03:21 ωνω om [mezuza@die.m0f0.com] has joined #phrack
03:22 fucking talktive tonight
03:23 why would a chan ban ~*@*.*
03:23 people without ident
03:24 or people without spoofs ;p
03:24 ωνω flatline` [~lick@flatline.xs4all.nl] has joined #phrack
03:24 f ident
03:24 yo spendy
03:24 yo yo
03:24 doing some elec stuff heh
03:24 you should give a #phrack lecture on grsecurity
03:25 i could
03:25 COOL
03:25 i could lecture on other topics as well
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03:25 LIKE?
03:26 hrm, like set theory, cardinality, proofs
03:26 cool
03:26 physics
03:26 i think phrack could use a good lecture on cardinality
03:26 cardinality is nifty
03:26 ωνω SignOff democow: #phrack (Ping timeout: no data for 244 seconds)
03:26 have you taken a class on it yet?
03:26 ωνω om [mezuza@die.m0f0.com] has joined #phrack
03:26 no i have no knowledge on the subject, i desire very much to hear your lecture ;))
03:27 haha
03:27 teach us spendy!
03:27 hrmm
03:27 ωνω SignOff int1r: #phrack ([BX] They killed Kenny! THOSE BASTARDS!)
03:27 ok
03:27 so numbers can be broken up into different categories
03:27 π LiLTrip74/#phrack returned (6m29s)
03:27 according to their size
03:27 ωνω _bl [blazt@ghettobox.eurocompton.net] has joined #phrack
03:27 the size of a set of numbers is its cardinality
03:28 y-0 _bl we're having a #phrack lecture
03:28 cardinality is a relatively new field of mathematics...only a hundred years or so old
03:28 <_bl> oh ya? what's the topic
03:28 ωνω mode/#phrack [+v _bl] by abhaya
03:28 so, you have finite sets of numbers, denumerable sets, and uncountable sets
03:29 denumerable sets are infinite in size, but can still be counted
03:29 cool can you tell us what cantor did with infinite sets?
03:29 the natural numbers are an example
03:29 yea
03:29 there's the cantor schroeder berstein theorem
03:29 dj bersteni?
03:30 berstein
03:30 which says that two sets are equal in size if a one-to-one relationship exists between them
03:30 meaning there's a one-to-one from set A to set B, and a one-to-one from set B to set A
03:30 thats injective right?
03:30 the_uT: not sure..
03:30 yes
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03:30 onto is surjective
03:30 both onto and one-to-one is bijective
03:30 kool
03:31 sets are also equal in size if a bijection exists between them
03:31 yeah i think dj berstein helped formulate that theorem
03:31 why are they called natural numbers, if numbers are all artificial - ie, dictated by the mind of man and defined as such?
03:31 he's offering $500 to anybody that can disprove the theorem
03:31 haha
03:31 well
03:31 ωνω om [mezuza@die.m0f0.com] has joined #phrack
03:31 heh
03:31 it's unprovable that there's any sets between aleph naught and the continuum
03:32 it's called the continuum hypothesis
03:32 it's been proven that it's unprovable ;p
03:32 so...the set { 1, 2, 3} is finite
03:32 the natural numbers are denumerable
03:32 ωνω int1r [~entropy@pool-151-202-182-105.ny5030.east.verizon.net] has joined #phrack
03:32 the rational numbers are denumerable also
03:33 ωνω inc [~inc@81.84.4.162] has joined #phrack
03:33 because it's equivalent to the set N x N
03:33 "denumerable"
03:33 how can a numeral be denumerable?
03:33 haha
03:33 sigh this is boring, now i remember why i slept thru discrete maths
03:33 it has to do with the sizes of the sets
03:34 so it means you can't put a specific number on it
03:34 because it's infinite
03:34 but it can still be counted
03:34 cantor says if you arrange all the natural numbers in a box diagonally
03:34 you can play checkers!
03:34 you can count them all
03:34 haha
03:34 that too
03:34 ;p
03:35 how can you count them all
03:35 another fact is the power set of a set results in a set of greater cardinality
03:35 well
03:35 you can't count horizontally
03:35 or vertically
03:35 because if you do that, you'll go on forever on the first line
03:35 and will never get to the second line
03:35 what about the power set of R
03:35 ωνω SignOff int1r: #phrack ([BX] The Power Rangers use BitchX. Shouldn't you?)
