[2011-May-18] Mathness of 1

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Re: Mathness of 1 [2011-May-18]

by Oldrac the Chitinous » Fri May 20, 2011 3:26 am

Edminster wrote:All money is controlled by the global jewish conspiracy
There you go.

Re: Mathness of 1 [2011-May-18]

by Edminster » Fri May 20, 2011 3:19 am

my money is on the global jewish conspiracy

Re: Mathness of 1 [2011-May-18]

by Apocalyptus » Fri May 20, 2011 2:50 am

But how did you know that, RC? Or are you part of the global Jewish conspiracy too?


edit:Uhh Roman's comment seems to have disappeared, or am I going mad?

Re: Mathness of 1 [2011-May-18]

by DuckReconMajor » Fri May 20, 2011 1:40 am

Here is the question that is the question and that is which one is the guy I guess not the one on the left I think we've seen him before and the one on the right is a chick i think and Darrell is probably not the name of a chick.

Re: Mathness of 1 [2011-May-18]

by Guest » Fri May 20, 2011 1:31 am

At WolframAlpha: http://www.wolframalpha.com/input/?i=e^%28pi%2F2%29+*+i^i

Re: Mathness of 1 [2011-May-18]

by Astrogirl » Thu May 19, 2011 1:15 pm

The clones, the clones are a-coming!

Re: Mathness of 1 [2011-May-18]

by Edminister » Thu May 19, 2011 8:34 am

Guest wrote:
Edminster wrote:So do none of you guys know that if you hover over the red button you get a further comic? Because Zach already knows about this stuff and it makes you look kinda retarded to go over the same material over and over.
Thank you for pointing that out, Edminister. However, that only works if you have javascript enabled. And it is still hidden. Plus, it doesn't really depend on definition, it is undefined, there is no other reasonable mathematical explanation.

The fact that Weiner even has a little thing that requires javascript, without any note specifying so, shows that he sucks at HTML too. Although the 84 errors say the same thing.
I wasn't the one that pointed it out, but thanks for giving me credit?

Re: Mathness of 1 [2011-May-18]

by Felstaff » Thu May 19, 2011 8:28 am

It's against the law for any scientist to be out of their labcoat at any time.

Re: Mathness of 1 [2011-May-18]

by Rileyc » Thu May 19, 2011 3:08 am

Mathematicians are also not allowed to not wear glasses, apparently!

Re: Mathness of 1 [2011-May-18]

by Kimra » Thu May 19, 2011 3:03 am

So, apparently when I look at this tread it just looks like a whole lot of people drawing incomprehensible smiley faces.

Re: Mathness of 1 [2011-May-18]

by Guest » Thu May 19, 2011 2:33 am

Edminster wrote:So do none of you guys know that if you hover over the red button you get a further comic? Because Zach already knows about this stuff and it makes you look kinda retarded to go over the same material over and over.
Thank you for pointing that out, Edminister. However, that only works if you have javascript enabled. And it is still hidden. Plus, it doesn't really depend on definition, it is undefined, there is no other reasonable mathematical explanation.

The fact that Weiner even has a little thing that requires javascript, without any note specifying so, shows that he sucks at HTML too. Although the 84 errors say the same thing.

Re: Mathness of 1 [2011-May-18]

by Guest » Wed May 18, 2011 11:12 pm

You could say e^{\pi/2}i^i is a set valued mapping, so maybe the rightmost mathematician is saying "We're the cardinality of the natural numbers!"

Re: Mathness of 1 [2011-May-18]

by Ben G » Wed May 18, 2011 10:04 pm

Astrogirl wrote:
>
K^2 wrote:
shining2k1 wrote:e^(Pi/2-Pi/2 - 2*Pi*n)=e^(-2Pi*n)=1 for all whole
> numbers n
> e^(-2i*Pi*n) = 1 for all integer n, but what you actually get is only 1 for n=0.
> That doesn't go away on its own, and has to be part of definition of imaginary exponents.
> How does this have to be part of the definition of imaginary exponents? How would
> you decide which n you use? Don't say 0, I could just shift the index.
>

Okay, so a clarification of the ambiguity involved (for anyone who cares):

Euler's formula is that e^(ix) = cosx + isinx (e is Euler's constant, that is 2.71282..., i is the square root of -1 and pi is the ratio of circumference to diameter, that is 3.14159...). This means that e^(2pi*i) = cos(2pi) + isin(2pi) = 1. In fact, we can equivalently state that 1^n = [e^(2*pi*i)]^n = e^(2*pi*i*n).
So, now we have infinitely many ways of expressing any number by multiplying or dividing by 1 as many times as one pleases.
So, for example, "i" can be expressed as e^(pi*i/2), but it can also be expressed as e^(pi*i/2) * 1^n = e^(pi*i/2 + 2*pi*i*n), where n is any integer.
So far so good?
While the exponent of the expression for i has infinitely many potential values (corresponding to the choice of "n") there is only 1 value this expression represents, since we've been multiplying it by powers of 1. However, things change when we take the "i"th power of this expression:

i^i = [e^(pi*i/2 + 2*pi*i*n)] = e^(-pi/2 - 2*pi*n); n is any integer

this expression has infinitely many (non-equal) values, each of which is equally an answer to "what is i^i?" In fact, this is generally true when you take the complex or irrational power of a complex number.
If we were to stick with this convention, however, we would be stuck with a multivalued function, which in the context of practical computation can be unwieldy. So, often a single member from this solution set is chosen, and the one chosen is usually the one for which "n=0," which can mean different things in different contexts. In this context, we state that i^i = e^(-pi/2) is a representative, useful, selection from our solution set.

Re: Mathness of 1 [2011-May-18]

by Roman Cilicia » Wed May 18, 2011 9:08 pm

this is so ghey

what are we, xkcd?

okay, regarding the comic (get it? I was talking about this stupid layout):

this is so gay

what is this, xkcd?

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