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Comments:
<0> I guess it is 1
<1> No mbot, apparently.
<0> I was thinking of something else no doubt
<2> |Steve|: thread killed
<1> odd
<3> :)
<4> Wikipedia has had an influx of idiots on the 0^0 issue
<4> oh
<5> ok, so what's the math god's final word on 0^0
<5> i'm just a physicist
<4> 0^0 = 1
<1> Knuth said 1.
<4> Well, the real final word is that definitions are arbitrary
<4> but there's basically no advantage to leaving it undefined
<4> as long as you're not afraid of a function which is discontinuous at one point
<6> 0^0 can be anything you want. you can define it as "mom's apple pie" if you care to.
<4> leaving it undefined prevents it from being discontinuous, but only because it wouldn't be defined there
<6> you can define 1+1=the cutest kitten ever if you want
<7> hey guys
<4> All of mathematics is an arbitrary collection of formal constructions which we as humans find pleasant.
<1> Or useful.
<4> or useful sure
<7> (A-B)^2 = A^2 + B^2 - 2AB
<7> right?
<4> yep
<5> seriously, what happened to the 0^0 wikipedia entry, even it's history log is gone
<5> it had a nice summary of things
<8> they cracked down on that hard
<4> simu00: idiots :)
<5> I can't find the corresponding page on mathworld. Help?
<4> also, linking 0^0 to indeterminate form is misleading
<1> What do you need to know?
<5> just curious about it
<5> cale, why do you say that?
<4> whether something is an indeterminate form has nothing at all to do if whether it's defined
<4> or what it's defined as
<9> this again?
<4> Basically, indeterminate forms are just a handy way to remember the points at which functions are discontinuous.
<9> if i had a dollar for every time...
<6> you can define 0^0=1 if you want. or 4. or the ascii string "peter piper picked a peck of peppers" interpreted as an integer mod 257
<4> http://en.wikipedia.org/wiki/Exponentiation#Zero_to_the_zero_power
<1> dysprosia: You'd have about $15 from this channel.
<9> steve: oh no, i'm guessing it'd go into the hundreds of dollars
<9> which would be handy
<1> heh
<5> thanks cale
<4> Basically, there are lots of good reasons for defining it to be 1, and any reasons not to define it are really pretty weak
<1> Or to define it as 0.
<8> Am I correct in ***uming that 0^-1 is not 1/0
<4> 0^(-1) is undefined
<8> so is 1/0
<4> and so is 1/0
<8> thus I am asking the question
<4> 0^0 however, is usually defined as 1
<6> cale: or undefined, that's about equally common
<4> not as common
<8> true or false, 0^-1 = 1/0
<6> microacg: false, it's undefined
<5> speaking of other things, what's the name of the statistcs techniques used to untangle confounding variables?
<9> does equality make sense with undefined forms?
<8> ok
<4> microacg: neither of the sides of that equation have any meaning
<5> i simple forgot the terms so I can't google them
<4> (normally)
<8> Cale I doubt they have 'no' meaning
<8> but their meaning is probably limited
<8> compared to normal numbers
<9> if you have a rewriting system set up to emulate the transformation rules of arithmetic, you could transform either side to the other
<4> You're not technically allowed to write them down.
<4> You can of course define them in some new system
<8> lol
<8> you can write them down
<8> but I know what you mean
<1> What about that guy who decided that it had meaning?
<8> it's like saying x=infinity
<8> bad form
<4> Well, they can't occur as part of some proof.
<5> well, when I write them on the board, I quickly erase them before a mathematican walks by
<1> nulity or something.
<8> Cale, lim x->inf of x
<8> isn't that the same as 1/0 in some sense
<6> dysprosia: no, undefined is undefined. there is a whole there.
<8> if you think approaches anyway
<6> hole
<4> Sure, there are systems like that Anderson guy's which define 0^(-1) and 1/0, but they lose lots of the other properties we expect numbers to have.
<4> microacg: but that limit doesn't exist :)
<8> yeah usually when you are creative you just lose the ability to do math
<5> is that the britton school teacher, anderson?
<8> Cale, we often call it 'infinity'
<4> Well, no, you can be creative -- you just have to be careful about the way you state your creations.
<4> It's perfectly okay to say "I'm creating a new system called the projectively extended real numbers, where 1/0 will be defined."
<4> But if you're talking about real numbers, 0 is not invertible
<4> There's no real number corresponding to the expression 1/0.
<4> (Nor is there a complex number)
<6> cale: unless you want to define 1/0=17
<4> In general, in any field, 0 is not invertible, but every other number is.
<4> Once you define the inverse of 0, you no longer have a field.
<6> cale: true, but if you give that all up, distributive, invertable, etc., you can define 1/0=17
<4> And if you don't give it all up, well...
<4> You end up being able to prove that all your numbers are equal :)
<7> hey guys
<4> that is, you're in the trivial ring
<7> how do i integrate 1/(1-T^2)
<6> cale: don't mean to beat a dead horse but it's all just definitions. you want to define 0/0=1 or something that's fine, 0^0=1 is fine too. math is just defs and consequences
<4> Fields generally specifically exclude the possibility that 0 = 1 though
<9> trwbw: what i said makes sense
<4> so the trivial ring isn't counted as a field
<4> TRWBW: I agree with you
<4> TRWBW: I'm just saying that when you do that, it's much better style if you give your object a new name
<4> That way, people know that you're not talking about any usual system of numbers.
<6> cale: sure, or at least be clear
<4> right
<7> how do i integrate 1/(1-T^2)
<4> % Integrate[1/(1-t^2), t]
<4> that might not work
<7> ?
<9> is mbot dead again?
<9> yep
<4> yes, it tends to die when someone makes a request while my machine is at 100% CPU usage
<1> % Integrate[1/(1-t^2), t]
<2> |Steve|: -Log[-1 + t]/2 + Log[1 + t]/2
<9> ahh
<4> I should fix that
<9> so that's why it keeps dying
<9> yeah
<10> does anyone have any resources for learning about procedually generated content, such as roads?
<7> humm
<7> thats all fine and dandy
<7> but id like to know the thinking behind that
<9> % Integrate[1/(1-t^2), t] // Simplify
<2> dysprosia: (-Log[-1 + t] + Log[1 + t])/2
<9> oh whoops, i misread
<7> how do i get to that result?
<4> mm, looks like substitution to me
<4> log is the integral of 1/t
<4> so it's quite likely that this is the result of substituting u = 1 - t^2
<7> meh
<4> Symbolic integrals are a pain. I'm really glad that I was only ever forced to do 8 of them in undergrad :)
<7> hmm
<7> my pen tastes funny
<1> ...
<7> how do I integrate xsqrt((X-1)/(X+1))
<7> X*sqrt
<4> ouch, that's a painful one
<4> looks like trig substitution
<8> there should be a 'tricky integral' field of mathematics that only specialists go into, and then they charge money to do the integrals for physicists and other people
<9> well, there's compooters to do that sort of thing now
<7> meh
<6> cale: can you make mbot check its load and say "I'm busy, work it out of your butt with a pencil."
<4> hehe
<7> i need food
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