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Comment by Xcelerate | Hacker News Reader

I actually got fussed at for my answer to a variant of this question this past semester. I have a professor who talked about when he was in college and his instructor had the challenge: what is the biggest number you can make with three nines?

His answer was 9^(9^9). Of course, I thought this question warranted further discussion and I mentioned that Knuth's up arrow notation allows an even bigger number and demonstrated it on the board. The professor seemed annoyed and I asked him about it later; I believe he mistook my interest in contributing to the discussion as trying to one-up him (which was NOT my intention at all).

I've been much quieter in that class since :(

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9! (9! up arrows) 9!

Of course, you can also have 9!! and 9!!! and 9!!!! or even 9! factorial signs after the 9, etc.

The original problem statement of "write this in 15 seconds using standard notation" is less easy to game. But I think the right answer is to just have 9 (up arrow with 9 under it) 9 and then make the 9s bigger using factorials until your 15 seconds run out.

How pointless.

Keep in mind, though, that you would want to write it (9!)! or ((9!)!)!. 9!! is actually the double factorial, which is defined as 9!! = 1 * 3 * 5 * 7 * 9. So 9!! < 9!.

I've never heard of that, but sure, do (9!)!. Since the problem as stated by the OP (not the article itself) specifies that only 9s are limited, it doesn't make a difference.

When talking about big numbers, I would definitely consider up arrow notation as standard notation.

At the very least there should be !s after those 9s.

Or, (9!^9!)!^(9!)

I find it amusing that anyone could think they've "won" a game such as this, there is just so much potential for incredibly large numbers, even if you omit the possibility of using thing's like Knuth's up arrow notation.

I think it all hinges on what's meant by "with three nines".

Are you allowed non-digit symbols? In that case, there's obviously no upper bound. Just e.g. keep adding !s after a 9 and the number gets bigger and bigger.

Are you only allowed the 9s, with the only possibly difference in meaning being the positioning? Then 9^9^9 (where the ^ is represented purely by positioning on paper) looks to be the best you can do. I don't believe things like up-arrow notation can be represented with just positioning.

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