Quote:Original post by gumpy macdrunken
64 = 65
Everybody knows that one. There's a hole between the "triangles" in the second figure that adds up to exactly one square.
which is your favourite equation?
Everybody knows that one. There's a hole between the "triangles" in the second figure that adds up to exactly one square.
Quote:Original post by ChurchSkiz
Not sure if someone listed this, didn't feel like reading through 4 pages of equations.
Girls Require Time and Money
Girls = Time*Money
Time is money
Time=Money
Girls = Money^2
Money is the root of all evil
Money=sqrt(evil)
Girls=sqrt(evil)^2
Girls=EVIL!
Someone already said that, with a picture, no less. The main problem is that requiring isn't the same thing as equalling. It also misquotes the Book of Timothy, a closer translation is:
"x Î Evil . love(money) = √x
I like Newton's Law of Universal Gravitation, mostly because it's of the same form as Coulomb's law, and they both work, I just think that's pretty amazing.
Quote:Original post by agi_shiQuote:Original post by jfclavetteQuote:Original post by etothex
wow, a bug in google? horrible and amazing...
I mean google is really good - but can they really redefine mathematics??
0^0 has three correct answers, depending on how a grumpy mathematician feels a certain day: 'indeterminate', 'undefined' and '1'. So Google is [at least partially] correct.
Wow. C++ and C told me it's 0 :).
Did you use the ^ operator? In C++, ^ is the XOR operator not the exponentiation operator, so 0^0 in C++ does not mean 00.
Quote:Original post by EnselicQuote:A simple counterexample is the principle argument function on the complex plane. This function does not tend to a limit at any point on the negative real axis, but it is most certainly defined there.
I am probably confused here as I am used to swedish mathematical terms, but if you refer to the 'angle' function arg z, then arg z = π for all numbers on the negative real axis.
Depends on which argument function we are talking about. Does yours have the same limit if you approach the axis in a clockwise fashion?
Quote:Original post by NotAnAnonymousPosterQuote:Original post by etothexI am puzzled by how many people use this argument, and it makes me wonder how they were taught maths. What you are saying here is that every function must tend to a limit on its domain, but this is not true at all. A simple counterexample is the principle argument function on the complex plane. This function does not tend to a limit at any point on the negative real axis, but it is most certainly defined there.
I suppose so - if you had to pin me down to a value 1 is a good assumption. After all, it fits the pattern x^0 = 1 and also works in other cases like the binomial theorem. So google squeaks by on this one :)
But mathematically, it really is indeterminant - for the function f(x,y) = x^y, the limit clearly does not exist approaching (0,0) and you can't magically make it so by adopting a convention.
So basically you're saying that a function doesn't have to be continuous, or have double-sided limits, etc. That's like the first week of calculus class. I don't need people trolling about how I learned math, thank you.
I just gave an example of why 0^0 should be indeterminant, not a proof that it is. For a function as important as x^y, magically introducing a definition for (x,y)=(0,0), would imply discontinuity in the otherwise continuous and differentiable constant function f(x)=0^x, which is not really good at all. For the principal argument function, it's business as normal - for the power function, it doesn't fit the pattern.
Quote:Original post by SnailyQuote:Original post by EnselicQuote:A simple counterexample is the principle argument function on the complex plane. This function does not tend to a limit at any point on the negative real axis, but it is most certainly defined there.
I am probably confused here as I am used to swedish mathematical terms, but if you refer to the 'angle' function arg z, then arg z = π for all numbers on the negative real axis.
Depends on which argument function we are talking about. Does yours have the same limit if you approach the axis in a clockwise fashion?
The arg I am talking about is even continous on the negative real axis, so it is probably not the argument function he meant. I meant the complex argument function.
Quote:Original post by jperalta
The Riemann Zeta Function.
Oh, and what does that is useful for? :)
EDIT: Heh, I remember now.
[Edited by - owl on March 5, 2006 3:52:42 AM]
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