[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 80 KB, 1024x768, Dwight-the-office-420011_1024_768.jpg [View same] [iqdb] [saucenao] [google]
6066769 No.6066769[DELETED]  [Reply] [Original]

i = (-1)^.5
(-1)^.5 doesn't exist because there is no x that x*x = a negative number
why don't we do something similar for dividing by zero?
e.g k=1/0

>> No.6066818

http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml

https://en.wikinews.org/wiki/British_computer_scientist%27s_new_%22nullity%22_idea_provokes_reaction_from_mathematicians

>> No.6066830

>>6066769
you have to show that it's well-defined, which happens to be impossible

>> No.6066846

>>6066769
what would that solve?
besides, a number divided by zero IS undefined, how many times does zero go into one?

>> No.6066951

>>6066769

The problem is that the algebra would end up being either inconsistent or too complicated.

For example, if:

k = 1/0

then you've got to decide what 2/0 is. Some reasonable choices are:

k = 2/0

or

2k = 2/0

The first one is going to lead to inconsistencies when 1/0 = 2/0 and you multiply both sides by 0 and cancel out.

The second one requires you to define the relationship between k and 2k. Are they the same number? If so, you're back to the problem in the previous paragraph. If not, then you've got to define how 2k is different from k. Then you'll end up with 3k, 4k, etc., and things will get a lot more complicated.

Inevitably, you'll end up with some over-complicated stuff that doesn't really end up being a useful tool for solving problems.

>> No.6067337

>>6066830
>which happens to be impossible
Wrong.

>> No.6067342

>>6066818
>https://en.wikinews.org/wiki/British_computer_scientist%27s_new_%22nullity%22_idea_provokes_reaction_from_mathematicians
Oh man I remember I mailed that dude when I was 15, I removed some stuff from his algebra because it was redundant.

He was kind enough to answer me back.

>> No.6067345

I never liked defining as sqrt(-1)

i^2 = -1 always looked much better to me

>> No.6067372

>>6067345
>any of those
>definitions
what a fag

>> No.6067373

>>6066818
>https://en.wikinews.org/wiki/British_computer_scientist%27s_new_%22nullity%22_idea_provokes_reaction_from_mathematicians
Is this supposed to be a joke?
It's like a pleb version of nonstandard analysis.

>> No.6067385

>>6067372

i^2 = -1

is, as far as I know, the definition of i. Got a better one?

sqrt(-1) = i

won't work, because anyone on this board can tell you that sqrt is a multivalued function

>> No.6067389

Michael Studencki has solved it

http://science.mistu.info/Math/Numbers/Creative_numbers_and_division_by_zero.html

>> No.6067408
File: 28 KB, 500x318, 1373006145510.jpg [View same] [iqdb] [saucenao] [google]
6067408

>>6067389

>> No.6067819

>>6067385
>is, as far as I know, the definition of i.
It's because you're still in HS.

One POSSIBLE formal definition :
working in R^2
define +' as
(a,b)+'(c,d)=(a+a',b+b') (+ is the usual + of R)
(a,b)*'(c,d)=(a*b-c*d,a*d+b*c) (*,+,- are the usual +,- of R)

You can easily prove that (R,+',*') is a field (and other properties).
definition of i : (0,1)

then you can show that it is consistent and useful to write and use
(a,b)='a+ib
i^2=-1 (cause (0,1)*'(0,1)=(-1,0)='-1)

as you do.

>> No.6069528

>>6067819
>consistent
"Imaginary" fairy tales are always inconsistent.

>> No.6069766

>>6069528
:) "consistent" has to bee understood according to its formal logic meaning, not to its english common one.

>>6067819
Doing this, it's just playing with symbols and rules I choose. I don't say "uuuuhh look, a^2<0 is possible". What bothers you ?


Also, small mistake
(a,b)+'(c,d)=(a+a',b+b')
--> (a,b)+'(c,d)=(a+c,b+d)
of course