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#math
<dn4> Does anyone know of a good way to understand why lim x->0 sin(x)/(x) = 1
<g0th> yes
<jbinder> is mbot offline?
<jbinder> meh whatever
<g0th> do you know the sum for sin?
<Papageno> No wait... hemo is blood not homeo... blah
<cyclicFifths> it appears so... i didn't know that though
<g0th> how did you define sin?
<octoberdan> I'll reword my question slightly... Is there a method for creating functions that, if iterated, will have a limited range?
<g0th> or use the rule that limit f/g is equal to f'/g' if "it makes sense"
<g0th> ok the "it makes sense" part is cheated ;)
<g0th> but you can look the conditions up in your book
<g0th> they're all obvious
<octoberdan> Does my question make sense?
<g0th> limited range?
<g0th> makes no sense to me, sorry :(
<g0th> and what do you mean by method and iterated
<g0th> and what sort of functions
<g0th> well in short, I have no idea what you're trying to do
<asphyxia> If I have a set X, with some given elements a_1,...,a_p, and I define a permutation y(a_1)=a_2, y(a_2)=a_3, ..., y(a_(p-1)) = a_p and y(a_p) = a_1 and finally y(x) = x when x is not in the set {a_1, a_2,...,a_p}, is it then what you would call a p-cycle of length p?
<asphyxia> (I'm trying to find english terms for the danish terms in my textbook)
<g0th> "p-cycle of length p" *g*
<g0th> isn't there a p too much ?
<asphyxia> oh maybee
<g0th> but don't ask me about english terms ;)
<asphyxia> cyclic permutation :)
<asphyxia> according to wikipedia
<octoberdan> "method" as in "way." iterated as in f(f(f(f(f(x))))). Limited range as in the result of each iteration would be confind between two numbers
<g0th> I have a method
<g0th> you simply take the 0 function
<g0th> if you iterate the 0 function the range is always 0 thus always limited
<g0th> problem solved :)
<octoberdan> hehe
<g0th> so the answer is: yes!
<g0th> there is a "method"
<cyclicFifths> octoberdan: do you know the fixed point theorem?
<octoberdan> cyclicFifths: Not yet
<g0th> it somehow sounds like fixed point theorem yes
<g0th> but I think you should first try to understand the question
<g0th> before trying to answer it
<g0th> and I go to bed now
<g0th> gnight all
<cyclicFifths> night
<octoberdan> http://mathworld.wolfram.com/FixedPointTheorem.html Eureka!
<octoberdan> cyclicFifths: Thank you
<cyclicFifths> np
<asphyxia> Ok, I have a 'main theorem' in my book, which states: 'Let X be a finite set. Then (1) Any permutation o of X can be constructed as a product of transpositions (2) If a in X is a given element, then there can be chosen transpositions on the form (ax) for x in X\{a} for the construction'
<diseaser> did mbot die?
<cyclicFifths> % mbot, hello?
<diseaser> how do you get mathematica to do what mbot does? :)
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