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<lament> mbot: 1 + 2
<Anil> @math 1+1
<mbot> Anil: 2
<apfel> What's the interpretation of N^* = \cup_{k \in N} N^k (where N are the naturals)? Is it N^* = N^1 \cup N^2 \cup N^3 \cup ... ?
<Fox-> nice
<kercyr> it's the union of finite sequences of natural numbers.
<_llll_> yes, it's a countable union
<_llll_> you can also say it is the smallest set containing all the N^k (smallest meaning "smallest wrt inclusion")
<Cale> you can consider it recursively as satisfying N^* = {{}} union N x N^*
<Cale> or perhaps {()} rather than {{}} -- though any one-element set will do
<cherzog> Guys? Got a screen, 16:10 and it's 12" - how do i find out how long the two sides are? any hints? it looks damn easy and i'm willing to read :-)
<_llll_> the 12" is the diadonal, presumably
<Fox-> do you know pythagore?
<Fox-> and square triangles
<cherzog> _llll_: yep
<_llll_> and the 16:10 gives the ratio of the sides, ie one equation. and pythagorus makes two equations for the 2 unknowns (but not linear). solve them
<Fox-> 12" ^2 = lenght ^2 + (16/10 * lenght) ^2
<Fox-> smth like that
<cherzog> well, then my system is underdetermined, isnt it? hm. it wasnt, if it was linear.
<Fox-> second degree equation to solve
<apfel> OK, thanks.
<Cale> (16x)^2 + (10x)^2 = 12^2, so x = 6/sqrt(89) after some calculation, and we get that the sides are 96/sqrt(89) = ~10.176, and 60/sqrt(89) = ~6.36
<Fox-> I hope your under ten years old
<cherzog> ahm. no :-)
<awayfromHome> im confused about the idea of identical elements in a set, its true that a set's elements must be unique from one another, but according to the wiki article, the set {1,2} = {1,1,2,2}
<Cale> Fox-: hey, be nice to people :)
<awayfromHome> in other words, repitions dont change the value of the set
<_llll_> Fox: with grammer like that, i hope you're not a native english speaker
<Fox-> i'm not
<awayfromHome> but i didnt think you could have repitions in a set
<Fox-> "you are" sorry
<pattm> hey if m and n are probabilities, how do I find the limit of ( m^(k+1) + n^(k+1) ) / (m^k + n^k) as k approaches infinity
<Cale> awayfromHome: the point is that the set doesn't record the repetitions
<awayfromHome> thats 1
<awayfromHome> i think, pattm
<Cale> awayfromHome: things are either in the set, or they're not
<awayfromHome> cale: so {1,1,2} is legal form?
<Cale> awayfromHome: yeah, why not -- it's a little redundant, but there's nothing wrong with it
<awayfromHome> ok thanks
<lament> awayfromHome: {1,1,2} is just notation.
<lament> Really there's no such thing.
<lament> Something is either in a set, or not in a set.
<awayfromHome> well i need to have proper syntax
<awayfromHome> so i asked hehe
<lament> 1 is in a set
<lament> and 2 is in a set
<lament> s/a/the
<lament> everything else is not in the set.
<awayfromHome> ok
<Cale> pattm: I think it's either m or n depending on which has greater magnitude
<lament> but in terms of notation, {1,1,2} is legal.
<cherzog> okay. that screen problem was real easy, you're right. I guess i need to catch some sleep :-)
<awayfromHome> fair enough. pattm: i looked at http://en.wikipedia.org/wiki/Infinity#Mathematical_infinity and infinity/infinity is undefined
<pattm> awayfromHome: but they're probabilities
<Fox-> {1,1,2} = {1,2}
<pattm> awayfromHome: so they are both getting smaller and smaller, not bigger and bigger
<Fox-> in terms of set
<pattm> (they are between 0 and 1 inclusive)
<pattm> Cale: hmmm
<Fox-> pattm: your expression tends to 1 when k tends to infinity
<Cale> awayfromHome: it's a limit
<pattm> Fox-: I was thinking about if m and n are both .5 as a test case...
