Image transcription

“what is the biggest number”

AI Overview

The biggest number in the world is so big that mathematicians don’t even think it exists.

Top 5 biggest numbers, according to me.

  1. 5
  2. 1 Million
  3. 100 Billion
  4. 999 Trillion
  5. Brazillian

Original post: https://xcancel.com/ChatgptLunatics/status/1995441330986598532

  • groucho@lemmy.sdf.org
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    5 months ago

    Here’s a fun game: ask gemini to accurately represent all digits in the largest number possible with a 64-bit float. So far I’ve gotten 0,000 and a 65,013-digit number that’s mostly zeroes.

    • Lemminary@lemmy.worldOP
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      5 months ago

      Interesting. This is what ChatGPT came up with which at least sounds plausible:

      The largest finite value representable in an IEEE-754 64-bit (double precision) float is

      DBL_MAX=(2−2−52)×21023=(253−1)×2971

      Its exact decimal expansion (all digits) is:

      179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368

      (309 decimal digits).

      Commonly shown in scientific notation: approximately
      1.7976931348623157 × 10^308 (this is the usual rounded display).

      • groucho@lemmy.sdf.org
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        5 months ago

        That … is doing a lot of the heavy lifting. Insist on accuracy in all 309 places and see what happens.

        Then ask it to find the prime factors.

        edit: it’s not about getting the right answer. it’s about hurting computers.

        • Lemminary@lemmy.worldOP
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          5 months ago

          I would but I don’t have the depth of knowledge for this. I just wanted to see if it’d spit out some nonsense. 😅

    • underisk@lemmy.ml
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      5 months ago

      They aren’t deterministic. There are a few common ones that are cached, but if you get bad (or good?) RNG in the response generation you’ll never manage to get the same result as someone else.

    • Random Dent@lemmy.ml
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      5 months ago

      I asked the Brave search AI thing and it said this:

      what is the biggest number

      There is no largest number because the set of natural numbers is infinite; for any number you can think of, adding one produces a larger number. While infinity is often mentioned, it is not a number but an abstract concept representing boundlessness.

      Among named numbers, a googol ( 10^100 ) is a 1 followed by 100 zeros, and a googolplex ( 10^googol ) is 1 followed by a googol of zeros, making it vastly larger than a googol. The googolplex is so large that writing it out would require more space than the observable universe contains.

      However, even larger numbers exist in mathematical contexts. Graham’s number, used in a proof in Ramsey theory, is significantly larger than a googolplex and was once considered the largest number used in a legitimate mathematical proof. It is so immense that it cannot be expressed using standard scientific notation and requires special notations like Knuth’s up-arrow or Conway chained arrow notation.

      Other extremely large numbers include TREE(3), which grows faster than any primitive recursive function and is independent of weak arithmetic systems, and Friedman’s SSCG(3), which is much larger than TREE(3). The Busy Beaver function produces numbers that are uncomputable and exceed any computable function.

      Rayo’s number is defined as “the smallest positive integer bigger than any finite positive integer named by an expression in the language of first-order set theory with a googol symbols or less” and is considered one of the largest named numbers. Similarly, BIG FOOT is a number proposed as even larger than Rayo’s number.

      In summary, while numbers like a googolplex are often cited as the largest named numbers, mathematical constructs such as Graham’s number, TREE(3), and Rayo’s number are vastly larger and demonstrate that there is no upper limit to how large a number can be.

      No idea if that’s accurate or not but it sounds legit lol.

  • [object Object]@lemmy.ca
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    5 months ago

    It’s true. If you ask a mathematician what number is the biggest they won’t give you a straight answer.

    Like, what even is an aleph?

    • jambudz@lemmy.zip
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      5 months ago

      There is no biggest number. By virtue of the real numbers (the largest orderable set) being unbounded, for every number in R you can find a number larger. You can also find a number smaller for any number.

    • prime_number_314159@lemmy.world
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      5 months ago

      In set theory, sets containing an infinite number things are relatively easy to describe. For example, “All the counting numbers” is a set with an infinite number of things in it.

      Many sets with an infinite number of things have a one to one correspondence to each other, meaning that we can describe a function that takes elements of one set as an input, gives elements of the other set as an output, and spans both sets - no element is skipped on either side.

      “All the even counting numbers” has a one to one correspondence with “All the counting numbers”. You can look into Hilbert’s Hotel for a good demonstration of how this works.

      Not all sets with an infinite number of things correspond with the set of all counting numbers, because some are fundamentally bigger. This difference in size doesn’t happen just once (e.g. there are countably infinite sets, and uncountably infinite sets, and that’s all we need to know), there are actually an infinite number of sets of progressively bigger infinite numbers of elements.

      Because this is a confusing mess, we needed a way to keep track of how infinitely big each infinitely big set is, and the aleph cardinalities are the preferred way to do that. Any set with cardinality of aleph zero (aka “aleph null”) has a one to one correspondence with any other set with cardinality aleph zero. The same is true for every other aleph cardinality. Two sets of cardinality aleph thirty seven have a one to one correspondence with each other.

      Anyways, busy beaver(tree(aleph omega)) is the biggest number.

    • kromem@lemmy.world
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      5 months ago

      It’s quite plausibly real. Gemini can def get in shitposty basins and has historically had a fairly inconsistent coherence across samples.

    • Swaus01@piefed.social
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      5 months ago

      It’s so funny that Webb and Mitchell made that sketch, clearly poking fun at the tradition of gameshows in the UK, only for David Mitchell to end up marrying Victoria Coren, the host of Only Connect.

      I wonder if it came up during a date, and she forced him to pledge allegiance to only connect.