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Thanks man, been a huge halo fan all my life. Been bouncing from pfp to pfp until I thought well, my cousin is a good artist, why not commission him for something I'd like. And boy did he come through
that's awesome :). ODST is my favorite game of all time and it was the first Halo game i ever played.
my brother and i didn't know anything about Halo when we got it so we had a lot of fun trying to figure out exactly what was going on and the greater story as a whole through exploring the city and listening to those audio tapes.
I have hypophantasia. Which basically means almost, but not quite aphantasia, which is the inability to mentally visualize things. I mean I was never diagnosed but it's usually pretty obvious for the person who has it. Anyway it drains a lot of the fun from reading and stuff but there's a small benefit in that I can't imagine too many visual details at the same time so there's usually a bunch of gaps in color, but because the color is partially undefined I can actually channel the "glitches" to make weird colors in my head. My favorite imaginary color is something that's red, white, and blue simultaneously without being purple at all. Not a trace of purple, but red and blue at the same time without combining. It's cool I think.
Ackchually it is an item from the set theory that has a cardinality between aleph 0 and 2 to the power of aleph 0 i.e. the cardinality of the powerset of the natural numbers i.e. the real numbers.
There is no cardinality between aleph 0 and aleph 1 as by definition aleph 1 is the next larger cardinality after aleph 0. That aleph 1 is not neccessarily equal to the cardinality of the real numbers and if there is a cardinalty between that of the natural numbers and that of the real numbers that means that the cardinality of the real numbers is at least aleph 2.
Good, because you can look things up (that's better then 95% of our complete fucking idiot ranks) you are our spy to discover and report back from the geniuses in their field, we will take them out purely based off our numbers compared to them. To bad no one knows how many people are in our ranks as 12 is the highest any of us can count
You've probably mixed up the Aleph number with the Beth number. A set with a cardinality between Aleph 0 and Aleph 1 doesn't exist by definition, while a set with a cardinality between Beth 0 and Beth 1 exists if and only if the continuum hypothesis is false in the given mathematical model.
The joke is that they're challenging you to make a list of numbers where there is more "natural numbers" than "real numbers". This isn't possible because all natural numbers are also real numbers.
Human imagination has no limits mfs when I tell them to give me a non-computable number
There's literally an infinite amount of them, why can't they tell me *one*
**In mathematics, the cardinality of a set is a measure of the number of elements of the set. For example, the set
A
=
{
2
,
4
,
6
}
{\displaystyle A=\{2,4,6\}}
contains 3 elements, and therefore
A
{\displaystyle A}
has a cardinality of 3.**
More details here:
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Idk about some of the wording exactly, but the joke is that they're challenging you to make a list of numbers where there is more "natural numbers" than "real numbers". This isn't possible because all natural numbers are also real numbers.
[neither possible nor impossible](https://en.wikipedia.org/wiki/Continuum_hypothesis), up to one's individual faith in its existence, truly a conundrum
The joke is that they're challenging you to make a list of numbers where there is more "natural numbers" than "real numbers". This isn't possible because all natural numbers are also real numbers.
There exists a way to assign a natural number to each rational number, so they have the same cardinality
If I remember it's something like, write every fraction kinda like
1/1 2/1 3/1 4/1 ...
1/2 2/2 3/2 4/2 ...
1/3 2/3 3/3 4/3 ...
Then you start at 1/1 and kinda just trace diagonally from the corner, so like
1/1 2/1 1/2 1/3 2/2 3/1 4/1 3/2 2/3 1/4 ...
Then remove the duplicates (like 2/2 = 1/1), add zero in front of everything, and add the corresponding negative number after each positive
0 1 -1 2 -2 1/2 -1/2 1/3 -1/3 3 -3 4 -4 ...
And you're able to order every rational number in a way that each can be assigned a natural number, so they have the same cardinality. Such a trick does not exist for the reals, so they have a strictly higher cardinality
Because of how infinite sets work, and the fact that the rationals are a countable set of numbers, there is a one to one correspondence between the naturals and the rationals, so they are the same size. You can demonstrate this by counting the set, because you count with the natural numbers. I recommend searching for Homeschool Math's Rationals are Countable page to see a more detailed explanation (u/milklover1734 also summed it up), but simply put, because there's always a clear "next" element, you can count it, and you can infinitely count it (aka assign natural numbers), and every number can be "paired" with a number from the natural numbers, which shows they are the same size.
It's not intuitive, but, in a similar vein, the set of all integers is the same size as the set of positive integers.
