We now join our hero, Captain Constructor, at Decidability Deli where he is brunching with his arch-nemesis, Doctor Destructor. (The thoughts and ideas presented herein by Doctor Destructor are expressed in a shade of red, while those of Captain Constructor are blue.)
So you see, my good captain, the number of infinities is itself infinite.
Of course. And the number of finities is finite. By the way, are you enjoying that Pi?
Yes, yes! It’s absolutely irrational! But back to more serious matters. I have just discovered a delightful sequence of numbers which is sure to stump you until well after the end of the universe.
On second thought, perhaps inviting you to brunch was a sub-good idea. Must we talk numbers now?
Usually you are quite game, Captain. There must be something debilitating in that Turing Tart of yours.
Sadly, I think you’re right. Yet I cannot resist.
Every Achilles has his heel. Just like every cowboy sings a sad, sad song.
Every villain likes to hear himself talk. On with the number sequence!
Dr. Destructor clears his throat and begins…
If I were to tell you that a certain sequence began with the numbers 0, 1, and 2, what would you guess is the next number?
It seems only natural to assume that the next number is 3. Three is, after all, the next of the natural numbers.
It is indeed, old capt. However, 3 is not the next number in this particular sequence. The next number is actually 2.601218943565795100204903227081e+1746, which is clearly not easy to pronounce.
Clearly. Wouldn’t it be easier to pronounce it as 720 factorial?
Very astute, Captain Number Crunch. You were awfully quick to find that reduction. But can you quickly explain the relationship of 720! to 2, 1, and 0? Nevermind the quickly. Can you even explain it at all? Mua ha ha ha ha!!!
Join us next time for the exciting conclusion!
