imagine

Comments

• exasperation@lemmy.dbzer0.com ⁨1⁩ ⁨month⁩ ago

  I’m imagining a set of big naturals

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  • MacNCheezus@lemmy.today ⁨1⁩ ⁨month⁩ ago

    Real

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  • humanspiral@lemmy.ca ⁨1⁩ ⁨month⁩ ago

    But that is smaller than the naturals

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• ivanafterall@lemmy.world ⁨1⁩ ⁨month⁩ ago

  I just imagined it? Now what?

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  • IrateAnteater@sh.itjust.works ⁨1⁩ ⁨month⁩ ago

    Well now you just triggered a false vacuum decay on the far side of the galaxy. Way to go.

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  • MajinBlayze@lemmy.world ⁨1⁩ ⁨month⁩ ago

    Now wrote a paper showing that your set is neither countably nor uncountably infinite and become the most famous mathematician I’ve replied to today

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    • ivanafterall@lemmy.world ⁨1⁩ ⁨month⁩ ago

      No, it’s private. You have no right to the things I imagine and that wasn’t the deal!

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    • Fedegenerate@lemmynsfw.com ⁨1⁩ ⁨month⁩ ago

      I have discovered a truly marvelous proof of this, which this margin comment is too narrow to contain.

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    • elevenbones@sh.itjust.works ⁨1⁩ ⁨month⁩ ago

      The proof of this has been left to the reader…

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• Monster96@lemmy.world ⁨1⁩ ⁨month⁩ ago

  Image

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• Kolanaki@pawb.social ⁨1⁩ ⁨month⁩ ago

  The limit is trying to be 100% unique and novel.

  Like, try to imagine a creature that has 0 inspiration from everything you know about real life.

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  • wagesj45@fedia.io ⁨1⁩ ⁨month⁩ ago

    Sounds like you're asking the human brain to fire in a pattern it's not even wired for. Random noise in the web, or even definitionally impossible as "totally alien" might imply a configuration of neurons opposite of what we have. I feel like I'm having a hard time describing my thought here.

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  • TheGuyTM3@lemmy.ml ⁨1⁩ ⁨month⁩ ago

    xighfkfutjgihugkghjgkckggdjjxubkctqjfhghhkhmhkhnvkcjfgrgshhgjdkguhjfjejtjgjffkcufjgjtiritu

    Okay i did it, now what

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    • Kolanaki@pawb.social ⁨1⁩ ⁨month⁩ ago

      You used english characters. Disqualified.

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• MonkderVierte@lemmy.zip ⁨1⁩ ⁨month⁩ ago

  Please translate.

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  • Batman@lemmy.world ⁨1⁩ ⁨month⁩ ago

    the cardinality of a set is the number of things in it.

    some sets have infinite items in them such as the counting numbers (there’s always a bigger fish dot jpeg). but not all infinities are equal some are larger.

    equality: if we can map a 1:1 rule between items in two sets with infinite items they are said to be equal infinities.

    greater: but if we can map all in one set to another and note that there are still items left over, the first set has more things in it so if the other set has infinity items in it, this collection must have an even larger set of items in it, a greater tier of infinite.

    a common example in math classes is mapping items in the real number between 0 and 1 to the counting numbers (1,2,3,…) using the rule 1>1/1, 2>1/2, 3>1/3,… we can see (0 to 1) has a 1:1 mapping but there are still more items (for instance 1/1.5). this shows there are more items in the real number line from 0 to 1 than there is items in the counting numbers. though both are infinite one infinity is larger.

    so the meme. it’s asking you to imagine a collection items that has greater number than the counting number infinity, but less than the next tier of infinity, those in the real number line. something which is hard to imagine because if it were easy we would have plugged that infinity tier into our tiering system.

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    • MonkderVierte@lemmy.zip ⁨1⁩ ⁨month⁩ ago

      Thanks!

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• BarbedDentalFloss@lemmy.dbzer0.com ⁨1⁩ ⁨month⁩ ago

  There are more rational numbers than natural numbers. There are more real numbers than rational numbers.

  Checkmate meme.

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  • procrastitron@lemmy.world ⁨1⁩ ⁨month⁩ ago

    The problem is that rational numbers can be mapped to the integers (e.g. just encode each rational number as an integer), so there are not more rational numbers than integers.

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    • BarbedDentalFloss@lemmy.dbzer0.com ⁨1⁩ ⁨month⁩ ago

      No that’s not true. There are rational numbers in between the integers. Therefore the mapping between integers to rational numbers is injective and thus there are more rational numbers than integers.

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  • TheGuyTM3@lemmy.ml ⁨1⁩ ⁨month⁩ ago

    Well, there are more integers than naturals, yet both share the same cardinality. Also, I thing hilbert’s hotel problem shows that rationals and naturals also share the same cartinality, somehow. You could arrange every rational in a line like the naturals and the integers.

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  • borokov@lemmy.world ⁨1⁩ ⁨month⁩ ago

    That’s not how cardinality works when dealing with infinite. For ex, there are the same number of prime number than number of integer. Yes, there are many non prime inter between 2 prime integer, but as long as you can “count” them, they have the same cardinality, which is called “aleph 0”.

    But you cannot “count” real number. There are actually more real between 0 and 1 than there are interger. This value is called “aleph 1”.

