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Comments:
<0> JohnFlux: hmmm now there's an intersting thought
<1> i guess Given's method is an answer
<2> i asked moreon's question internally every thinks its spam :(
<3> zaphyBeeble: hrmm?
<3> azi: your question doesnt make any sense :P If you have an infinite set of random numbers... then what are you doing trying to prove that the sequence is random? You just said it's random :P
<4> moreon: no he said "random"
<4> moreon: meaning he doesn't know
<4> zaphyBeeble: your sentence didn't parse
<2> i said i asked the 4 4s problem internally got bashed up guys said go away and all that :(
<2> they would rather discuss the latest tax savings mechanism and its intricate details, something which a qualified accountant anywas handles for them
<5> consider n people handshaking. Then <handshakes>=n(n-1)/2. I 'd like to correlate the pairs of people handshaking with unique integers (preferably in the range 1 to <COH==count of all handshakes>). I don't necessarilly seek a function, rather an algorithm. I tried y=f(A^n*B), (A must be the smaller), but it does not take into account the double handshakes. Do you propose any reading/etc to get started?
<6> you can map the pairs (i,j) with 1<=i<j<=n to (i-1)*n+j
<4> revil: do they shake their own hands :)
<6> no, otherwise their number wouldn't be n(n-1)/2
<5> JohnFlux, no, neither. My 'formula' does not take into account that either. I think i found a recursive algo. but i want to avoid it. I'm woring on what lieven said now :) heh!
<4> revil: btw i don't think there's really a difference between a function and an algorithm
<0> hmm
<0> can a function modify its parameters in maths?
<4> zaphyBeeble: dude
<4> cast: uh what
<4> cast: all variables are unmodified
<7> cast - the question makes no sense
<4> cast: all variables are unmodifyable
<7> cast - a function f: A -> B is simply a subset of A x B
<5> JohnFlux, well, in a function, some things are impossible. eg. f(a,b) (i think) can't return the smaller of the 2
<4> sure it can#
<4> "let f(a,b) be a function that returns the smaller of the 2"
<4> here you go
<0> so if the variable is an array, surely we could sort it? can a function do an in place sort like that? was kind of what i was thinking about
<4> zaphyBeeble: most of your sentences don't parse
<4> zaphyBeeble: you should work on that ;-)
<7> cast - you're confusing mathematics with programming.
<2> how so? :)
<0> i suppose it doesn't work...translating programming ideas to maths
<4> cast: it does work
<8> :)
<9> DEFINITELY NOT
<9> sheesh
<4> cast: I do it all the time. My first degree was computer science
<4> cast: the mistake is just translating it wrongly
<0> i **** at both math and cs :)
<10> You can have multiple definition of a function based on "guards"
<10> Like |x| = x if x >= 0, -x if x < 0.
<4> that's a single definition
<2> :) or multiple
<10> Hmmm, multiple expressions, ok?
<4> good enough for me
<10> f(a,b) = a if a <= b, b if a > b.
<4> but saying "f(a,b) returns the bigger number" is just as valid a function definition as a more mathematical one
<4> just to be clear on that
<7> you were fine up until you said 'more mathematical'
<4> but saying "f(a,b) returns the bigger number" is just as valid a function definition as a more algebriac one
<10> ``Consider the function f with f(x) = 1 if x is rational and f(x) = 0 if x is irrational.''
<4> xerox: okay done.
<7> the point is: functions can be defined with formulas, but need not be.
<10> Right!
<2> a hash is a function too
<4> xerox: consider that I considered it
<4> it's like at uni when they said that computers can't accurately hold say PI
<4> sure they can "PI" there you go ;-)
<10> f = {(0,1),(1,2),(2,3)} would also work, right? :
<10> :)
<5> ok, I'll have that in mind myself. I should have been more precise with this
<5> zaphyBeeble, a hash can be represented algebraicallythough, can't it? (actually, i am looking for a hash funtion myself. F(a,b) is a hash function))
<5> of ccourse not always..
<2> i dont know revil i always look at "this means this" like oui means yes :)
<2> i am not good with words as johnflux said
<5> lol! he said something about parsing.. We are beyond that. We are humans. I tink he is teasing you :p
<2> dont worry everyone says i always solve the problem backwards
<2> im used to it
<5> lol.. you should take advantage of that. If you work with a person that solves the same problem forwards, you could reach the solution in half the time!
<5> you must be really valuable!
