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
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The largest number representable in 64 bits
21–30 of 98 posts
Re: The largest number representable in 64 bits
#22I'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…
As I've replies several times before, we don't allow arbitrary mappings.
We allow computable mappings but consider only obviously non-cheating languages like Turing machines
or lambda calculus or Linux's bc or any existing programming language, that are not geared toward outputting insanely large numbers.
Re: The largest number representable in 64 bits
#23It all goes over my head, but, what does the distribution of values look like? e.g. for unsigned integers its completely flat, for floating point its far too many zeros, and most of the numbers are centered around 0, what do these systems end up looking like?
Re: The largest number representable in 64 bits
#24Given 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
That is not a number, that is infinity.
The (implicit) rules of the game require the number to be finite. The reason for this is not that infinity is not obviously "the largest" but that the game of "write infinity in the smallest number of {resource}" is trivial and uninteresting. (At least for any even remotely sensible encoding scheme. Malbolge[1] experts may chime up as to how easy it is to write infinity in that language.) So if you like, pretend we played that game already and we've moved on to this one. "Write infinity" is at best a warmup for this game.
(I'm not going to put up another reply for this, but the several people posting "ah, I will cleverly just declare 'the biggest number someone else encodes + 1'" are just posting infinity too. The argument is somewhat longer, but not that difficult.)
Re: The largest number representable in 64 bits
#25Re: The largest number representable in 64 bits
#26I'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…
As I've replies several times before, we don't allow arbitrary mappings. We allow computable mappings but consider only obviously non-cheating languages like Turing machines or lambda calculus or Linux's bc or any existing programming language, that are not geared toward outputting insanely large numbers.
I would say that all of those seem both arbitrary and geared toward outputting insanely large numbers (in the sense that the output of any Turing-complete language is). Now if you can make these claims in a mathematical rigorous way (i.e. without relying on a particular mapping like Turing Machines / Lambda Calculus, and without silly "up to a constant factor" cheats) then that would be more interesting.
Re: The largest number representable in 64 bits
#27Whatever largest number you can express in your system, I can represent a larger one in only one bit, using the following specification.
0=your largest number 1=your largest number + 1
Re: The largest number representable in 64 bits
#28Whatever largest number you can express in your system, I can represent a larger one in only one bit, using the following specification. 0=your largest number 1=your largest number + 1
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Re: The largest number representable in 64 bits
#29[deleted]
Re: The largest number representable in 64 bits
#30Whatever largest number you can express in your system, I can represent a larger one in only one bit, using the following specification. 0=your largest number 1=your largest number + 1
To be pedantic, that is a instance of the Berry paradox [1] and no you can not [2] as that would be a violation of Godel's incompleteness theorems.
edit: To clarify further, you could create a new formal language L+ that axiomatically defines 0 as "largest number according to L", but that would no longer be L, it would be L+. For any given language with rules at this level of power you could not make that statement without creating a new language with even more powerful rules i.e. each specific set of rules is capped, you need to add more rules to increase that cap, but that is a different language.
[1] https://en.wikipedia.org/wiki/Berry_paradox
[2] https://terrytao.wordpress.com/2010/11/02/the-no-self-defeat...