    Yes, there is also aleph 2, aleph 3,… There is not a single “infinite”, but there are several one that don’t have the same size.

    Have a look to Hilbert’s hotel paradox en.wikipedia.org/…/Hilbert's_paradox_of_the_Grand…

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• chuckleslord@lemmy.world ⁨1⁩ ⁨month⁩ ago

  Imagine a 4D object if you think human imagination is limitless. Good luck

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  • gandalf_der_12te@discuss.tchncs.de ⁨1⁩ ⁨month⁩ ago

    x ∈ ℝ⁴, there done

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  • Tetragrade@leminal.space ⁨1⁩ ⁨month⁩ ago

    Ok I did. Im just built different.

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  • Venus_Ziegenfalle@feddit.org ⁨1⁩ ⁨month⁩ ago

    You can project a 4D object onto a 3D space just like you can project a 3D object onto a 2D plane. If you use stereoscopic trickery you can for example watch a tesseract rotate on a phone screen. Don’t ask me how I know but if you spend an evening doing that sorta thing on shrooms 4D geometry might start feeling intuitive to you. Your physical senses are limited to three dimensions, your mind genuinely isn’t.

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  • borokov@lemmy.world ⁨1⁩ ⁨month⁩ ago

    She did: en.wikipedia.org/wiki/Alicia_Boole_Stott

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  • BrilliantantTurd4361@sh.itjust.works ⁨1⁩ ⁨month⁩ ago

    moves a cube

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• gigastasio@sh.itjust.works ⁨1⁩ ⁨month⁩ ago

  I imagined a bunny wearing a kimono singing Bring Me the Horizon covers. ❤️

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  • reseller_pledge609@lemmy.dbzer0.com ⁨1⁩ ⁨month⁩ ago

    That actually sounds awesome. I’d pay to go to that show.

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• TriangleSpecialist@lemmy.world ⁨1⁩ ⁨month⁩ ago

  Georg Cantor in shambles.

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• Siegfried@lemmy.world ⁨1⁩ ⁨month⁩ ago

  What about all reals > 0?

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  • suckdings@sh.itjust.works ⁨1⁩ ⁨month⁩ ago

    Same as the cardinality of all reals. In fact, the cardinality of the set of all reals between 0 and 1 is the same as the cardinality of the set of all reals. en.wikipedia.org/…/Cardinality_of_the_continuum#S…

    Glad you made me look though, I hadn’t thought about whether there were sets with cardinality greater than the cardinality of the continuum.

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• rmuk@feddit.uk ⁨1⁩ ⁨month⁩ ago

  Maybe I would if my spare brain capacity wasn’t being used to rotate cows.

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  • marcos@lemmy.world ⁨1⁩ ⁨month⁩ ago

    Just imagine them invariant to any 3D rotation.

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    • rmuk@feddit.uk ⁨1⁩ ⁨month⁩ ago

      Great, now I’m imaging a universe rotating around a stationary cow.

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• Dadifer@lemmy.world ⁨1⁩ ⁨month⁩ ago

  Another way of stating the difference between natural vs. real sets is that you can’t count every real number. What’s in between? A set where you can count some significant portion?

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  • FishFace@piefed.social ⁨1⁩ ⁨month⁩ ago

    Are you saying that there’s nothing in between? Prove it, and turn modern mathematics inside out!

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• umbrella@lemmy.ml ⁨1⁩ ⁨month⁩ ago

  [deleted]

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  • JackbyDev@programming.dev ⁨1⁩ ⁨month⁩ ago

    Olo is a good example. It’s due to a quirk of human perception and the structure of our eyes. They basically designed a machine to try and stimulate the green detecting cones without stimulating the red detecting cones. Normally if something pure green hits your eyes, it stimulates those red cones too. So this is something our bodies are capable of perceiving but not something that we can ever perceive under normal circumstances.

    Is it a “new color”? Not exactly. Did it take a good bit of imagination to conceive trying to get our brains to see it? Yes.

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    • HulkSmashBurgers@reddthat.com ⁨1⁩ ⁨month⁩ ago

      That’s wild. So the only people who have seen olo are ones who’ve had their eyes laser beamed.

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• kryptonianCodeMonkey@lemmy.world ⁨1⁩ ⁨month⁩ ago

  The set of Real numbers excluding the Naturals

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• mEEGal@lemmy.world ⁨1⁩ ⁨month⁩ ago

  Correct me if.I’m wrong but the Continuum Hypothesis was proven undecidable. So we can chose to add CH (false or true, whichever we like) to ZFC without changing anything meaningful about ZFC.

  But then, if we chose it to be true, could we construct such a set ?

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  • kogasa@programming.dev ⁨1⁩ ⁨month⁩ ago

    If you could construct such a set, it wouldn’t be independent of ZFC

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    • mEEGal@lemmy.world ⁨1⁩ ⁨month⁩ ago

      Thanks for the insight !

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• hakunawazo@lemmy.world ⁨1⁩ ⁨month⁩ ago

  Brain: Inhale, exhale…

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• Ad4mWayn3@sh.itjust.works ⁨1⁩ ⁨month⁩ ago

  I just imagined the set of countable ordinals, and there’s a universe where I’m right

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• thoughtfuldragon@lemmy.blahaj.zone ⁨1⁩ ⁨month⁩ ago

  If there was one, would that imply cardinality might be continuous rather than discrete?

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