Why is 0! =1 Should it not be 0! = 0?

Yeah, I know it sounds strange, but it's true.

You should Google this as there are a lot of great answers to zero factorial = 1

Good luck!

:)

Many, many things make more sense with 0!=1.

For one explanation:

You could view this in the traditional sense, but it quickly becomes complicated.

This would mean the product of all the integers up to it. However, one DOES NOT include 0 within that list; otherwise all factorials would be 0.

Therefore, as 3!=3*2*1, 2!=2*1, 1!=1, then 0!=? has no numbers in it; you have one less number each time, and 0 ends up being the product of no numbers.

The product of no numbers equals one: though I don't have a formal explanation, think of it like this: the sum of no numbers is clearly 0, the additive identity. In an analogous manner, the product of no numbers is 1, the multiplicative identity.

Another way to think of it is that if you try to sum all the numbers in a set, such as {1,4,5,2}, it would give you 12. Taking out one number at a time leaves you with the original sum minus the number you took out. {1,5,2} sums to 8. {5,2} sums to 7. {2} sums to 2. It would only make sense if {} would sum to 0. The exact same logic applies to a function that would take the product: {3,5,7} gives 105, {3,5} gives 15, {5} gives 5, and {} gives 5/5=1,

A second explanation for 0!=1:

If there are 4 people in a line, there are 4! ways to order it. If there's one person, there are 1! ways.

If there are zero people, there are 0! ways. There's one way to order it, which is just empty space. This isn't a particularly strong argument though, as one could argue that there are really no ways to order the line.

A third explanation:

5!/5=4!

4!/4=3!

3!/3=2!

2!/2=1!

1!/1=0! by this pattern, which yields 1.

It's a definition. Division by 0! appears often in the first term of series expressions, thus the need to give it a value different from zero; 1 works out nicely.

it's because n!/(n-1)! = n

so when n = 1, and n-1 = 0, the quotient is 1!/0! = n, and n = 1, and 0!(1) = 1! = 1, so 0! = 1

Hello again...

Can you ask more religiously charged questions? I am getting bored with the typical minds on the R and S section.