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Today's post is about a picture that has been mystifying and frustrating people. Frustrating because it seems so blatantly and completely wrong. Mystifying because people in the know just smile knowingly as though it's a joke.

Some jokes need to be explained, so here's the picture:

It seems quite clear, doesn't it? PEMDAS gives us our order of operations. We evaluated 85 + 65 first: 85 + 65 = 150.

So now we have 25 - 55 + 150, which should be evaluated in order from left to right: 25 - 55 = -30, and -30 + 150 = 120.

So how in the world did they get 5?

The answer is: they didn't get 5. They got 5!

You see, this is one of those horrible times when mathematics hijacks innocent punctuation marks and forces them into hard labor for nefarious, non-grammatical purposes.

The exclamation mark is used in mathematics not to epxress excitement or astonishment, but to indicate that we are calculating the *factorial* of a number.

What's a factorial? A factorial is what you get when you multiply all the integers between 1 and some number. For example, 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.

So before we declare this image bogus and invalid, we probably should check to find out what 5! equals.

5! = 5 x 4 x 3 x 2 x 1 = 120.

Oh! (And I'm using that exclamation mark to indicate astonishment) it really does equal 5!

And if I'm truly astonished, I might say that it equals 5!!

Except someone might get hoodwinked into thinking I meant 120!, which is about 6.8 x 10^{198}. That's not what I meant. I promise. I'm just *that *excited!