Question

A quick question.

Answer 1

\[0!=\text{______}\]

Answer 2

a quick answer
done

Answer 3

DO you see my question?

Answer 4

By definition, 1.

Answer 5

Can you explain why please?

Answer 6

Simple answer: 0! (read "Zero Factorial") is defined to equal 1.

Involved answer(s):
There are several proofs that have been offered to support this common definition.

http://www.zero-factorial.com/whatis.html

Answer 7

It's defined as 1 partly because otherwise a lot of mathematical formulas don't work.

Keep in mind that n! is really just a shorthand way of writing an expression, like n*(n-1)(n-2)...

Answer 8

I know what the exclamation mark mean, agent0smith, because otherwise I would not have asked this question.
@Directrix, I don't really get the prove ion your link (sorry).
Shouldn't it be zero?

Answer 9

zero factorial is 1

Answer 10

@WHAT?! If you understand that factorial is a shorthand method, why not accept that 0! can be defined as 1?

Answer 11

O just don't get how it is 1, might be difficult for you to understand how come I don't get it ik, but I don't....

Answer 12

A lot of things in math are the way they are because... that's how they are defined.

Answer 13

if you can give a good reason why it should be zero, then go ahead

Answer 14

mathematical consistency is a must though

Answer 15

Or it should be equal to anything or undefined just like 0/0.

Answer 16

Because you aren't taking a factorial of anything

Answer 17

go back to the definition

Answer 18

You don't have to get why it's 1. Some things are just defined that way.

How many ways can you put 10 objects in order? 10P10, or
\[\frac{ 10! }{ (10-10)!}\]
By your definition, (10-10)! would be zero, giving us 10!/0, an undefined number of ways.

Answer 19

if\[3!@=1 \times 2 \times 3\] \[.......\]\[2!=1 \times 2\]\[1!=1\]shouldn't \[0!=0\]or shouldn't \[0!=~~ANYTHING\]

You guys are trying to tell me that Idk the definition when I do....

Answer 20

@ next to the 3 is a typo...

Answer 21

What if
3! = 1*3*2*1
2! = 1*2*1
1! = 1*1
0! = 1

Answer 22

btw i'm not "trying to tell you that you don't know the definition"

Again though, how else do you find 10P10 \[\frac{ 10! }{ (10-10)!} = \frac{ 10! }{ 0! }\]

Answer 23

or nPn, \[\Large _{n} P _{n} = \frac{ n! }{ (n-n)! } = \frac{ n! }{ 0!} = ???\]

Answer 24

by definition 0! = 1
that is all that you need for now

Answer 25

Unless 0! is 1, how do you solve n!/0! ?There are a countable number of ways to order a set of objects, there isn't just any number of ways.

Answer 26

if you accept that x/0 is undefined and 0/0 indeterminate

Answer 27

then you should also accept that 0! = 1

Answer 28

^exactly.

Why is 2 greater than 1? Because the number line was defined that way.