319 Comments

  1. “I’m more than willing to believe that estimate, but I’d love to know how you calculated it.”

    A long time back I wrote a programmable calculator in REXX. REXX will handle an indefinite number of digits, but mine is limited to 30. I typed “!(2019)” and the result was, “1.91137104864715283355211760081E+5798”.

  2. @ Arthur – The embarrassing thing is that I knew what REXX was without having to look it up. I played with it a very tiny bit, but never actually wrote anything useful in it. I still have an old PC (in the attic) that would boot up OS/2 if I turned it on.

  3. ” The embarrassing thing is that I knew what REXX was without having to look it up. ”

    I was familiar with the Commodore implementation, AREXX. Never did anything with it, though.

  4. Kilby: If you want to approximate large factorials with just a hand calculator, you can always use the Stirling series. Using just the first term gives 2019! as 1.9113 * 10^5798, as Arthur and Wolfram Alpha said. Adding in just the first correction term gets the first nine digits correct.

  5. Kilby: Also, the number of zeroes at the end is Floor(2019/5)+Floor(2019/5^2)+Floor(2019/5^3)+Floor(2019/5^4)=502. The proof is left as an exercise for the reader.

  6. @ B.A. – Questions like that should be submitted to CIDU Bill so that they get their own thread and can be discussed by everyone therein.

  7. @ WW – At least you had the decency not to use the tiresome adjective “alert” when describing the “reader”. I always hated that word in physics and math textbooks.

  8. Kilby: I figured the reader didn’t need to be that “alert,” since the proof is “trivial.”

  9. According to Feynman, that statement is a tautology — he discovered that mathematicians used the word “trivial” to mean “proved”, so he taunted them by saying that mathematicians could only solve trivial problems. And chiming in, it is annoying how all proofs in text books are “trivial”, but I guess I’m not a mathematician — the only interesting things are things not yet proved, I guess.

  10. larK: I was once in a math class (for math majors) where we (the students and the professor) were all working through a paper together. One of the students said “the paper says that this step trivially follows, but I don’t see why.” The professor looked at it and couldn’t figure it out, so we spent about 15 minutes in class with everyone coming up with, and shooting down, different explanations for the step. Finally, one of the students figured it out, and said “Oh, it is trivial, here’s why,” and explained it. Everyone (including me), nodded, and said “Oh, right, it is trivial,” and then we went on with the paper. It wasn’t until I got home that I realized (1) it had been silly to call something “trivial” that the whole class had been stumped by for 15 minutes and (2) we had done an approximate recreation of a common joke about mathematicians and “trivial” problems.

  11. ‘Trivial’ is in the eye of the beholder, as it were. Once in a 400-level math class the book gave a two-line proof of a theorem, and the professor felt that was inadequate, so he gave us a handout with his proof. Two pages.

    One man’s trivial is another man’s two pages, I guess.

  12. How to solve a difficult math assignment in 3 easy steps:
    1) Work down as far as possible from the initial equation.
    2) Work up from the final answer given in the back of the book.
    3) In the unsolvable gap remaining between 1) and 2), insert the magic formula: “It is intuitively obvious that…
    Q.E.D.

  13. P.S. Although it has been claimed that this method has worked with certain professors, I heard of one case in which the paper came back with the comment “It is to me, but I don’t think it is to you!” (and points deducted).

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s