They Would Never Say That!

[squidbob]

:lol: what does MEOW mean?

:lol: the circumfrence of the radiator of a peice of hair are maunually morphed together giving the birth of life and its many mysteries which is the meaning of life (2nd to expensive gas prices) which is congruent to squidward's nose's diameter and how tall plankton is in cm times 4000 and the sqaure root of barnacle boy's cranium and the width of my TV - the number of times squidward says yes when we ask him to go jellyfising with us compared to the circumfrence of the radiator of a peice of hair are maunually morphed together giving the birth of life and its many mysteries which is the meaning of life (2nd to expensive gas prices) which is congruent to squidward's nose's diameter and how tall plankton is in cm times 4000 and the sqaure root of barnacle boy's cranium and the width of my TV - the number of times squidward says yes when we ask him to go jellyfising with us compared to the circumfrence of the radiator of a peice of hair are maunually morphed together giving the birth of life and its many mysteries which is the meaning of life (2nd to expensive gas prices) which is congruent to squidward's nose's diameter and how tall plankton is in cm times 4000 and the sqaure root of barnacle boy's cranium and the width of my TV - the number of times squidward says yes when we ask him to go jellyfising with us compared to the circumfrence of the radiator of a peice of hair are maunually morphed together giving the birth of life and its many mysteries which is the meaning of life (2nd to expensive gas prices) which is congruent to squidward's nose's diameter and how tall plankton is in cm times 4000 and the sqaure root of barnacle boy's cranium and the width of my TV - the number of times squidward says yes when we ask him to go jellyfising with us compared to etc...

larry: HELLO WORLD I'M A WEAKLING! ANYONE WANNA FEEL MY PUNY ARMS?

 

[sp0ngyb0b23]

:krabsx: I wanna give all of my money to people in Bikini Bottom.
:squidx: Spongebob, you're my best friend!

 

[revolution]

:patx: : According to some Calculus textbooks, 0^0 is an "indeterminate form." What mathematicians mean by "indeterminate form" is that in some cases we think about it as having one value, and in other cases we think about it as having another.

When evaluating a limit of the form 0^0, you need to know that limits of that form are "indeterminate forms," and that you need to use a special technique such as L'Hopital's rule to evaluate them. For instance, when evaluating the limit Sin[x]^x (which is 1 as x goes to 0), we say it is equal to x^x (since Sin[x] and x go to 0 at the same rate, i.e. limit as x->0 of Sin[x]/x is 1). Then we can see from the graph of x^x that its limit is 1.

Other than the times when we want it to be indeterminate, 0^0 = 1 seems to be the most useful choice for 0^0 . This convention allows us to extend definitions in different areas of mathematics that would otherwise require treating 0 as a special case. Notice that 0^0 is a discontinuity of the function f(x,y) = x^y, because no matter what number you assign to 0^0, you can't make x^y continuous at (0,0), since the limit along the line x=0 is 0, and the limit along the line y=0 is 1.

This means that depending on the context where 0^0 occurs, you might wish to substitute it with 1, indeterminate or undefined/nonexistent.

Some people feel that giving a value to a function with an essential discontinuity at a point, such as x^y at (0,0), is an inelegant patch and should not be done. Others point out correctly that in mathematics, usefulness and consistency are very important, and that under these parameters 0^0 = 1 is the natural choice.

The following is a list of reasons why 0^0 should be 1.

Rotando & Korn show that if f and g are real functions that vanish at the origin and are analytic at 0 (infinitely differentiable is not sufficient), then f(x)^g(x) approaches 1 as x approaches 0 from the right.

Some textbooks leave the quantity 0^0 undefined, because the functions 0^x and x^0 have different limiting values when x decreases to 0. But this is a mistake. We must define x^0=1 for all x , if the binomial theorem is to be valid when x=0 , y=0 , and/or x=-y . The theorem is too important to be arbitrarily restricted! By contrast, the function 0^x is quite unimportant.

As a rule of thumb, one can say that 0^0 = 1 , but 0.0^(0.0) is undefined, meaning that when approaching from a different direction there is no clearly predetermined value to assign to 0.0^(0.0) ; but Kahan has argued that 0.0^(0.0) should be 1, because if f(x), g(x) --> 0 as x approaches some limit, and f(x) and g(x) are analytic functions, then f(x)^g(x) --> 1 .

The discussion of 0^0 is very old. Euler argues for 0^0 = 1 since a^0 = 1 for a not equal to 0 . The controversy raged throughout the nineteenth century, but was mainly conducted in the pages of the lesser journals: Grunert's Archiv and Schlomilch's Zeitshrift. Consensus has recently been built around setting the value of 0^0 = 1 .

