Assorted Afflatuses
Style Over Substance
I will take a moment to break from my frenetic studying to write a word or two about the Cantor Diagonal Method, which one might use to prove there cannot be a bijection between the reals and the naturals.
To this point everything in my five-day-a-week, 5-hour-a-day mathematics course, while not always intuitive, has at least been proven or presented with elegant mathematics. The Cantor Method, though, lacks that elegance. I cannot deny its usefulness, or even indispensableness, however, a proof written with his method, rather than flowing elegantly from one statement to another, relies upon a hideous morass of numbers in an equally hideous table.
I can only hope some other mathematician comes up with a more deft way to do what George managed.
I'm not sure which proof you're talking about. The proof that the rationals are countable that you do by writing out rows of fractions is agreeably ugly, but I always thought the proof that there can be no surjection from a set to its power set was pretty neat.