Question

!Derangement¡

Answer 1

⁄irrationality°

Answer 2

\[!x=x¡\]\[\quad=\quad?\]

Answer 3

can someone please explain the concept of Derangement

Answer 4

*

Answer 5

What does that "*" mean? @mukushla

Answer 6

lol...it means i have no information on this topic...and i'll wait for the others posts

Answer 7

Oh, okay... we never see that star :P

Answer 8

\[!n=(n-1)(!(n-1)+!(n-2))\]

or something

Answer 9

Unkle i didnt knew it until u mentioned.. this is interesting
http://en.wikipedia.org/wiki/Derangement

Answer 10

A permutation of elements such that none are in their original position. What exactly do you want to know?

Answer 11

suppose u have 4 letters and 4 corresponding envelopes then the arrangement in which none of the letters go to the correct envelope is an example of dearrangement

Answer 12

say letter no. can only go into envelope numbered say (2,3,4)
i.e for letter numbered 1 u have three choices
and now say for example say No.1 goes in Env no.2
then for letter no. 2 there are again 3 ,say for eg letter no.2 goes in 4
then for letter no. 3 there is only 1 choice that is envelope no.1 and thus for letter no 4 thers is only one choice that is 3
hus the total number of deaarngements here is 3X3X1X1=9

Answer 13

can i write a derangement in a more simple way

Answer 14

*
good to know :)

Answer 15

*
me too;)

Answer 16

equals to ln(-1) !!!!

Answer 17

@SNSDYoona can you explain that a little?

Answer 18

cause a complex number z = cos x + i sin x
Provided we can differentiate complex numbers, this would seem resonable,
\[\frac{ dz}{ dx } = - \sin x + i \cos x\]
\[= i^2 \sin x + \cos x\]
=\[i( \cos x + i \sin x)\]
\[= iz\]

and when we differentiate exponential functions we get,

\[\frac{ d }{ dx } {e}^(kx) = ke^(kx) \] <<< its e to the power of (kx)

This suggests that cos x + i sin x = e^(ix)

The exponential form of complex number therefore is re^(ix) where r is radius

cis x = e^(ix)
when x = pi
cos pi + i sin pi = e^(ipi)
cos of pi = -1 therefore...
-1 = e^(ipi)
and if we take the natural logs off both side we get
(ln-1) = ipi