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Hard NOP Life posted:How can you put all the integers in a list in the first place if its infinite? I know this is a numbershit 101 for you guys but this just doesn't seem intuitive at all to me i can write a program that prints them out in order, one by one. (assuming bignums :3 ) it might not ever finish, but I can given a number, tell you it's position. putting in a list, i mean, making an ordered sequence. tef fucked around with this message at 04:52 on Feb 11, 2013 |
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Feb 11, 2013 04:49
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this is all about relative sizes of infinite sets so "doesn't seem intuitive at all" is about right
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Feb 11, 2013 04:52
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the rationals are a bit funky but if you visualize the top right of the coordinate plane and then make a zig zag motion through it you can see how it works. let me see if i can find a picture
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Feb 11, 2013 04:52
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FamDav posted:the rationals are a bit funky but if you visualize the top right of the coordinate plane and then make a zig zag motion through it you can see how it works. let me see if i can find a picture calkin wilf sequence is my favourite mapping, as mentioned earlier.
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Feb 11, 2013 04:54
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Feb 11, 2013 04:55
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dad, stop please, dad
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Feb 11, 2013 04:58
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all this maths talk reminds me of reading gödel escher bach in high school unsure if that permanently expanded or permanently damaged my mind
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Feb 11, 2013 05:05
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go to your room and don't come back downstairs until you've written down a(4,4)
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Feb 11, 2013 05:06
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Nevergirls posted:all this maths talk reminds me of reading gödel escher bach in high school given it wasn't martin gardner i'd opt for the latter
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Feb 11, 2013 05:06
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fond memories of big rudin in grad school sorry I mean the opposite of fond hostile
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Feb 11, 2013 05:18
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Internaut! posted:fond memories of big rudin in grad school http://www.okcupid.com/match?keywords=Big%20Rudin&only_text=1 its like the 6th entry on google for big rudin
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Feb 11, 2013 05:22
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tef posted:given it wasn't martin gardner i'd opt for the latter bastard
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Feb 11, 2013 05:44
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tef posted:yes. not really, I mean, there are transcedental numbers like e and pi who are also computable numbers. the uncountable part of the real numbers is the weird infinite tricky poo poo
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Feb 11, 2013 06:00
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yospos needs a maths thread for discussions about how cool grigori perelman is
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Feb 11, 2013 06:03
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Symbolic Butt posted:yospos needs a maths thread for discussions about how cool grigori perelman is here is fine, it's a nice change from people in denial about how bad c-languages and j-languages are
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Feb 11, 2013 06:05
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yaoi prophet posted:(also like famdav said 'truth' of an axiom is kind of a weird thing to talk about) yes, and yet some putative axioms are clearly impossible to square with other axioms going a level of abstraction above mathematics, it is clear that you can't have a logical system wherein the Axiom of Non-contradiction and some putative Axiom of Sometimes-Contradiction both exist. we call things axioms when we believe them this *holds hands far apart* much and can't prove them, and assert that they cannot be disproven inasmuch as no other axioms contradict them  ; there are plenty of mathematicians who either think aoc is a Lie, or only believe it this much *holds hands somewhat closer together*; calling it or any other thing that not everyone in the field believes an axiom is really an act of intellectual violence
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Feb 11, 2013 06:12
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gently caress you i need to go to bed
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Feb 11, 2013 06:14
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i love math stuff but gently caress how do you educate yourself in math im reading up on matrices lately because i discovered PDL and want to do stupid poo poo with it.
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Feb 11, 2013 06:35
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Jonny 290 posted:i love math stuff but gently caress how do you educate yourself in math poo poo, good luck i'm getting educated in math right now and the book is only moderately helpful. everything useful comes from the prof, or from other students in the math center
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Feb 11, 2013 07:18
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Sniep posted:a massive attack album
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Feb 11, 2013 07:36
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Otto Skorzeny posted:yes, and yet some putative axioms are clearly impossible to square with other axioms i think you're putting too much into the word axiom. while you are absolutely correct about the acceptance of zfc -- though the gross majority of mathematics do accept it and i dont why you call it an outright lie like you did -- that doesnt mean that it isnt an axiom as stated. it is a premise of a particular formulation of set theory, and you have the joy or lack thereof to work within the axioms of that particular formulation. In much the same way, you have the freedom to include the parallel postulate in your formulation of geometry or you don't. In short, axioms are not always putative and they dont have to be ps which putative axiom are you suggesting contradicts the axiom of choice?