:P : I love MR. Krabs!

:krabsx: : Money is crap!

 

[Band Geek]

:gary: Bite me!!
:scooter: Lordy Lordy, I do declare this so-called "coral" craze is making me dizzier than seven tipsy kittens in a fully-functioning tumbledrier set to Fastest Spin Ever.
You're all talk no action.
:squidx: I'd gladly work for free; I just love this job so much!

(That last one was from a fan-fic, by the way, so thanks to the author of Gary's Opposite Adventure.)

 

[Stinkoman 20X6]

;) Ah, I love being cashier.

Squillium: Wow, Squidward! I'll never be quite as good as you! Ever!

:scooter: (with chainsaw) DIE GOO LAGOON!!!

:sbx: Waaaaaaaaa!!!! I hate being fry cook!!!!

:squidx: Yuck, I hate Krabby Patties!

:gary: Hey, SpongeBob! Plankton's not evil, he's just misunderstood.

:patx: What's this best friend thing?

:P CAN'T BREATHE!!!! NEED...WATER!!!

:gary: (with chainsaw) DIE SPONGEBOB!!!!

:P (with chainsaw) DIE MONEY!!!

:sbx: (with chainsaw) DIE PATRICK!!!!

(with chainsaw) DIE KING JELLYFISH!!!!

 

[Band Geek]

Dude, what's with all the chainsaws?


OK, he would say that.

 

[maxmyles]

Someone else knows the word Pneumonoultramicroscopicsilicovolcanoconiosis besides me! Wow.

 

[no username.]

:patx: To find the sine of a cosine of a tangent in a circle with the circumpherence of 6 and an unknown radius...oh no! my brain turned off again.

 

[Mr. Fittz]

Mr. Krabs: Money brings me nothing but pain and misery.

Patrick: 22/7 = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196
4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273
7245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094
3305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912
9833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132
0005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235
4201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859
5024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303
5982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989
3809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151

 

[no username.]

Patrick: 22/7 = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196
4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273
7245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094
3305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912
9833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132
0005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235
4201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859
5024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303
5982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989
3809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151

BWAHAHAHHAHAHAHAHA!

:sbx: : Yay! Guess what, Patrick?

:patx: : what?

:sbx: : I got my P.hD. in Bio Chemestry today!

:patx: : HOLY! MY EYES!

 

[Band Geek]

Hey, you guys should read the fan-fic that Douglas12 just did based on this topic. It's pretty good.

 

[SBRoxMan]

:sbx: I don't want to go to the Krusty Krab today!
:sbx: I'd rather work for Plankton than Mr. Krabs!
:squidx: You're my best friend SpongeBob!
:jellyfish: Money is so horrible!
:squidx: Free money for everybody!
:patx: I don't feel like sleeping or eating!
:patx: I think I'll do some running today!
:squidx: I hate Texas!

 

[Mystery]

Hey, you guys should read the fan-fic that Douglas12 just did based on this topic. It's pretty good.

Yay! I actually have a fanfic based on a topic I made!

:patx: : *sophisicated voice* I am going to say correct punctuation and spelling, I will not use these so called "slang" words. What, I am not whom who should be saying this? *dude voice* Shaw, dude. Who's up for some of that pizza?

:patx: : *sohpisticated voice* I am going to say correct punctuation and spelling, I will not use these so called "slang" words.

:krabsx: and Pearl: Boys Who Cry? What's that stupid band?

:sbx: :
(He ain't saying anything )

 

[Stinkoman 20X6]

:P Pearl, you haven't asked for enough expensive birthday presents!

 

[Band Geek]

:P And exactly why do I work here?!

 

[Smitty Werben Man Jensen]

:) I am closing the Krusty Krab...
:squidx: No!
:sbx: Yes! Finally! I will use this to rule the world! MUAHAHAHAHAHAHAHAHAHAHAHA!

 

[SBRoxMan]

:sbx: I hate jellyfishing! Why can't I do anything fun, like play the clarinet?
:squidx: Can I work 24 hours tomorrow?
:patx: 1+1=2

 

[patrickbob green pants]

:squidx: : Woof!

:patx: : good Day!

 

[Band Geek]

:squidx: *sigh* I'm in love...

 

[Singapore Resident]

:( Hi Patrick. I said hi to Flats the flounder 364,635,471,893,573,980 times today.It's a record!Oh yes, remind me to kick his butt later today.

I'm ready!I'm ready!I'm ready!