51–60 of 98 posts
The largest number representable in 64 bits - https://news.ycombinator.com/item?id=38414303 - Nov 2023 (105 comments)
The largest number representable in 64 bits - https://news.ycombinator.com/item?id=35677148 - April 2023 (42 comments)
(I haven't put 2023 in the current title since the article says it's been significantly expanded since then.)
What's the biggest up-arrow notation number you can spell with 64 bits? https://mathworld.wolfram.com/KnuthUp-ArrowNotation.html
`9↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑9` seems like a reasonable guess (barring encoding cheats/trickery like @masfuerte commented!) Edit: I've misread the above comment and my number is is 64 bytes (significantly more than 64 bits . The largest 64 bit number through my approach would be `9↑↑↑↑↑↑9`, which is significantly smaller.
I'm going to agree with the downvoted people and say that this sort of approach is largely meaningless if you allow arbitrary mappings. IMO the most reasonable mathematical formulation given the structure of the integers (in the sense of e.g. Peano) is that to truly represent an integer you have to represent zero and each other representable number has a representable predecessor, i.e. to say you can represent 5 you…
You're imposing an abitrary set of preferred numbers, which is boring and useless for measuring large things.
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To find the largest number that is computable by a program of at most 64 bits in a non-cheating language; i.e. one that's not geared toward producing large numbers.
Do you have a mathematical formulation, or? Ultimately you seem to pick a random definition of computing and size and then work with that?
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It isn’t actually infinite since it can only do a finite number of iterations per second (though it would be large!), and there are only a finite number of seconds in the universe (near as we can tell).
This game assumes the computations run to completion on systems that will never run out of resources. No one in this universe will ever compute Ackerman's Number, BB(6), or the final answer given in the post. Computations that never complete are infinite. If you are playing this game and can't produce a number that doesn't fit in this universe you are probably better suited playing something else. That's just table s…
Earlier quoted context omitted.
Do you have a mathematical formulation, or? Ultimately you seem to pick a random definition of computing and size and then work with that?
"Computable" has a well-known standard definition in this context, meaning a computable function[1]. In a given model of computation, a computable function is one for which an algorithm exists which computes the value of the function for every value of its argument. For example, the successor function adds 1 to an input number, and is computable. The halting problem (determine whether a program given in the argument…
Earlier quoted context omitted.
`9↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑9` seems like a reasonable guess (barring encoding cheats/trickery like @masfuerte commented!) Edit: I've misread the above comment and my number is is 64 bytes (significantly more than 64 bits . The largest 64 bit number through my approach would be `9↑↑↑↑↑↑9`, which is significantly smaller.
Is there any intuition on how big this number is?
Given time, this will output a bigger number, and it is only 48 bits: B0 39 mov al,'9' //load character '9' to AL CD 29 int 29h //print to screen EB FA jmp short -6 //go again
Hi guys, I've come up with a new 64 bit number representation where 0xFFFFFFFF is infinity. Hell you know what every value is just infinity.