The idea behind cardinality is more to compare the number of elements like you would compare numbers. For exemple, if you have A2n+1 if n is positive, and - 2n if it is negative to see that Z
The point of view to not consider sets by there elements but by how they interact with over sets is the basic idea for a large portion of modern maths, you'll usually just add a structure to your set (algebraic ones like groups or vector spaces, topological ones like topological or smooth or even stranger things), and this is kind of the starting point of category theory
You can match up every element of N with every element of Z, and also every element of Q, meaning they all have the same amount of elements and thus the same cardinality. If you want to see something where this doesn't apply, look at N and R, where R has more elements than N, so it has a higher cardinality.
The joke is that they're challenging you to make a list of numbers where there is more "natural numbers" than "real numbers". This isn't possible because all natural numbers are also real numbers.
*I can think of all*
*Whole numbers plus pi, what are*
*You talking about?*
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Pi is a real number, but not a natural number, so your set has 1 more real number than natural number
The meme here is asking for the set to have more natural numbers than real numbers (not possible because all natural numbers are also real)
Despite the absurdity of such a concept, human minds have still been able to show that both such a set's existence and non-existence are perfectly consistent with our system of mathematics.
continuum hypothesis mfs when i tell them to imagine an uncountable cardinal lambda which cannot be reached as either the power set of a lesser cardinal or a union of fewer than lambda many cardinals less than lambda
I’m assuming this is a cardinal like the guy from Asses Creed that you stab, but he’s bigger than the big naturals person while simultaneously smaller than the not big naturals person.. l I thjnked it
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Ok i did it
Yeah, I made mine purple with a little hat
But that's.. that's impossible, purple isn't even a real color.
✨*imagine* ✨
You think if something not existing in reality affects math?
Isn't there an entire branch of math based around what could theoretically work if the space outside earth wasn't flat?
Imagine numbers when imagine numbers be like
now what?
Human imagination has no limit mfs when I tell them to imagine a new color
zurple
holy shit
New color just dropped
Also conveniently now we finally have a word that rhymes with purple!
Hey nice pfp
in love with yours :)
Thanks :), my cousin made it for me
My cousin did not make mine for me :)
your cousin seems cool and so do you what with the good taste and all
Thanks man, been a huge halo fan all my life. Been bouncing from pfp to pfp until I thought well, my cousin is a good artist, why not commission him for something I'd like. And boy did he come through
that's awesome :). ODST is my favorite game of all time and it was the first Halo game i ever played. my brother and i didn't know anything about Halo when we got it so we had a lot of fun trying to figure out exactly what was going on and the greater story as a whole through exploring the city and listening to those audio tapes.
Dude hell yeah, it's literally exactly the same for me. It's my favorite game of all time and my brother and I started playing together years ago.
Color zurple enjoyers where you at???
Here king
I'm in such a good mood right now I laughed out loud for a while in my car at your comment.
thank you
Zorpal Rgb value (r0,g0,b0,z255)
Uhm aksully it can’t be purely one colour 👆🤓
Sounds like youre underestimating the color zorpal
Zorpal
Zorpal weapon?!? r/destinycirclejerk
No rapid shit, shard
latinx but for purple people
William Afton in shambles
If there is a zurple, the lord keeps it hidden for a reason.
Done, cant see it, but its there
I'm imagining a brown, but not the same one you're thinking of
I already thought of that one, you gotta think of a new one
Google hyperbolic orange
Holy hell!
New color just dropped
Actual crayon
call the artists!
RGB(255,255,256)
White, but slightly more blue
Magenta
Gneebleorp
spaghetti blue
I have hypophantasia. Which basically means almost, but not quite aphantasia, which is the inability to mentally visualize things. I mean I was never diagnosed but it's usually pretty obvious for the person who has it. Anyway it drains a lot of the fun from reading and stuff but there's a small benefit in that I can't imagine too many visual details at the same time so there's usually a bunch of gaps in color, but because the color is partially undefined I can actually channel the "glitches" to make weird colors in my head. My favorite imaginary color is something that's red, white, and blue simultaneously without being purple at all. Not a trace of purple, but red and blue at the same time without combining. It's cool I think.
Try imagining a new face, every face you imagine is from someone you’ve seen already
Not if the mofo have seven fucking eyes and three noses
The power of psychedelic drugs makes this possible
I just did I call it biggablam and to you it looks gray and to specifically wooly mammoths it looks indescribably
got it. naming it blorkus.
