Math: Why is it okay that √(9!)=6 on this crazy clock?

Link to crazy clock in question.

My feeling is that it’s an error. The only way to get √(9!)=6 is to write it as √(9)!=6. That means moving the factorial symbol out from under the vinculum.

Or is there some bizarre rule pertaining to the factorial operation (which, as far as I know, is just multiplication) that makes it acceptable to write it this way?

You’re right, the clock is in error: The only rule of mathematical notation is clarity, and that is quite clearly wrong. There’s no special mathematical rule which makes the square root of nine factorial equal to six.

To be fair, they don’t have the parentheses on that clock. They screwed up - the square root symbol should only extend over the 9, and not over the !.

Well they used a vinculum, which is a form of grouping just like parentheses (to show the radicand whose root is being indicated). The only reason I substituted parentheses was because I didn’t know how to create a vinculum here.

It’s just a matter of notation, but, yes, I think you’ll find that everyone agrees this was a screw-up.

But then, there’s a lot odd about this clock. Like their apparent need to use three "9"s for every number except 1.

The use of three 9s is just a mathematical recreational puzzle, like the “four 4s” https://en.wikipedia.org/wiki/Four_fours .

They could’ve used this for “1”:


  _
9.9 - 9

Right, it’s just odd that they abandoned that gimmick for 1 when, as you note, they could easily have handled that in line with their other solutions.

The whole thing even seems more contrived than usual for such clocks. Most positions seems to be little more than x/x, (x+x)/x and so on. Apart from perhaps selling well to adherents of the Bahá’í faith I can’t see the attraction.

The picture I see in that link doesn’t have a factorial expression for any of the hours. For 6, I see: 9-(9/sqr9).

Check the representation for 5 - it uses the cited rep for 6, as 6 - 1 = 5

Look at 5.

ETA: Er, I had not refreshed this page, apparently…

I concur with everyone else that it’s an error.

I also object to its being called a “Math Equation Clock,” when there’s nary an = to be seen.

It seems to me that you also need to move the vinculum to be inside the parentheses, like this: (√9)!
Now it unambiguously means “three factorial”. When the “9” is inside the parentheses all alone, the parentheses don’t really clarify anything.

Don’t feel bad; I switched between this page and the linked page about 7 times before I realized the title wasn’t giving the equation for 6 o’clock.

Really? I can think of a potential audience:

Which, given it’s flawed, would be especially funny.

If you look at the seven o-clock position, it says 9 - √9 + (repeat).9.

That would imply that 0.9999… is exactly equal to one. I think we should debate that.

Oh you.

Not if you’re gonna be all imprecise and use ellipses. Finish your number and then we’ll talk.

Actually, the line is over both the decimal point and the nine, so the implication is really that .9.9.9.9.9.9… = 1. As far as I know there’s no standard mathematical notation which uses multiple decimal points in this manner, so I think this is yet another error in the clock.