<2> yes but sometimes the other person considers it as egg on his face
<5> :p
<2> its really difficult to be direct and learn, its even more difficult not to be direct and learn because then you take things for granted
<5> ah.. work on that. I can't figure the real matter, since i have not seen you in action. Do you walk on the road backwards?
<5> :p
<7> @quote fear
<11> We were somewhere around Barstow, on the edge of the desert, when the drugs began to take hold.
<2> there is no matter, its like i never dont take dope because i didnt want to, it is just how someone is
<5> that would be my second point. somewhat close to this at least.
<4> revil: I wasn't teasing. i really don't understand most of zaphyBeeble sentences
<4> revil: I can't figure them out. human or not ;-)
<2> nutbot :)
<10> Catfive: :)
<5> i don't know. maybe different educational background. Try talking to a philosopher about chaos with mathematical terms
<2> i want to talk to pythagoras and ask him how he got the triangle thing, and how was he so sure or was it just an observation which we could not fade out over time
<4> zaphyBeeble: The series "The ascent of man" talks about how he came across it
<2> its like saying "you cannot divide 3 by 2" but a few years later "oh yes you can it is 1.5" :)
<4> um, because you can prove it's true?
<5> zaphyBeeble, I can answer you the same question about Archimedes
<4> we will never disprove pythagoras theorem
<2> i agree we never will
<4> pythagoras himself proved it to be true
<2> how did he? no calculus back then. graph paper?
<4> zaphyBeeble: he did it with triangles
<4> zaphyBeeble: you can build a square with triangles
<4> and rearrange them
<4> zaphyBeeble: he proved it geometrically
<2> you can always cut a square and say area is half
<2> but to proove that the diagnol is square.. confuses me
<2> draw 4 squares
<2> :(
<4> http://www.cut-the-knot.org/pythagoras/index.shtml
<4> zaphyBeeble: ^^ lots of different proofs by drawing
<4> zaphyBeeble: #4 is nice
<2> u can do it with squares i know for sure
<4> zaphyBeeble: ah #9 is better
<4> zaphyBeeble: see proof #9
<4> Pythagoras argued that there are three kinds of men. The lowest consists of those who come to buy and sell, and next above them are those who come to compete. Best of all are those who simply come to look on.
<5> I think i found a solution to my problem, yet i haven't proved it correct.
<12> in a way you are right zaphyBeeble since pythagoras theorem depends on space being euclidean
<12> nowadays it is recognised firstly that physical space is not euclidean, and that geometry can be done on noneuclidean space
<5> but in macro physics it is.
<12> so it kind of has already 'faded out over time'
<5> or however normal phusics is called..
<2> johnflux those who come to buy and sell are sometimes constrained because that is the only way to "look on"
<12> hey _llll_
<13> hello
<12> we were just discussing how a functor is different from an arrow
<7> it's like an arrow, but thicker
<13> a functor is an arrow
<13> in the category Cat
<10> I.e. functors are arrows in the category of categories?
<13> yes
<10> Interesting.
<10> Monads have a description as simple as this one?
<7> (strictly speaking Cat is the category of small categories)
<13> yes, a monad is a monoid in a functor category [C,C]
<10> I am not sure about what is a functor category.
<13> or a monad is a lax bifunctor from the terminal bicategory to the 2-category Cat
<10> OK no idea whatsoever.
<2> umm johnflux what is so obvious about the pythogora's theorem in the figure?
<13> if C and D are categories, we geta new category [C,D] (or sometimes written Cat(C,D) or CAT(C,D) or D^C or...)
<13> the objects of [C,D] are functors from C to D, and the arrows are natural transformations
<10> How do you call in words the category [C,D] ?
<13> "the category of functors from C to D"
<10> Alright!
<13> (you usually name categories after the objects, 'category of groups', 'of sets', etc)
<10> For 'arrows' you meant the morphisms?
<12> the category of functors from the category of categories to itself?
<10> (They are probably the same thing, just making sure.)
<13> yeah, arrow/1-cell/morphism/map, i use these interchangeably
<13> mnvl - that would be [Cat,Cat]
<10> Thanks much.
<13> so anyway, a monoid internal to [C,C] is exactly a monad on C
<12> k
<12> for a good explanation of monads in haskell (which relates them a little to categroy theory)
<12> http://sigfpe.blogspot.com/2006/08/you-could-have-invented-monads-and.html
<14> what's the relationship between diophantine equations and the extended euclidian's algorithm?
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