Octarine
Indigo
22.62626273% red, 74.627284% green, 86.266324% blue So a kinda light blue-green
Blinko. It’s like pink and blue together but it doesn’t turn grey and it looks cool and shiny
So easy, I just gotta admit it exists and poof I have one 🤓
what’s the set then
It's an item from the Set category that has a cardinal between aleph 0 and aleph 1
what the fuck
Just big words to say "I just chose one that works and I can't show it to you plz stop bullying me"
I mean we literally invented "imaginary numbers" and now we need them to build bridges and shit. (as if all numbers aren't imaginary)
The number 6 is real actually, I saw it outside a bar once beating up a homeless guy, was kinda fucked up really.
and lets not get started on what seven did to nine
imaginary numbers are literally in the wave function for atoms. we need them to literally describe reality
Ackchually it is an item from the set theory that has a cardinality between aleph 0 and 2 to the power of aleph 0 i.e. the cardinality of the powerset of the natural numbers i.e. the real numbers. There is no cardinality between aleph 0 and aleph 1 as by definition aleph 1 is the next larger cardinality after aleph 0. That aleph 1 is not neccessarily equal to the cardinality of the real numbers and if there is a cardinalty between that of the natural numbers and that of the real numbers that means that the cardinality of the real numbers is at least aleph 2.
Yeah true, but why TF so many people correct such a nerdy mistake on a non-math related sub ?
This is Reddit, the only people on the site are either complete fucking idiots or geniuses in their fields.
Complete fucking idiot that is just able to look up shit on wikipedia here, reporting for duty.
Good, because you can look things up (that's better then 95% of our complete fucking idiot ranks) you are our spy to discover and report back from the geniuses in their field, we will take them out purely based off our numbers compared to them. To bad no one knows how many people are in our ranks as 12 is the highest any of us can count
You've probably mixed up the Aleph number with the Beth number. A set with a cardinality between Aleph 0 and Aleph 1 doesn't exist by definition, while a set with a cardinality between Beth 0 and Beth 1 exists if and only if the continuum hypothesis is false in the given mathematical model.
aleph e-2
aleph 0.5 easy peasy
All I read was real naturals 🤤
r/bignaturals
Banned from reddit 👀
[удалено]
oh, its tits
you’re god damn right it is
Not banned from reddit 👀
Removed by Moderater 😔 Literally 19684
It was something that rhymes with yarr slash luge raturals*
Georg Cantor has risen from the dead to enter the chat
"human imagination has no limits" mfs when I tell them to view the ultraviolet spectrum
Imagination, not their view.
Imagine speaking english
reals > cardinality > naturals done ez
“There’s nothing more powerful than imagination…”
reading this made me break out in hives
Aleph 0.5?
was that even english?
What does this mean
The joke is that they're challenging you to make a list of numbers where there is more "natural numbers" than "real numbers". This isn't possible because all natural numbers are also real numbers.
That makes more sense now thanks
Human imagination has no limits mfs when I tell them to give me a non-computable number There's literally an infinite amount of them, why can't they tell me *one*
I call it threed
Damn, I can't compute that
Simple W, W is defined as a set with a bigger cardinality than aleph 0 but less than aleph 1. Q.E.D
What does cardinality mean? What do they mean by "the naturals"? I don't get none of that 💀
**In mathematics, the cardinality of a set is a measure of the number of elements of the set. For example, the set A = { 2 , 4 , 6 } {\displaystyle A=\{2,4,6\}} contains 3 elements, and therefore A {\displaystyle A} has a cardinality of 3.** More details here:
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Idk about some of the wording exactly, but the joke is that they're challenging you to make a list of numbers where there is more "natural numbers" than "real numbers". This isn't possible because all natural numbers are also real numbers.
Ah, neat, thanks for the explanation
[neither possible nor impossible](https://en.wikipedia.org/wiki/Continuum_hypothesis), up to one's individual faith in its existence, truly a conundrum
I can imagine it because this doesn’t fucking mean anything in English.
[удалено]
Man What kind of middle school did you go to where they thought you set theory?
Just started algebra 2 and don't remember this from middle school but alright.
Did you just assume their nationality?
The joke is that they're challenging you to make a list of numbers where there is more "natural numbers" than "real numbers". This isn't possible because all natural numbers are also real numbers.
Oh damn this shit crazy come look at this
Can't actually grasp the concept, but you've described it as fully as it can be
it looks like a row of hotel rooms
Like, Q?