<Cale> awayfromHome: that list just defines a bunch of arithmetical properties used when dealing with the extended real line
<pattm> Fox-: and if they are both .5 then it is definitely .5
<pattm> Fox-: so i dont think it's always 1
<Fox-> if both m and n are < 1 it's another problem
<sloshytiger> awayfromHome: there is a very easy way to think about it. two sets are equal if each element of one set is an element of the other set. go through your list of elements of both sets and you will see that not only is {1,1,2} = {1,2} but {1,1,2} is redundant notation
<pattm> Fox-: They are probabilities
<pattm> Fox-: probabilities by definition are less than or equal to 1
<pattm> and greater than or equal to 0
<Fox-> true
<lament> the more fundamental question is
<_llll_> if m>n, divide both top an bottom by [m^k]
<lament> is 1 and 1 the same number? :)
<Cale> _llll_: yes :)
<pattm> ahhh so it approaches whichever is greater, m or n
<daedric> lament does 0 exist?
<Cale> pattm: right
<pattm> nice that makes sense
<pattm> awesome.
<lament> daedric: will one go insane thinking about infinity for too long?
<Cale> pattm: if they're both the same, then it will approach the common value -- good thing you're not allowing for negative measures, or it would potentially be undefined for things like m = 1/2, n = -1/2
<pattm> thanks guys
<daedric> he will go insane as fast as you will go blind trying to focus the infinite :)
<Fox-> lament: Cantor went crazy and suicide himself
<pattm> that totally makes sense, why didn't I think of that
<awayfromHome> cantor killed himself?
<Cale> Whether mathematical concepts "exist" depends on context.
<awayfromHome> i just read he died in a mental hospital
<daedric> who??
<Fox-> Cantor
<lament> he didn't kill himself
<awayfromHome> georg cantor
<lament> he did die in a mental hospital
<Fox-> well he let death coming
<lament> most mathematicians working with set theory went insane. It's natural.
<lament> er, yes
<daedric> LoL
<awayfromHome> well, thinking about the power series of the infinite set would make anyone go crazy
<lament> awayfromHome: not really
<awayfromHome> power set*
<lament> awayfromHome: people seem to manage, for the most part
<daedric> mathmatics is a "crazy person" thing...
<Fox-> and the sets of all the sets can't contain itself... right
<awayfromHome> i think it can
<Fox-> -s
<awayfromHome> the power set of a set includes the set
<lament> mathematics wisely chose to ignore that particular paradox
<Fox-> so it's like a mobius thing
<awayfromHome> if i remember from todays lecture
<daedric> where i live... i say that a math degree (or whatever you called it) is something that you easly accepted... but from where you'll never leave.. :)
<lament> s/ignore/byp***
<awayfromHome> isnt it, proper power set?
<awayfromHome> the power set that doesent include the original set
<_llll_> A is a subset of A, so A is a member of P(A)
<lament> awayfromHome: not sure why would anybody ever need any such thing
<awayfromHome> i dont know, they teach me these things for a reason, i dont question :/
<awayfromHome> its in discrete math
<lament> that's good
<Cale> I remember hearing that Cantor ending up in a mental hospital had a lot to do with Kronecker.
<lament> be obedient
<lament> always follow orders
<awayfromHome> well, i think its standard for discrete math to teach sets
<awayfromHome> i know that much
<lament> Cale: it certainly had little to do with infinite sets.
<magicwindow> Discrete math is aaaallll about the sets
<lament> Cale: but a pretty tale nonetheless
<_llll_> I think that no-one really knows why Cantor had his break-downs, it is possible that Kronecjer's persecution and criticisms had something to do with it
<lament> magicwindow: well, math is all about sets
<awayfromHome> well, maybe he wasnt driven to insanity, maybe he just had a mental disability
<lament> i mean ***
<awayfromHome> bipolar disease
<lament> disorder
<Fox-> like John Nash
<lament> poor john nash - he didn't like Go!
<lament> no wonder he went insane
<MathKiD> haha
<Cale> lament: well, Kronecker prevented Cantor from publishing based on the view that the objects which Cantor was considering (infinite sets) didn't exist.
<magicwindow> I think the more insane thing is the whole one to one correspondence between rationals and natural numbers
<awayfromHome> is it necessary for a physical infinity to exist for set theory to be true though?
<awayfromHome> i dont get that
<Cale> I seem to recall that he made various remarks about Cantor's work being meaningless.
<awayfromHome> it could just be a useful construct, not necessarily real
<lament> Cale: heh
<koro> phyisical infinity_
<koro> ?
<lament> Only *** is real. Everything else is mathematicians' inventions.
<Kampen> yet look whose work is more important.
<Cale> awayfromHome: no -- physical infinity doesn't even mean anything :)
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