I fully get it seems weird...

But there is a written definition of what factorial means, and a given way to calculate it. You aren't supposed to just get the answer by manipulating other products which include the definition, that's circular reasoning.

And apparently negative numbers are excluded because they don't want you counting backwards from one. Well you have to count backwards from one to get to zero. If you actually go ahead and do it, it would be 1*0, so 0! would be 0, although I think it would make more sense to say that 0! was undefined / outside of the definition, instead of arbitrarily saying it equals 1. Although maybe there is some important reason mathematicians want it to equal 1 that I don't know about.

Control+u 1000000 i

0! is the number of ways to arrange zero things = 1
1! is the number of ways to arrange one thing = 1
2! is the number of ways to arrange two things = 2
3! is the number of ways to arrange three things = 6
etc

(-1)! is the number of ways to arrange negative one things = ERROR

is always how I've understood it

Can you "arrange zero things"?

yeah, you can

The definition I have always seen mentions multiplication, not arranging.

Instead of arranging n things think about how many states there are for a set containing n different items to be in.

The empty set can be in 1 state and hence 0! = 1

Negative numbers can be in sets too though, so why not have factorial for those?

negative numbers can be in sets, but a set cannot contain a negative number of unique items

Imaginary set?

aye

So.... does "aye aye" mean "negative"?

Can't you answer all the questions with

You could go even simpler :

111>6

Solve this any way you like....

There are three bare light bulbs in the attic. In the basement there are three switches, one for each light. They are all in the off position.

You are in the basement. What do you do with the switches to determine which switch controls each light? You only get one-trip up to the attic for confirmation.

"Note" All lights/bulbs/circuits etc are in working order.

I did this one years ago.

Edit: Then use a switch on my pony

yup....this is a pretty common one so I figured it would be easy..

Hi Folks

I know there are lots of people in POG who specialize in math, and that there at least a few who teach math in High School, College or University.

I encountered this article when I was finishing an M.Ed (Adult Education) years ago. Though the authour was a math teacher, the message about the flaws related to "competency" is relevant in any subject matter area.

It is only a couple of pages. I'd be interested if the message resonates with those of you with a math and/or teaching background.

http://https://podnetwork.org/content/uploads/V4-N2-Smith.pdf

Got shown this today and felt pretty good about myself for solving it within a couple of minutes:

I got that instantly.

Took me a few minutes but I just got it. Nice one.

easy