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03:35 what about the power set of the null set
03:36 haha
03:36 the power set of R has greater cardinality than R
03:36 R is an uncountable set
03:36 it has cardinality of c
03:36 continuum
03:36 spendy??
03:36 the power set of the null set is the null set heh
03:37 i should have clarified and said sets having elements ;p
03:37 so whats the cardinality of the null set and what is the cardinality of the null set's power set
03:37 ok
03:38 how can it security professionals utilize the concept of these 'sets' in their day-to-day work?
03:38 hrmm
03:38 well
03:38 it actually has lots of applications
03:38 wow
03:38 set theory can be used in security models
03:38 lets say you have two subjects
03:38 each containing objects, with specific permissions to each object
03:39 kinda like the grsec ACLs?
03:39 the intersection of the two subjects gives useful information
03:39 as does the union
03:39 yes
03:39 cooooool
03:39 ωνω akcess [~akcess@visp151-27.visp.co.nz] has joined #phrack
03:39 haha
03:39 yo
03:39 but there's also lots of other applications
03:39 like partitions
03:39 like?
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03:39 i wont even try to get into this convo
03:40 i lub math
03:40 partitions??
03:40 yea
03:40 filesystem structure in general
03:40 is based on set theory
03:40 ;p
03:40 cantor diagonalizations are yummy
03:40 ωνω om [mezuza@die.m0f0.com] has joined #phrack
03:40 oh wait
03:40 partitions are sets wherein each set is not the empty set
03:40 so how come you can count them diagonally
03:40 but not left-to-right etc
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03:41 because
03:41 what you're counting is N x N
03:41 reminding me of discrete !0!
03:41 so think of a graph
03:41 you have x coordinates and y coordinates
03:41 the coordinates go on forever
03:41 agree
03:41 so if you start at (0,0) and begin counting right
03:41 you'll never stop counting that line
03:42 and you'll miss all the stuff above
03:42 k
03:42 and you'll miss all the stuff above
03:42 i dont understand what u mean
03:42 like
03:42 you'll miss the point (0,1)
03:42 and (0,2), (1,2)...etc etc
03:42 everything above the x axis
03:43 this isnt interesting
03:43 haha
03:43 spendy
03:43 CONTINUE
03:43 i know it isn't for your aempirei ;p
03:43 it is
03:43 so points on a graph i am missing.
03:43 :P
03:43 go on
03:43 stfu aempirei or im gonna lock down this channel like the rLOCKsley
03:43 well, but the points represent a pair of rational numbers
03:44 ok, well...
03:44 so what happens when u count diagonally
03:44 1,1 2,2 3,3 4,4 ad infinitum
03:44 ?
03:44 an interesting corrolary of the cantor schroeder bernstein theorem
03:44 no no
03:44 ωνω SignOff om: #phrack (changing servers)
03:44 it would be like
03:44 no acceleration.
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03:44 (0,0), (1,0), (0,1), (2,0), (1,1), (0,2)
03:45 ωνω om [mezuza@die.m0f0.com] has joined #phrack
03:45 so not like the line f(x) = x
03:45 but f(x) = -x + c
03:45 where c is 0, 1, 2, 3, etc
03:45 so anyways
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03:46 the diagonalization for a proof of countability of Q is so cheesy cause the arbitraty elimination of reducable fractions seems so ad hoc
03:46 ωνω sandnig0r [sandnigg0r@user-uinj1h3.dialup.mindspring.com] has joined #phrack
03:46 r u saying you can count all numbers in a set that stretches infinitely in both directions on a number line?
03:46 well, you don't use that to prove it ;p
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03:46 you prove by showing a bijection exists
03:46 the_uT: but it doesn't
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03:46 each time it's a finite set
03:47 a denumerable collection of finite sets
03:47 'but it doesnt' <- hardly an answer to a question of the form 'are you saying...'
03:47 nerd shit
03:47 which is denumerable
03:47 :)
03:47 <_bl> eckis, 4real
03:47 ωνω glaive [glaive@maia.vaned.net] has joined #phrack
03:47 like the first time, you have 1 element, then 2 elements, then 3...
03:47 all finite
03:48 but you must an infinite times, no?