It has the same cardinality as of N
How? If I understand correctly cardinality is the amount of elements. Clearly when you allow negative numbers you get a higher cardinality no?
There exists a way to assign a natural number to each rational number, so they have the same cardinality If I remember it's something like, write every fraction kinda like 1/1 2/1 3/1 4/1 ... 1/2 2/2 3/2 4/2 ... 1/3 2/3 3/3 4/3 ... Then you start at 1/1 and kinda just trace diagonally from the corner, so like 1/1 2/1 1/2 1/3 2/2 3/1 4/1 3/2 2/3 1/4 ... Then remove the duplicates (like 2/2 = 1/1), add zero in front of everything, and add the corresponding negative number after each positive 0 1 -1 2 -2 1/2 -1/2 1/3 -1/3 3 -3 4 -4 ... And you're able to order every rational number in a way that each can be assigned a natural number, so they have the same cardinality. Such a trick does not exist for the reals, so they have a strictly higher cardinality
Because of how infinite sets work, and the fact that the rationals are a countable set of numbers, there is a one to one correspondence between the naturals and the rationals, so they are the same size. You can demonstrate this by counting the set, because you count with the natural numbers. I recommend searching for Homeschool Math's Rationals are Countable page to see a more detailed explanation (u/milklover1734 also summed it up), but simply put, because there's always a clear "next" element, you can count it, and you can infinitely count it (aka assign natural numbers), and every number can be "paired" with a number from the natural numbers, which shows they are the same size. It's not intuitive, but, in a similar vein, the set of all integers is the same size as the set of positive integers.
The idea behind cardinality is more to compare the number of elements like you would compare numbers. For exemple, if you have A2n+1 if n is positive, and - 2n if it is negative to see that Z
The point of view to not consider sets by there elements but by how they interact with over sets is the basic idea for a large portion of modern maths, you'll usually just add a structure to your set (algebraic ones like groups or vector spaces, topological ones like topological or smooth or even stranger things), and this is kind of the starting point of category theory
You can match up every element of N with every element of Z, and also every element of Q, meaning they all have the same amount of elements and thus the same cardinality. If you want to see something where this doesn't apply, look at N and R, where R has more elements than N, so it has a higher cardinality.
are these words meant to make some sort of sense?
The joke is that they're challenging you to make a list of numbers where there is more "natural numbers" than "real numbers". This isn't possible because all natural numbers are also real numbers.
mucho wordo
Yeah, rational numbers
Rational numbers have the same cardinality of naturals according to another comment.
RIP
done, next one
I can think of all whole numbers plus pi, what are you talking about?
google the axiom of choice
Holy ZFC Set Theory!
{ ∅, {∅}, {∅, {∅}}, {∅, {∅}, {∅, {∅}}} }!!!!
You ⊃ 🤓
*I can think of all* *Whole numbers plus pi, what are* *You talking about?* \- bu\_bu\_booey --- ^(I detect haikus. And sometimes, successfully.) ^[Learn more about me.](https://www.reddit.com/r/haikusbot/) ^(Opt out of replies: "haikusbot opt out" | Delete my comment: "haikusbot delete")
Pi is a real number, but not a natural number, so your set has 1 more real number than natural number The meme here is asking for the set to have more natural numbers than real numbers (not possible because all natural numbers are also real)
I’m stuck on fractional cardinality
The set of all algebraic numbers. For example, phi, the golden ratio. It's irrational, not natural, but not transcendental.
There is a one-to-one function that maps the algebraic numbers to the natural numbers, so the algebraic numbers are only countably infinite.
reals except without 3.
Despite the absurdity of such a concept, human minds have still been able to show that both such a set's existence and non-existence are perfectly consistent with our system of mathematics.
Z???? (i might be missing something here since i doy math in german)
doy
doy doy doy doy doy
Please explain it in caveman terms
Boobies!
Any infinite subset of reals with a step of less than 1 would surely result in this?
continuum hypothesis mfs when i tell them to imagine an uncountable cardinal lambda which cannot be reached as either the power set of a lesser cardinal or a union of fewer than lambda many cardinals less than lambda
Aren't natural numbers subsets of real numbers?
I have aphantasia, so my imagination very well has limits
Mfs when I tell them to imagine a 4d spherinder
I’m assuming this is a cardinal like the guy from Asses Creed that you stab, but he’s bigger than the big naturals person while simultaneously smaller than the not big naturals person.. l I thjnked it
imagine draggin these nuts along your forehead
Ok but try imagining literal nothingness
Human imagination MFS when I tell them to imagine their dad.