something by saying it over again; that only works in politics, and even there it is usually considered desirable to repeat the proposition hundreds of times before considering it as definitely established.

— Carl E. Linderholm, "Mathematics Made Difficult"

(There are many more good quotes to be found in this book.)