03:48 now if this only had a point i would cream.
03:48 yes, a denumerable number of times
03:48 it's infinite, but countable
03:48 spender, if u had an infinite set of data... say in the form of an mysql database.... how long would it take me to rm it?
03:48 lol
03:48 the_ut 1 : spendy 0
03:48 dye, #phrack
03:48 well it would depend on if i were running openbsd
03:48 ;p
03:48 lol
03:48 thx spender btw i havent learned about it in school :D
03:49 f openbsd do debian+grsec
03:49 haha
03:49 well
03:49 since i carry across ip tagging over stream unix domain connections
03:50 everybody knows theres no security holes in grsec... except for the one `cat /proc/1/fd/ssh_login_passwords`
03:50 haha
03:50 /proc restrictions wouldn't allow that
03:50 i rewrote them recently so that the directory isn't even displayed if you don't have permissions to view inside it
03:50 /proc/self sorry
03:51 chroots also can't view outside processes
03:51 ptrace them, or do about 30 other things ;p
03:51 all architecture-independent
03:51 but anyways
03:51 cool
03:51 as i was going to say
03:51 cause im sure returning -ESYS is highly architecturee dependent
03:51 the cantor schroeder bernstein theorem relies on the axiom of choice
03:52 no, -EPERM or -EACCES actually
03:52 ahhhh
03:52 doing a ptrace restriction would normally be architecture-dependent
03:52 since each architecture provides its own implementation
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03:52 ωνω thn [~ech0@h68-147-17-177.cg.shawcable.net] has joined #phrack
03:53 right cause
03:53 ωνω _metaray [~joe@Ottawa-HSE-ppp258802.sympatico.ca] has joined #phrack
03:53 but i did a trick to deny ptraces and a bunch of other things (kill, setsid, setpgid, etc) all in one pice of code
03:53 causing ptrace to return -EPERM if you're chrooted is highly architecture dependent!
03:53 cool
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03:53 so anyways
03:53 some mathematicians don't like the axiom of choice
03:54 because if you believe the axiom of choice, there's other things you must believe as well
03:54 some of them seem rational, others seem very strange
03:54 there is a god?
03:54 ωνω om [mezuza@die.m0f0.com] has joined #phrack
03:54 i just saw joowee in cnn
03:54 so if it's possible to prove something without the axiom of choice, mathematicians like it better if you do that
03:54 talkin bout the mssql wurm
03:55 said he was an ex hacker and know published writer
03:55 speaking of worms, anyone know what he mp3 file attribute was that was overflowable in xp a month or two ago?
03:55 i think he should be hangin from a tree, with no vaseline
03:55 so one of the cool corollaries of the CSB theorem is you can take all the points in a real-valued line of length 10, and make it into a filled in box of 100 square units
03:56 just a match, and a littel bit of gasoline
03:56 ok
03:56 ωνω mode/#phrack [+v spendy] by the_uT
03:56 ωνω mode/#phrack [+m] by the_uT
03:56 haha
03:57 go spendy, its your birthday, gogogo
03:57 hmm
03:57 i forget an example of the axiom of choice that is really strange
03:57 the pressures of sucess no doubt
03:57 maybe :\
03:57 got anything else u can lecture on?
03:57 ωνω om^ [scb@62.128.45.224.knet.co.il] has joined #phrack
03:58 what classes are you taking again
03:58 well there's lots of other stuff related to set theory that i didn't talk about
03:58 oh
03:58 right now i'm taking mechanics, differential equations, discrete structures (it's a repeat of the logic and proofs class i took last semester), electrical engineering, and a mips assembly class
03:59 cool
03:59 you gonna do some irix exploits
03:59 ??
03:59 haha
03:59 maybe for a project
03:59 well
03:59 ωνω subd [~Hulac@syr-66-67-98-42.twcny.rr.com] has joined #phrack
03:59 we're learning mips32
03:59 the r2k r3k processors
03:59 im in introduction to algebra
03:59 :D
03:59 awesome, lots of irix binaries are still in O32 format
03:59 you could own a lot of shit if u pay attention in that class
03:59 that's true
03:59 haha
04:00 well i've been playing with that and x86 assembly
04:00 can you lecture about some broad topics in mechanics
04:00