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      CommentAuthorCody56
    • CommentTimeApr 26th 2007
     

    Yes, to deceive us!

    •  
      CommentAuthorTrance
    • CommentTimeApr 26th 2007
     

    Paradox!

    •  
      CommentAuthorCody56
    • CommentTimeApr 26th 2007
     

    Or Orthodox, Kyle hasn't said if he is Jewish or not, and if he did I wasn't here.

    •  
      CommentAuthorUdoboy
    • CommentTimeApr 26th 2007
     

    Perhaps Kyle discovered "Hero" and told us it's his side account to throw us off of his REAL side account.

    Ah so, grasshopper.

    •  
      CommentAuthorCody56
    • CommentTimeApr 26th 2007
     

    Who are you calling grasshopper, grasshopper?

    •  
      CommentAuthorhero
    • CommentTimeApr 26th 2007 edited
     

    Haha. Actually, I am a completly different Kyle, from the DC area. I happen to be a born Catholic, but I don't agree with many of the beliefs, not jewish. Also, I am younger than 21, if I am correct on his age.

    • CommentAuthorPanoply
    • CommentTimeApr 26th 2007
     

    Wait, I think I know what should happen, all the Kyle's should go out and have a Kyle party.

    •  
      CommentAuthorcmseagle
    • CommentTimeApr 26th 2007
     
    Posted By: Panoply

    Wait, I think I know what should happen, all the Kyle's should go out and have a Kyle party.

    I believe there was something like that in England, 600 people with the same name showed up (first and last). Can't remember the name itself off the top of my head though.

    •  
      CommentAuthorhero
    • CommentTimeApr 27th 2007
     

    I think when the movie Meet the Fockers came out, they had 25 people who really had the last name Fockers get together for a party.

    •  
      CommentAuthornyarfdude
    • CommentTimeApr 29th 2007
     
    Posted By: hero

    Haha. Actually, I am a completly different Kyle, from the DC area. I happen to be a born Catholic, but I don't agree with many of the beliefs, not jewish. Also, I am younger than 21, if I am correct on his age.

    Sure...

    •  
      CommentAuthorCody56
    • CommentTimeApr 29th 2007
     

    We all know you celebrate Yom Kippur.

  12.  

    "Kyle" is a word in 42 languages, with various meanings, such as "tasty" (Armenian), "swamp grass" (Tahitian), and "fall behind" (Yucatec).

    •  
      CommentAuthorPaulustrious
    • CommentTimeApr 30th 2007 edited
     

    The meaning of Kyle (and everything else) is now much clearer.

  14.  

    Back on topic, try out this one - I haven't figured it out after several attempts. Sure, your calculator will solve it no problem, but my steps on paper often lead to a dead end (embarassing but true). HELP! :confused:

    (e^b) + a = 2
    [e^(1+b)] + a = 6

    (Notes: I used ^ to notate "to the power of". Also, there's 2 variables to solve for.)

    •  
      CommentAuthorPaulustrious
    • CommentTimeMay 15th 2007 edited
     

    a = -0.32790682747730569754000802043605 (ish)
    b = 0.84496950650697250985610788798368 (ish)

    b = ln(4/(e-1))

    And I've been to the kyle of lochalsh

    •  
      CommentAuthorHaoest
    • CommentTimeMay 15th 2007
     

    why not set it up as

    (e^b) + a = [e^(1+b)] +a - 4
    then
    (e^b) = [e^(1+b)]-4
    I am stuck here, lol. Is this any simplier than before?

    •  
      CommentAuthorAthene
    • CommentTimeMay 15th 2007
     

    Well, if you solve for a in each equation, you get

    a= 2 - e^b
    a= 6 - e^(1+b)

    therefore

    2 - e^b = 6-e^(1+b)

    and

    e^(1+b) - e^b = 4

    Does that help somewhat?

  18.  

    Thank you Athene. And carrying on...

    e . e^b - e^b = 4

    e^b . ( e - 1) = 4

    e ^b = 4 / (e - 1)

    b = ln( 4 / (e - 1) )

    • CommentAuthorGandalf9
    • CommentTimeMay 15th 2007
     

    after that, my head hurts. And all I can think of now is how to solve 3 variable equations....

  20.  
    Posted By: Udoboy

    Perhaps Kyle discovered "Hero" and told us it's his side account to throw us off of his REAL side account.

    Ah so, grasshopper.

