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#math
<asphyxia> oh, maple said so... nevermind then
<tiglionabbit> h'lo
<tiglionabbit> for a 3D graphics project, given a point, I'm going to need to find the closest point to it on a given triangle..
<chessguy> is the point inside the triangle, outside, or what?
<Hansfire> Hey can you guys help me
<profmakx> Don't ask to ask. Ask.
<MatiaB> Hi. I have given a bijective f: X -> Y, and now i have to prove that if s is a permutation of X, then fs := f o s o f^(-1) is a permutation of Y, is it enough to proove that it is injective and surjective for fs? or do i have to proove it for f o s o f^(-1) ? :)
<MatiaB> Its in group theory
<Syzygy-> How did you define permutations?
<Hansfire> Its not for home work just curiosity i was wondering is there a way that you could calculate when you have the global coordinates when i my coordinates are are in the occupied by other coordinates in another time. Example A) coordinates Europe Netherlands and B) coordinates America USA so when at which times does the USA occupy the space of the Netherlands and when does the Netherlands occupy space of the USA and if not can i just track whic
<MatiaB> f: X -> Y, or normally a permutation is f : X -> X, but since its said it bijective, then its the same for f: X -> Y
<Hansfire> i dont have any math skills you guys are my only hope
<Hansfire> and i dont have good grammar or punctuation either
<Syzygy-> MatiaB: Nonono, don't try to rebuild the definition for this situation. Just tell me what your definition of permutation is.
<Hansfire> i just have a curiosity to know
<MatiaB> Okay, that would be X, which have been switched a little around, and then is different from X
<Syzygy-> MatiaB: Does "A permutation p is a bijective map p:X -> X" ring any bells?
<Hansfire> and i mean when the you put a grid over the earth and the earth moves underneath it
<MatiaB> Syzygy-, jep
<Syzygy-> Good. THAT was what I wanted to hear from you. :P
<Hansfire> can someone give me some pointers please
<MatiaB> Syzygy-, hehe. :)
<Syzygy-> Now. If f: X->Y and g:Y->Z are bijective, then g o f is bijective. (prove this for yourself, please)
<Syzygy-> Also, if f is bijective, then so is f^-1.
<Hansfire> i think i need to know how the earth moves and around its own axis and around the sun and the sun in the milky way but lets concentrate on our solar system first
<Hansfire> is this the right channel for my question?
<Syzygy-> Hansfire: No.
<Hansfire> But its a math problem
<Jafet> No, it's an attitude problem. Yours, as a matter of fact.
<Syzygy-> Not quite: it involves the real world. :P
<MatiaB> Syzygy-, i dont get the f: X -> Y and g:Y->Z, do i want to proove that something is transtive?
<Hansfire> you guys are my last hope i am sorry i am nervous
<Syzygy-> MatiaB: Once you have proven all this, just note that since f and s are bijective, so is f o s o f^-1. And finally, since f: X->Y, f^-1=Y->X and s:X->X, you'll get f o s o f^-1:Y->X->X->Y is a bijection inside of Y.
<Syzygy-> MatiaB: Well, you have a bunch of bijective functions. And you can plug them into each other.
<Syzygy-> And since bijectivity doesn't change by plugging them into each other (which you should prove btw), the result of plugging things together is a bijection from wherever it starts to wherever it stops.
<Syzygy-> And f o s o f^-1 has just the right start and stop.
<Hansfire> I am working on a google earth plugin
<Syzygy-> Hansfire: Good for you.
<Hansfire> i am an intern at google
<Jafet> Well, if you don't have leet math skillz, go learn some.
<MatiaB> Syzygy-, okay, so i would have to proove that s is a bijection, and then proove that they can be stuffed together?
<Jafet> Hansfire: You need to state your problem exactly as well. Vague, pathetic pleas are of no help to either of us.
<Hansfire> and my idea was that somebody could enter there location and current time (or any given time) and get a list of places that also crossed that location when you have a grid that isnt dynamic and doesnt rotate
<Hansfire> Jafet i have basic skills
<Syzygy-> MatiaB: If s is a permutation, it is a bijection.
<Hansfire> nvm i'll use the hyperspace forum :)
<Syzygy-> This I am used to see as a definition.
<Syzygy-> Hansfire: You do that.
<Hansfire> this isnt abstract enough i did the calculations already btw just curious to check if i didnt make any mistakes
<MatiaB> Syzygy-, hehe yes, it seems very easy, if it should just be used. What i would like to do is exactly that s is a permution of f, so i that fs := f o s o f ^(-1) is a permutation of Y
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