4 ms·

Why not mention factorials? 9!! is way bigger than 9^9^9. And you can write many exclamation marks in 15 seconds.

• vacri 12y ago
  Wow, 9!! is so large that the exponent almost needs it's own exponent. 9^9^9 =~ 2e77 9!! =~ 1.6e1859933
  • peterjmag 12y ago
    Correct me if I'm wrong, but aren't you supposed to evaluate stacked exponents from the top down? That is, 9^(9^9) instead of (9^9)^9. If that's the case, 9^(9^9) is much larger than 9!!. Though I'm not sure how much larger, since I couldn't find any big integer calculators online that would give me an actual result for 9^(9^9).
    • cradle 12y ago
      9^(9^9) is ... wait for it... 4e369693099 bigger than 9!! http://www.wolframalpha.com/input/?i=9%5E9%5E9+-+9%21%21 http://www.wolframalpha.com/input/?i=9%5E9%5E9+-+9%21%21
      • peterjmag 12y ago
        Ah thanks! How could I forget Wolfram Alpha? =)
      • BhavdeepSethi 12y ago
        Shouldn't it be (9!)!? http://www.wolframalpha.com/input/?i=9%5E9%5E9+-+%289%21%29%21 http://www.wolframalpha.com/input/?i=9%5E9%5E9+-+%289%21%29%...
    • vacri 12y ago
      It seems you're correct - I was just pounding the values in sequence into a calculator, much like a determined monkey would.
• baby 12y ago
  Good one! I was only thinking of e^e^9 which is way smaller than 9!!
• tcai 12y ago
  As peterjmag indicated in his comment, 9^9^9 looks like 9^(9^9) which is actually greater than 9!!. A different way of looking at it is n! < n^n. We can see from here that factorization isn't really the new paradigm that the author is looking for; it's just a part of the exponentiation paradigm. Furthermore, factorials don't really scale or stack easily. What the author is getting at in the relevant location is stacking the same concept: 1. Multiplying is just adding the same number several times. 2. Exponentiation is just multiplying the same number several times. 3. Tetration is just exponentiation several times. 4. Etc. This allows us to generate the infinite hierarchy easily expressible by the ackerman numbers (which is basically A(i) = f_i(i,i)), which doesn't generate itself as easily with factorialization in place of exponentiation.
• splat 12y ago
  When writing factorials you would want to write (9!)! since 9!! is actually a different operation (the double factorial). 9!! = 9 x 7 x 5 x 3 x 1, so 9!! is less than 9!.