    Posted By: Cody56

    Who are you calling grasshopper, grasshopper?

    I would have been more offended by being called Ah So!

    •  
      CommentAuthorcritdragon
    • CommentTimeMay 15th 2007
     

    i always thought that because
    0^5 - 0
    0^4 - 0
    0^3 - 0
    0^2 - 0
    0^1 - 0
    0^0 - ? wouldnt that then be 0
    0^-1 - 0
    0^-2 - 0

  22.  

    Thanks all - Palustrious in particular - wonderful people all of you *sniff*

    •  
      CommentAuthorUdoboy
    • CommentTimeMay 15th 2007
     
    Posted By: critdragon

    i always thought that because
    0^5 - 0
    0^4 - 0
    0^3 - 0
    0^2 - 0
    0^1 - 0

    If these are supposed to be "=" instead of "-" then y ou're doing well so far.

    0^0 - ? wouldnt that then be 0

    Not necessarily

    0^-1 - 0
    0^-2 - 0[/p]

    ****ERROR****

    0^(-1) = 1/0; this is undefined.
    0^(-2) = 1/0^2; this is undefined.

    So now it does make sense that 0^0 would be undefined.

    •  
      CommentAuthorcritdragon
    • CommentTimeMay 16th 2007
     

    we had this in a maths lesson in school before and our teacher came to the answer that she didnt know and didnt care.. lol..

    •  
      CommentAuthorPaulustrious
    • CommentTimeMay 16th 2007 edited
     
    Posted By: Udoboy

    So now it does make sense that 0^0 would be undefined

    U is the main man. Correct.

    Though Microsoft's Calculator gives it as 1 I think.

    •  
      CommentAuthorTrance
    • CommentTimeMay 16th 2007
     

    That's because Bill Gates designed it, he can't comprehend the value of "0".

    Hey, what the crap?! Dictionary.com lists my first name next to "Uncomprehend."

    •  
      CommentAuthorjsimpleton
    • CommentTimeMay 16th 2007
     

    0^0 is undefined because of continuity problems. its kinda that simple

    •  
      CommentAuthorcritdragon
    • CommentTimeMay 16th 2007
     
    Posted By: Trance

    That's because Bill Gates designed it, he can't comprehend the value of "0".

    Hey, what the crap?! Dictionary.com lists my first name next to "Uncomprehend."

    he wouldnt have designed it, someone would have designed it for him. and they get paid to give simple answers, not to say that you cant get an answer.

    •  
      CommentAuthorTrance
    • CommentTimeMay 16th 2007
     

    *sighs and averts gaze*

  30.  
    Posted By: jsimpleton

    0^0 is undefined because of continuity problems. its kinda that simple

    Step one way off the tightrope and you fall down. Step the other way and you fall somewhere else. I was fascinated when I first learned of pathological functions. (Mathematical ones that is)

    •  
      CommentAuthorHaoest
    • CommentTimeMay 16th 2007
     
    Posted By: jsimpleton

    0^0 is undefined because of continuity problems. its kinda that simple

    Can you elaborate on that simple thing?

    •  
      CommentAuthorjsimpleton
    • CommentTimeMay 16th 2007
     

    let f(x,y)=x^y

    given y=0 lim x->0+ f(x,0)=1
    given x=0 lim y->0+ f(0,y)=0

    0!=1 so continuity problem. so its undefined

    •  
      CommentAuthorjsimpleton
    • CommentTimeMay 16th 2007
     

    i don't know the formal definition of a patholigical funtion

  34.  

    Neither do I. But within a given range it is definable for all x but differentiable at none.

    •  
      CommentAuthorcritdragon
    • CommentTimeMay 16th 2007
     

    should we just say 0^0=? lol that works

    •  
      CommentAuthorPaulustrious
    • CommentTimeMay 16th 2007 edited
     

    I've been staring sideays at the screen for 10 min trying to understand that smilie. I've got the bearded, screaming surprised snorkeller bit but the question mark is throwing me.

    •  
      CommentAuthorjsimpleton
    • CommentTimeMay 16th 2007
     
    Posted By: Paulustrious

    Neither do I. But within a given range it is definable for all x but differentiable at none.

    so is it like brownian motion?

