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well see to a mathematician, like me, numbers exist independent of any computer hardware in a world of pure abstraction, like in a mathematical sense, and what do you mean there's different kinds of numbers?
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Feb 11, 2013 01:20
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real numbers is seriously crazy poo poo
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Feb 11, 2013 01:27
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let me tell you about complex numbers
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Feb 11, 2013 01:30
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the set of numbers that can be computed is countable, and there are uncountably many real numbers also js and lua probably don't have bigints because bigint arithmetic is slower than float/double arithmetic
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Feb 11, 2013 01:33
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I couldn't imagine
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Feb 11, 2013 01:33
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i for one am disappointed that the c++11 committee didn't include a class that exactly represents nth roots, cmon guys do you want to build a world-class language or not?
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Feb 11, 2013 01:35
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yaoi prophet posted:also js and lua probably don't have bigints because bigint arithmetic is slower than float/double arithmetic I think the idea is that since these are languages for "small programs" having different numeric types would confuse people. poo poo like: "How come 1/2 doesn't equal .5" I mean, it's a bullshit reason, but that's what I think was going on at the time.
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Feb 11, 2013 02:15
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Zaxxon posted:I think the idea is that since these are languages for "small programs" having different numeric types would confuse people. poo poo like: "How come 1/2 doesn't equal .5" More like they're supposed to be type-free, so having two different kinds of 1 is sort of contradictory. 1 and "1" is bad enough already.
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Feb 11, 2013 02:17
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rotor posted:WHAT THE gently caress IS A MEZZANINE a massive attack album
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Feb 11, 2013 03:09
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it's an entresol
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Feb 11, 2013 03:22
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yaoi prophet posted:the set of numbers that can be computed is countable, and there are uncountably many real numbers do you have a proof handy for that bc it does;t seem obvious to me
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Feb 11, 2013 03:52
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Nomnom Cookie posted:do you have a proof handy for that bc it does;t seem obvious to me fix some language L (with a finite alphabet) to do your computation in. if a number is computable, it can be computed by some program of finite length in L, by definition. so there are as many computable numbers as there are finite programs in L, which is countable (since you can just enumerate the length 1 programs, the length 2 programs, etc.)
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Feb 11, 2013 03:56
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this is boring lets discuss how signed integer arithmetic is just constrained 2-adic arithmetic.
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Feb 11, 2013 04:02
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Nomnom Cookie posted:do you have a proof handy for that bc it does;t seem obvious to me CANTORS DIAGNONAL POSTING
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Feb 11, 2013 04:02
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let's ignore all the numbers and just look at the ones between 0 and 1 they're obviously countable, so let's put them in a list then, hang on, couldn't i make a new number for each digit, I go to that number in the list and make sure the digit is different it's a big, long number, but now it's totally not in the list I made how can this be maybe I can't put them in a list, like I can the integers. time works the same way
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Feb 11, 2013 04:05
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ps. all the fractions can be put in a list also, if there are infinitely many trancidental numbers why can people only name two?
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Feb 11, 2013 04:06
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tef posted:CANTORS DIAGNONAL POSTING mods make this my name tia also there's a little extra rigor involved in making sure you generate a new number and not just an alternative representation of another number, which is really just making sure you never pick an infinite string of 9's
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Feb 11, 2013 04:07
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but 1 = 0.99999999999999............
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Feb 11, 2013 04:08
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i did say 'let's put all the numbers in a list', not 'let's make a list of all the numbers, with duplicates' 
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Feb 11, 2013 04:09
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there are infinitely many transcendental numbers?
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Feb 11, 2013 04:09
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yaoi prophet posted:fix some language L (with a finite alphabet) to do your computation in. if a number is computable, it can be computed by some program of finite length in L, by definition. so there are as many computable numbers as there are finite programs in L, which is countable (since you can just enumerate the length 1 programs, the length 2 programs, etc.) durr i shouldve seen that
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Feb 11, 2013 04:11
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tef posted:but 1 = 0.99999999999999............ yeah exactly so if i never wrote down 0.9... and that's what i came up with as my new number and i already had 1 there'd be egg on my face also the fact that even though the rational numbers are countable they are dense in the real line also you can generate a subset of [0,1] that has infinitely many points but has zero length also you can actually split apart a sphere in a certain way to generate two spheres of the same size also (real analysis 101 fact)
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Feb 11, 2013 04:12
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Otto Skorzeny posted:there are infinitely many transcendental numbers? yes. there are countably infinite algebraic numbers so there must be uncountably infinite transcendental numbers lol
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Feb 11, 2013 04:14
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tef posted:ps. all the fractions can be put in a list bc no one cares about the other ones
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Feb 11, 2013 04:15
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Otto Skorzeny posted:there are infinitely many transcendental numbers? yes. the natural numbers, the integers, the algebraic numbers and the computable numbers are countable. when you take that all away, you're left with transcendental numbers. iirc. and you can't put them in a list
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Feb 11, 2013 04:21
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Feb 11, 2013 04:23
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CALKINS WILF SEQUENCE q' = 1/(2*floor(q)-q+1)
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Feb 11, 2013 04:24
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FamDav posted:also you can actually split apart a sphere in a certain way to generate two spheres of the same size iff the "axiom" of choice is true, which it isn't, and even then the "spheres" aren't actual spheres (have no surface area) iirc
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Feb 11, 2013 04:24
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georg cantor did 9/11
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Feb 11, 2013 04:25
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what's an anagram of banach-tarsky?
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Feb 11, 2013 04:27
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Crab Hat Yanks
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Feb 11, 2013 04:32
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bays crank hat
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Feb 11, 2013 04:35
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more like BAYES' CRUNK HAT imo
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Feb 11, 2013 04:36
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Sneaking Mission posted:Crab Hat Yanks Sneaking Mission posted:Crab Hat Yanks
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Feb 11, 2013 04:38
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Otto Skorzeny posted:iff the "axiom" of choice is true, which it isn't, and even then the "spheres" aren't actual spheres (have no surface area) iirc define truth for an axiom FamDav fucked around with this message at 04:49 on Feb 11, 2013 |
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Feb 11, 2013 04:42
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tef posted:maybe I can't put them in a list, like I can the integers. 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
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Feb 11, 2013 04:45
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Otto Skorzeny posted:iff the "axiom" of choice is true, which it isn't, and even then the "spheres" aren't actual spheres (have no surface area) iirc no they're completely normal spheres if you do it right (also like famdav said 'truth' of an axiom is kind of a weird thing to talk about)
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Feb 11, 2013 04:46
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it's an infinite list
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Feb 11, 2013 04:47
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you get as many natural numbers as you want (god's gift)
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Feb 11, 2013 04:48
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| # ? Jun 11, 2024 12:13 |
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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 The best way to think about it is that i can match up each number in my set X with one of the numbers in N, i.e. 0,1,2,3,4,5,6,7,8,9,... For integers ...-2,-1,0,1,2... I can do this by having all the even numbers x map to x/2 and all the odd numbers map to -(x+1)/2.
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Feb 11, 2013 04:48
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