Points for the idea; not so much for the execution.

I know this isn’t offensive like some (most) of the memes I cover, but there *is* a problem. If you’re going to make a clock wherein the numbers of the hours are written as mathematical expressions using only the digit 9, you probably want to check your math. Look at the 5 o’clock slot. You see that exclamation mark beside the first nine? No, the clockmaker is not expressing his enthusiasm about the number nine. I mean, it’s obvious that the designer *really likes the number nine*, but that’s not the purpose of the exclamation mark. In math, that bit of punctuation indicates a *factorial*. Since the name *factorial* does absolutely nothing to tell you what it is, I’ll elaborate.

To find the factorial of any positive whole number, you simply multiply all the whole numbers up to and including the number itself. So for example, 2! (read as “two factorial”) is equal to 1 x 2, or 2. Five factorial is 1 x 2 x 3 x 4 x 5, or 120. As you may well imagine, factorials get pretty huge pretty quick.

If you look closely, you’ll see that the factorial symbol is clearly beneath the square root (or radical). Following any logical order of operations, you should evaluate 9! first, then take the square root. Nine factorial is equal to 362,880, and the square root of 362,880 is approximately 602.4. (It’s actually irrational, which means the digits run on forever after the decimal point without repeating or terminating. Sort of like pi.)

If you subtract 9/9, which is the same as 1, you get about 601.4, which is clearly not what the clockmaker was going for. He or she should have placed the factorial symbol outside the radical…maybe like this:

Or better yet, like this:

In either case, one would find the square root of nine first (which is 3), then evaluate the factorial. 3! = 1 x 2 x 3 = 6. And of course 6 – 1 = 5.

I *have* seen versions of this clock that had the factorial correctly placed, so I’m not sure whether the “wrong” version is the original or a copy-cat. In any case, it seems mildly ironic to make a clock that would appeal to math nerds, then make a mathematical mistake on it.

Kudos, though, for understanding that 0.9 repeating is exactly the same as 1.

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Good explanation