Want a custom title?

[Flamingo]

epic title

[M.rSnow]

What? its not a post there now. [size=0pt]Hehe delete function[/size]

You are sneaky, M.rsnow.

Well its true. Look below my avatar.
Do i have to get a warning to get this off? I guess your plan of punching people that way isn't working in my case.

5. No vulgar, obscene or immature custom titles.
 - No ascii tits/asses/nuts, no insults, etc. Basically anything not safe for work will not be approved, and I'll take it as a request for me to screw with your title as I please.

Leadership rule one. Never break your own rules!
"I'm cheap" is refering to something sexual right?

[Flamingo]

I reserve the right to change these rules at any time, without telling you, and to make up rules as we go along.

[Lapis Lazuli]

Flamingowned, lolz.

[M.rSnow]

Well still. Change them if you want to change them. Your writing a law book whitout pages here.

[Lapis Lazuli]

And?

[mar77a]

The evaluation of 0^0 presents a problem, because different mathematical reasoning leads to different results. The best choice for its value depends on the context. According to Benson (1999), "The choice whether to define 0^0 is based on convenience, not on correctness."[2] There are two principal treatments in practice, one from discrete mathematics and the other from analysis.

In many settings, especially in foundations and combinatorics, 0^0 is defined to be 1. This definition arises in foundational treatments of the natural numbers as finite cardinals, and is useful for shortening combinatorial identities and removing special cases from theorems, as illustrated below. In many other settings, 0^0 is left undefined. In calculus, 0^0 is an indeterminate form, which must be analyzed rather than evaluated. In general, mathematical analysis treats 0^0 as undefined[3] in order that the exponential function be continuous.

Justifications for defining 0^0 = 1 include:

    * When 0^0 is regarded as an empty product of zeros, its value is 1.
    * The combinatorial interpretation of 0^0 is the number of empty tuples of elements from the empty set. There is exactly one empty tuple.
    * Equivalently, the set-theoretic interpretation of 0^0 is the number of functions from the empty set to the empty set. There is exactly one such function, the empty function.
    * It greatly simplifies the theory of polynomials and power series that a constant term can be written ax0 for an arbitrary x. For example:
          o The formula for the coefficients in a product of polynomials would lose much of its simplicity if constant terms had to be treated specially.
          o A power series such as \textstyle e^{x} = \sum_{n=0}^{\infty} \frac{x^n}{n!} is not valid for x = 0 unless 00, which appears in the numerator of the first term of the series, is 1. Otherwise one would need to use the longer identity \textstyle e^{x} = 1 + \sum_{n=1}^{\infty} \frac{x^n}{n!} .
          o The binomial theorem \textstyle(1+x)^n = \sum_{k = 0}^n \binom{n}{k} x^k is not valid for x = 0, unless 0^0 = 1.[4] By defining 0^0 to be 1, a special case of the theorem can be eliminated.
    * In differential calculus, the power rule \frac{d}{dx} x^n = nx^{n-1} is not valid for n=1 at x=0 unless 0^0 = 1. Defining it this way eliminates the need for a special case for the power rule.

In contexts where the exponent may vary continuously, it is generally best to treat 00 as an ill-defined quantity. Justifications for treating it as undefined include:

    * The value 0^0 often arises as the formal limit of exponentiated functions, f(x)g(x), when f(x) and g(x) approach 0 as x approaches a (a constant or infinity). There, 00 suggests [lim f(x)]lim g(x), which is a well defined quantity and is the correct value of lim f(x)g(x) when f and g approach nonzero constants, but is not well defined when f and g approach 0. The same reasoning applies to certain powers involving infinity, \infty^0 and 1^\infty. A more abstract way of saying this is the following: The real function xy of the two nonnegative real variables x and y is not continuous at the point (x, y) = (0, 0), and so 00 is not determined by continuity.[5] That is, the function xy has no continuous extension from the open first quadrant to include the point (0,0).[6] The rule in calculus, that \lim_{x \to a} f(x)^{g(x)} = (\lim_{x \to a} f(x))^{\lim_{x \to a} g(x)} whenever both sides of the equation are defined, would fail if 00 were defined.
    * The function z^z, viewed as a function of a complex number variable z and defined as e^z log z is undefined at z = 0 because log z is undefined at z = 0. Moreover, because zz has a logarithmic branch point at z = 0, it is not common to extend the domain of zz to the origin in this context.[7]

[edit] Treatment in programming languages and calculators

The computer programming languages that evaluate 0^0 to be 1[8] include bc, Haskell, J, Java, MATLAB, ML, Perl, Python, R, Ruby, Scheme, and SQL. In the .NET Framework, the method System.Math.Pow treats 0^0 to be 1. Microsoft Excel issues an error when it evaluates 0^0.

Microsoft Windows' Calculator and Google search when used for its calculator function[9] evaluate 0^0 to 1.

Maple simplifies a^0 to 1 and 0^a to 0, even if no constraints are placed on a, and evaluates 0^0 to 1.

Mathematica simplifies a^0 to 1, even if no constraints are placed on a. It does not simplify 0^a, and it takes 0^0 to be an indeterminate form.

[M.rSnow]

I dont have time to read that. Anyway. When you come to your sences you should remove that title. Untill its gone i have close to no respect for you.

[Lapis Lazuli]

I dont have time to read that. Anyway. When you come to your sences you should remove that title. Untill its gone i have close to no respect for you.

my world is shattered

edit: guess you'll learn to read the entire post and follow instructions properly, then

[gedazz]

Alright! Thanks Lapis Lazuli!

[Mangled*]

Awesome, thanks Lapis Lazuli.

[Rhombus]

Hoping you won't give me anything I don't want, like a headache, I ask you to change my custom title into "Ooh I have a custom title". It's 25 characters exactly. I actually wanted an exclamation mark in the end, but that would be character no. 26, so I'll not ask for that.

And I actually thought moderators would ban people for no reason when they get bored.... This is actually really nice of you.



Edit: I remember why your name rings a big bell in my head.... has the ouden project completely died? I kind of hope not... it looked pretty interesting.

[{LAW} Gamer_2k4]

Send me a PM including the custom title you want

The amount of people here who can't read is truly mind-boggling.

[Rhombus]

Hey I'm just bumping the topic

[M.rSnow]

my world is shattered

Sorry to hear that.

Hey I'm just bumping the topic

It was on the first page..

[Iron Man]

feel free to give me a random one, maybe even related to the movie named after me

[Blue-ninja]

Meh, the rules aren't so hard to follow now that I've been good for some few months, give or take.

Do I want a custom title? Yeah, but I personally don't see any point to it.

Gimme the title "Death Note"

[Iron Man]

yaya, thanks lapis!

[Tactical Sniper]

Thanks for the title Lazuli, new coolest moderator. 

[Demonic]

Tsk, such a cheap way to make your popularity index go wild Lapis. ;o