Assorted Afflatuses

From Assorted Afflatuses

Style Over Substance

By Joseph on 8 May 2008 | Permalink

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.

1 Comments

Abraham Neben
15 May 08 at 09:03 (GMT -08:00)

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.

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