If the busy beaver sequence cannot be computed by turing machines and we have found the first few busy beaver numbers, does that make us at least as powerful as super-turing machines?
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Anonymous2010-08-01 16:31
999999999999999999999999999999999999999999999999999999999999999 mulitplied by 999999999999999999999999999999999999999999999999999999989999999999999.888999889999999999999
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Anonymous2010-08-01 18:24
I know this is a stupid question, but can someone explain to me what it means technically to grow faster than any computable function. I know a little recursion theory but I'm not familiar with function growth in any way, other than basic big-O notation, which is more in the realm of complexity than computability.
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Anonymous2010-08-01 19:32
The biggest number is 14.
Anything stated to the contrary is just a myth propogated by delusional atheists.
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Anonymous2010-08-01 23:53
>>4
No. Just because a sequence is uncomputable in general doesn't mean a specific term in the sequence cannot be computed.
>>6
A function g\colon\mathbb{N}\to\mathbb{N} grows faster than all computable functions if every computable function f\colon\mathbb{N}\to\mathbb{N} satisfies f(n)<g(n) for all sufficiently large n.
>>8
what's an example of a function that is not computable
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Anonymous2010-08-03 17:39
>>11
The function which translates its input into C code (e.g., via ASCII), returns 0 if the resulting program runs successfully, and returns 1 if the resulting program doesn't compile or runs forever.
>>13
A function with a typo in that case would return 1. However the important point is that you cannot always know ahead of time whether or not a program will run forever. This is known as the halting problem, and it's unsolvability is the reason why the function he gave is not computable.
This ceased being true in the 17th century, but be sure to keep on buying into your completely outdated numerical theory.
The greatest number is 1 million.
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Anonymous2010-08-24 3:11
When it said "you have 15 seconds," my first thought was to just stack up nines, like so:
999999...
The limitation would just be how many 9's you could write in 15 seconds.
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Anonymous2010-08-24 12:24
>>16
you can easily outdo that using Knuth's up arrow notation.
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Anonymous2010-08-24 15:18
>>16
But then I think you have to name it, so you better know what to call it.
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Anonymous2010-08-24 18:42
>>16
You could write diagonally so that the "nine to the power of..."s wrap around back the card, wrap back around the front, and meet up with the original nine as the "latest" power.
>>19
One of the rules is that the number can't be infinite.
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Anonymous2010-09-10 23:52
∞
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Anonymous2010-09-11 15:53
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 at the 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999th power
I'm sure that most of you failed to read the link. In all honesty, this is nearly impossible. Since we're naming, the obvious answer is a "Googolplex," right? Isn't quite infinite, but there's no way in hell you can grasp how vast it is. It's impossible to write out a Googolplex, and it would tank a hell of a lot of computing for a computer.
Uhhh... I have the biggest number.
You can't have a bigger number than mine.
When I reveal it to the world... you will gasp in awe that I was among you.
Its a secret... and its funny that none of you know it!
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Anonymous2010-09-16 1:55
^^^^^^
Mine is bigger than yours
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Anonymous2010-09-22 14:00
>>31
Impossible. No one can make a number bigger than mine, as it is Super Infinity. He leaps over infinitely huge buildings in a single bound.
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Anonymous2010-09-22 19:17
Try this for size:
Ley A(x,y) be the Ackermann function.
and let B(z) be the busy-beaver function.
J(x,y)=B(A(A(x,y),A(x,y)))
This bad boy is noncomputable and its growth rate will blow your mind.