    •  
      CommentAuthorUdoboy
    • CommentTimeMay 16th 2007
     
    Posted By: Paulustrious

    I've been staring sideays at the screen for 10 min trying to understand that smilie. I've got the screaming surprised snorkeller bit but the question mark is throwing me.

    ellohell

  39.  
    Posted By: jsimpleton
    Posted By: Paulustrious

    Neither do I. But within a given range it is definable for all x but differentiable at none.

    so is it like brownian motion?

    mmm, I've never seen a brownian motion equation. But no. On a position vector / time basis at any time 't' you could not evaluate it, although you may be able to differentiate it. (assuming we are looking at the light particles rather than the molecules in motion.)

    There are an inifnite number of pathological functions, such as the blancmange function. All fractals (I think) are pathological, as are all continually discontinuous functions. You now plumbing the depths of my knowledge. Quite wide, but extremely shallow.

    And you brought up the subject of continuity so don't blame me. I was happy with my tightrope answer.

    •  
      CommentAuthorFact totum
    • CommentTimeMay 17th 2007 edited
     

    This should clear up all your math fuzziness: Ma & Pa Kettle doin' 'rithmatic

    •  
      CommentAuthorjsimpleton
    • CommentTimeMay 17th 2007
     

    i think i understand now. continuous everywhere but not differentiable anywhere.

  42.  

    I still remember feeling of wonder when we derived this equation in class. I was 16 at the time.

    e^( i . π ) = -1

    •  
      CommentAuthorPriya
    • CommentTimeMay 17th 2007
     

    How do you derive that one, Paul?

    •  
      CommentAuthorHaoest
    • CommentTimeMay 17th 2007
     

    He misspelled: i eat pie

    •  
      CommentAuthorPaulustrious
    • CommentTimeMay 18th 2007 edited
     

    It comes from the formula:

    e^(i.Ɵ) = cos(Ɵ) + i.sin(Ɵ)

    and making Ɵ equal to π.

    You can prove it by expanding e, sin and cos as Taylor series (or Maclaurin series, I can never remember which is which) Examples of it are all over the internet. It is called Euler's identity but I don't remember that name from high school.

    And Sinh.Sinh - Cosh.Cosh = 1 was another.

    • CommentAuthorianweller
    • CommentTimeMay 18th 2007
     

    I never understood why 0^0 was undefined. I asked three upper-level math teachers at my school, and none of them knew. So I've recently contacted somebody from a local college. :D

    I'll report answers here, maybe.

    •  
      CommentAuthorHaoest
    • CommentTimeMay 18th 2007
     

    LOL. omg teachers.
    I used to think it's a divine job. I still think it is a divine job, it's just taken by the unmatched people.

  48.  

    JSimpleton's explanation is correct. Take time to understand what he is saying. I'll give a different example. It's not the same thing but it will give you a feel for it. Take the formula 1/x. As x gets smaller and smaller ( 1, .0001, .000000001) the result gets bigger and bigger. 'Eventually' we get an infinite number.

    Mathematically we would be tempted to say:

    Lim(1/x) as x->0 i = ∞

    However if we start from a negative side ( x=-1, x=-.000001) then the limit is minus infinity. Now you may have been told that all infinities are equal, but they are not. We can actually say:

    ∞ ≠ -∞

    So what is 1/x as x->0. Well the answer is 'undefined'. In a sense the question has no meaning, or is unanswerable. There is a point of discontinuity. You cannot draw a line from a-little-bit-to-the-left to a-little-bit-to-the-right'. Some discontinuity points can have defined values, but the two discussed do not.

    I am not sure if that helps. Someone out there in internetsville must have written a better explanation than mine...

    •  
      CommentAuthorPriya
    • CommentTimeMay 18th 2007
     
    Posted By: Paulustrious

    It comes from the formula:

    e^(i.Ɵ) = cos(Ɵ) + i.sin(Ɵ)

    and making Ɵ equal to π.

    You can prove it by expanding e, sin and cos as Taylor series (or Maclaurin series, I can never remember which is which) Examples of it are all over the internet. It is called Euler's identity but I don't remember that name from high school.

    And Sinh.Sinh - Cosh.Cosh = 1 was another.

    Thanks!

    •  
      CommentAuthorjsimpleton
    • CommentTimeMay 18th 2007
     
    Posted By: Haoest

    LOL. omg teachers.
    I used to think it's a divine job. I still think it is a divine job, it's just taken by the unmatched people.

    sounds like you don't like your teachers very much.
    my cousin is becoming a teacher, i think she's going to be good at it. She's very patient.

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