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the set of all prime numbers is still ℵ0 Zetsubou-san has a new favorite as of 11:02 on Apr 21, 2021 |
# ? Apr 21, 2021 10:52 |
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# ? May 24, 2024 14:50 |
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Zetsubou-san posted:the set of all prime numbers is still ℵ0 ?מה
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# ? Apr 21, 2021 11:21 |
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the set of anything countable but provably infinite has the same size as the set of all integers, hth
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# ? Apr 21, 2021 11:28 |
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FFT posted:"set of all prime numbers" would be smaller, "set of all values of Avogadro's Nx" (or similar) All infinite sets of integers are the same size. When you get to talking about the size of infinite sets you have to redefine what you mean by "size", and to make the concept work at all you have to abandon a lot of the intuition that holds true for finite sets. One of the pieces of intuition you abandon is the idea that removing and adding members to a set always changes its size.
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# ? Apr 21, 2021 11:28 |
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Zetsubou-san posted:the set of anything countable but provably infinite has the same size as the set of all integers, hth How do get from that to a stack of Lin Kuei?
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# ? Apr 21, 2021 11:32 |
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# ? Apr 21, 2021 11:34 |
Whybird posted:All infinite sets of integers are the same size.
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# ? Apr 21, 2021 11:35 |
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FFT posted:"set of all prime numbers" would be smaller, "set of all values of Avogadro's Nx" (or similar) Those sets are both the same size as the counting numbers. You can tell because you can make a 1-to-1 correspondence between them, for example this correspondence between the counting numbers and the primes: 1 :: 2 2 :: 3 3 :: 5 4 :: 7 5 :: 11 and so on. Since both lists go on forever, the correspondence never breaks down, and since it is well-defined and contains all the counting numbers on one side and all the primes on the other, the counting numbers and the prime numbers must be the same size. This holds despite the fact that everything on the latter list is on the former, but not everything on the former list is on the latter - infinity is weird like that. It's like how infinity plus one (or infinity times two or infinity divided by a billion or whatever) is still just infinity. However, you cannot make a 1-to-1 correspondence between the counting numbers and the real numbers; the famous proof is called "Cantor's diagonalization argument," which I won't lay out here but you can look it up if you want. It proves that the set of real numbers is larger than the set of counting numbers, even though they are both infinite. It is provably unknowable (in the standard formulation of mathematics) whether or not there are any sizes of sets in between those two sizes (google "continuum hypothesis" for info). Also there are infinitely many possible sizes of infinite sets, each one larger than the last, with the smallest being called the size of the counting numbers, aleph_0, and higher ones, aleph_1, aleph_2, and so on. (aleph is the first letter of the Hebrew alphabet and I have no idea why it's used here. presumably because mathematicians ran out of latin and greek letters.) So the trolley problem meme is comparing aleph_0 people and some other amount of people that is higher than aleph_0 (but it's unknowable which aleph it is). However, it doesn't really make any sense because the definition of "person" I would say definitely implies countability, so it does not make sense to have uncountably infinitely many people, in the same way you might have uncountably infinitely many positions on a number line.
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# ? Apr 21, 2021 11:41 |
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Hyperlynx posted:How do get from that to a stack of Lin Kuei? alephzero
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# ? Apr 21, 2021 11:42 |
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Stupid_Sexy_Flander posted:He has 5 extra. Perfect for 'ardly touched her.
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# ? Apr 21, 2021 11:48 |
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Mierenneuker posted:These crossovers are getting wild. Went to bed hoping I'd wake up to this.
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# ? Apr 21, 2021 11:49 |
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DontMockMySmock posted:Those sets are both the same size as the counting numbers. You can tell because you can make a 1-to-1 correspondence between them, for example this correspondence between the counting numbers and the primes: pee pee poo poo number big
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# ? Apr 21, 2021 11:53 |
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# ? Apr 21, 2021 12:00 |
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lol
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# ? Apr 21, 2021 12:04 |
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Zetsubou-san posted:alephzero Right, I can see that, but... ...wait a second. aleph[sub]zero[/sub]
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# ? Apr 21, 2021 13:12 |
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Edit: gently caress, new page.
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# ? Apr 21, 2021 13:36 |
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Ah, another ‘gas leak’ page
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# ? Apr 21, 2021 13:59 |
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I'm seeing a bunch of memes on twitter with labeled measures on stuff. Like this: |----------------something---------------| |------something else-----| What's that about
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# ? Apr 21, 2021 14:16 |
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# ? Apr 21, 2021 14:18 |
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burexas.irom posted:I'm seeing a bunch of memes on twitter with labeled measures on stuff. Like this: Post examples?
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# ? Apr 21, 2021 14:19 |
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no
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# ? Apr 21, 2021 14:20 |
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Thats okay I'll do it
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# ? Apr 21, 2021 14:27 |
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They seem pretty self explanatory to me
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# ? Apr 21, 2021 14:28 |
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|-------not getting the joke---| you are here |----birth of jesus---|img-timeline.jpg
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# ? Apr 21, 2021 14:34 |
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DontMockMySmock posted:Those sets are both the same size as the counting numbers. You can tell because you can make a 1-to-1 correspondence between them, for example this correspondence between the counting numbers and the primes: Found the narrator in the trolley meme.
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# ? Apr 21, 2021 14:58 |
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flavor.flv posted:Thats okay I'll do it cancel this meme sooner rather than later
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# ? Apr 21, 2021 15:01 |
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LifeSunDeath posted:cancel this meme sooner rather than later Done. |-haha, funny meme-||--------------------------cancelled------------------------|
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# ? Apr 21, 2021 15:04 |
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Paladinus posted:Done.
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# ? Apr 21, 2021 15:08 |
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90s Cringe Rock posted:Done. Lol, now that's funny
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# ? Apr 21, 2021 15:11 |
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LifeSunDeath posted:cancel this meme sooner rather than later Sorry about your lack of funny.
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# ? Apr 21, 2021 15:12 |
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MarcusSA posted:Sorry about your lack of funny. Oh drat.
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# ? Apr 21, 2021 15:15 |
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LifeSunDeath posted:Lol, now that's funny sorry
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# ? Apr 21, 2021 15:16 |
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90s Cringe Rock posted:not really Oof, drat. I've got it all wrong.
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# ? Apr 21, 2021 15:17 |
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How it started:90s Cringe Rock posted:not really How it's going: LifeSunDeath posted:Oof, drat. I've got it all wrong.
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# ? Apr 21, 2021 15:20 |
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First good picture in last 2 pages gently caress you all
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# ? Apr 21, 2021 15:39 |
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flavor.flv posted:Thats okay I'll do it I like these
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# ? Apr 21, 2021 15:59 |
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Regarde Aduck posted:First good picture in last 2 pages No u
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# ? Apr 21, 2021 16:12 |
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Regarde Aduck posted:First good picture in last 2 pages
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# ? Apr 21, 2021 16:39 |
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Ad bot?
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# ? Apr 21, 2021 16:41 |
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# ? May 24, 2024 14:50 |
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not much, what's ad bot with you?
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# ? Apr 21, 2021 16:42 |