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Feb 11, 2013 08:20
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FamDav posted:
axiom of omakase
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Feb 11, 2013 08:24
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Jonny 290 posted:i love math stuff but gently caress how do you educate yourself in math Get a textbook. Read and be bewildered by a chapter, then look it up on purplemath.com etc, then do the chapter exercises. P much the experience of a lot of college math students right there.
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Feb 11, 2013 08:45
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FamDav posted:ps which putative axiom are you suggesting contradicts the axiom of choice?
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Feb 11, 2013 09:32
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PrBacterio posted:When I was in college I once wrote a paper about an interesting one, postulating a generalisation of Zermelo's theorem to infinite games, i.e. it stated that there exist a winning strategy for all perfect-information two-player games, not just finite ones, as an axiom. This has a number of interesting consequences, for example one theorem that can be derived in ZFS with this axiom is that all subsets of R are Lebesgue measurable, which in turn proves this axiom to be in contradiction to the AC (because the AC implies that there are non-Lebesgue-measurable sets). so this is the axiom of determinacy, which is p cool and yields interesting results but is not a universally accepted axiom of set theory. its kind of contrived though. what im really looking for is him to say nothing because ZF is logically independent of AC. FamDav fucked around with this message at 09:54 on Feb 11, 2013 |
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Feb 11, 2013 09:50
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Jonny 290 posted:i love math stuff but gently caress how do you educate yourself in math read a martin gardner book. http://www.amazon.com/Colossal-Book-Mathematics-Paradoxes-Problems/dp/0393020231
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Feb 11, 2013 13:24
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FamDav posted:what im really looking for is him to say nothing because ZF is logically independent of AC. what's yellow and pro choice? zorn's lemon
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Feb 11, 2013 13:26
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tef posted:read a martin gardner book. 
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Feb 11, 2013 14:27
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just drop the axiom of infinity and become a strict finitist
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Feb 11, 2013 14:57
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FamDav posted:ps which putative axiom are you suggesting contradicts the axiom of choice? AD is incompatible with it. it would be cool if true sort of like supersymmetry or OMG STRINGS in physics
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Feb 11, 2013 15:57
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Jonny 290 posted:i love math stuff but gently caress how do you educate yourself in math same way a math student does, get some textbooks, start reading and most importantly, do the exercises linear algebra (matrix poo poo) is a great way to start as the concepts are much simpler than say vector calculus (imo), the mechanics are pretty straightforward and lend themselves very well to solution by computer, it's very practical in a lot of computery applications, and it's the foundation of quantum mechanics which is another cool thing to learn about but you won't be able to measure anything without knowing how hermitian operators work on state vector inner products in hilbert space not sure where your math's at right now but strang made a decent intro to linear algebra book
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Feb 11, 2013 15:59
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you can never have enough linal, you can never have too good of a feel for diffeqs (esp if you dabble in electronics like johnny and want to jump back and forth between the time domain, frequency domain, and simple but 'weird' stuff like the s and z planes that are really frequency but retain information about transients)
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Feb 11, 2013 16:03
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otto sniffed me out, i want to eventually do the electronics math. im going to go back over a linear book as that's probably about where i need to restart i got 36 math ACT blah blah could integrate and derive like a motherfucker, but that was like 4 presidential terms ago. been a minute
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Feb 11, 2013 17:54
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this should have a sign on it that says "you must be this smart to post in this thread".  *posts anyway*
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Feb 11, 2013 18:59
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also graph theory interests me too, i read up on that a little bit the other day
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Feb 11, 2013 19:03
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Jonny 290 posted:also graph theory interests me too, i read up on that a little bit the other day theory of lovely beep-boop music
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Feb 11, 2013 19:12
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Otto Skorzeny posted:AD is incompatible with it. it would be cool if true sort of like supersymmetry or OMG STRINGS in physics like i said bruh bruh, ad is not a putative axiom and its p contrived as part of set theory. i'd rather have every vector space has a basis than some nonse about games having solutions. Jonny 290 posted:also graph theory interests me too, i read up on that a little bit the other day graph theory is p cool and a lot of it is fairly intuitive. this is a p good book but kinda expensive so maybe find a library or something?
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Feb 11, 2013 19:14
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also real talk after you know a lot about linalg pick up a book on abstract algebra then buy a book on matrix groups and go h.a.m.
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Feb 11, 2013 19:16
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FamDav posted:like i said bruh bruh, ad is not a putative axiom hence the 'axiom' part of the name  FamDav posted:graph theory is p cool you can make any (cs) problem a graph problem if you squint a little 
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Feb 11, 2013 19:26
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Otto Skorzeny posted:hence the 'axiom' part of the name now i seriously have no idea what you were and are getting at, besides your weird idea of truth.
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Feb 11, 2013 19:55
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