/sci/ - 0! = 1 — World4ch

Name: Anonymous 2007-11-23 4:04

Prove me wrong.

Name: Anonymous 2007-11-23 6:44

Γ(x) = ∫_{0}^{infty} {t^(x-1)e^-t}dt = (x-1)! When x is a positive integer *cough*.

Therefore:

0! = Γ(1) = ∫_{0}^{infty} {e^-t}dt = [-e^-t]_{0}^{infty} = 1

OH WAIT.

Name: Anonymous 2007-11-23 14:29

0 != 1

prove me wrong

Name: Anonymous 2007-11-23 15:30

I do believe that the thread title and >>3 are both correct.

Name: RedCream 2007-11-23 15:58

So, if I say "0!=1", then I enter a state of quantum uncertainly where my statement is both correct and incorrect?

Observation and logic are not enough to collapse that function. So, what will?

Name: Anonymous 2007-11-23 16:39

0! is 1 by convention.

Name: Anonymous 2007-11-23 16:50

>>6
you mean by definition

Name: Anonymous 2007-11-23 17:00

0! = 1 is nice for:
-Binomial coefficients
-Power series
-Gamma function

Name: Anonymous 2007-11-23 20:10

>>7
There really isn't much of a difference between the two.

Name: Anonymous 2007-11-23 20:41

I can prove you wrong:

I can form the trivial field where:
There is a single element, 0=1
Where:
The 0 forms the single element group under multiplication
Where:
The 1 forms the single element group under addition
Thus:
The distributive law holds
Thus:
It is a field.

Therefore, 0=1, by the construction of this field.

Name: Anonymous 2007-11-23 20:50

>>9
except the meanings of the words and consequently the idea expressed in using one rather than the other, i suppose.

Name: Anonymous 2007-11-24 2:39

>>10

By definition, a field has a 0 and a 1 with 0 =/= 1. So the smallest field is of two elements, like Z/2Z.

Name: Anonymous 2007-11-24 3:54

Ok so 0!=1 is right in two ways, 0 does not equal 1, and 0 factorial is one, by definition

Name: Anonymous 2007-11-24 3:59

oh good lord

Name: Anonymous 2007-11-24 13:11

15 replies -_-

Name: Anonymous 2007-11-25 3:56

>>5
A whitespace.

Name: Anonymous 2008-09-08 6:19

0!!!!!! = 1!!!!!!

0! = 1

1 Name: Anonymous 2007-11-23 4:04

2 Name: Anonymous 2007-11-23 6:44

3 Name: Anonymous 2007-11-23 14:29

4 Name: Anonymous 2007-11-23 15:30

5 Name: RedCream 2007-11-23 15:58

6 Name: Anonymous 2007-11-23 16:39

7 Name: Anonymous 2007-11-23 16:50

8 Name: Anonymous 2007-11-23 17:00

9 Name: Anonymous 2007-11-23 20:10

10 Name: Anonymous 2007-11-23 20:41

11 Name: Anonymous 2007-11-23 20:50

12 Name: Anonymous 2007-11-24 2:39

13 Name: Anonymous 2007-11-24 3:54

14 Name: Anonymous 2007-11-24 3:59

15 Name: Anonymous 2007-11-24 13:11

16 Name: Anonymous 2007-11-25 3:56

17 Name: Anonymous 2008-09-08 6:19