Ryee

Too long, didn't read.

To pick up where Gynis left off: "...who's carrying whom*" Also, I find this whole Bentley and Ghost marriage quite scandalous. We told you straighties--hang around us long enough, and you're going to catch it.

A lot of these differences came about in the "Great Vowel Shift", a phenomenon that began during the 1500s as Middle English began it's evolution to Modern English. In Middle English, there were around 15 unique vowel sounds (not letters), whereas today Modern English has only about 11. Some of the sounds we lost merged into others, while some became diphthongs, and Modern English completely lost some original sounds. Middle English was the last form of english where vowels were "pronounced how they looked", like Latin for example. Consider the following 15 words; Time, See , East, Name, Day, House, Moon, Stone, Know, Law, Knew, Dew, That, Fox, Cut In Middle English, each of these words had a unique vowel sound. However in Modern English, we have merged see and east, name and day, stone and know, and knew and dew. In Shakespeare and Chaucer's time, the words food, good, and blood all had the same long vowel (u)--that is, they all rhymed with the way we say food today. In The Taming of the Shrew, shrew rhymed with woe. So the answer to your question is, English sucks, and is one of the most arbitrary languages in existence--seriously.

meh they are the same, but im jsut bored and forum trolling i agree that conditionally convergent series can be manipulated to equal whatever you want, and that you cant prove results like 0=1 based on it...it was just some silly math "joke" i still

I dispute your response. 1) The set of integers Z is a ring. That is, (Z, +), together with the binary operation * (multiplication) maintains the following 3 properties: i) a * (b * c) = (a * b) * c ii) a * (b + c) = (a * b) + (a * c) iii) (a + b) * c = (a * c) + (b * c) As such, it is easy to show that any ring (e. g. (Z, +, *)) is an abelian group with respect to addition. A group G is said to be abelian w.r.t. addition if for elements x, y in G, x + y = y + x. So having established that the set of integers maintains the commutative property of addition, there is an easy argument (not referenced due to lack of notation on this board) that shows that all subgroups of abelian groups are also abelian. So, the set {-1, 1}, being a subset of Z, also maintains the commutative property. In terms of adding these two elements ad infinitum, the associative law is never an issue in terms of the grouping in the original post. Any two elements may be transposed at any time thanks to the abelian nature of the set, and therefore there is no falsity in the above argument. What is interesting, however, is that there is a whole school of thought that deals with alternating series (which is what is given) that converge based on commutativity or lack thereof. For example, the original sum is not always convergent to the same value depending on grouping. 1 - 1 + 1 - 1 + 1...etc can be rewritten (thanks to commutativity) as 1 + 1 - 1 + 1 - 1 (transposing the order of every pair of elements excluding the first entry) and can be subsequently grouped as (1 + 1) - 1 + 1 - 1...which = 2 if taken infinitely often. As an aside, there is no way to write the sum of -1s and 1s using only commutativity which does not produce a convergent series. That is; lim n-->infinity from 0 to infinity of (-1)^n is a conditionally convergent series, it just turns out that the value the series converges to varies depending on the grouping of the terms. In conclusion, this is not an associative argument, nor two different series. hurray math

Consider the infinite sum of 1s and -1s; that is, 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1.......forever and ever. If you group the terms in pairs, you get (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) ..........forever and ever...which is really just 0 + 0 + 0 + 0............=0 On the other hand...if you group the terms as follows: 1 + (-1 + 1) + (-1 + 1) + (-1 + 1).........thats just 1 + 0 + 0 + 0 + 0.................=1 0=1?!?!?!?!?! THE END OF THE WORLD HAS BEGUN!

lawl what does it say?

omg XD i didnt know i had a birthday post :feels the love: thanks! i r 22 now its not a very interesting birthday

zomg good times to be had...they finished maintenance a whole...9 hours early!

Driveway[Heavy]1016-50-1 This is how I will be spending my time off from WoW....omg everyone play FFR! FlashFlashRevolution

i like the before picture of joesf the best personally.... /hides

i think ill be driving down sometime friday (hopefully sometime before it becomes rush hour in atl)....i know how to get to ATL alright....but uh after that im a little fuzzy so uh...help? and i will be sleeping in my car as of now which ive done before....anyone got a driveway? omg i dont know anyone

avert your eyes...prepare for blindness... http://www.weblogimages.com/v.p?uid=Ryee&a...;sid=gzX47gHTV8 you were warned