Sure you can construct a Turing Machine with bounded tape, as long as you can prove that the tape is long enough. If you are really picky about words - this machine with bounded tape is exactly equivalent to a "true" Turing Machine with unbounded tape, thus, for all senses and purposes, is a Turing Machine.
and most mathematicians probably have a strong expectation that it doesn't matter whether you pick some other foundation, Wiles' proof will still be valid.
what do you mean by a proof being valid in another set of axioms? that there is a simple way to translate the proof into the 2nd system and it'll be true then?
the set of all statements is countable, so is the subset of all true statements. however, it doesn't mean you can count it:) There "exists" a way to count it, but nobody knows how. (Some people think that's just B.S. and reject such mathematics)
that sounds good, except 1. number theory is not axiomizable, its truth is not effectively enumerable. 2. an axiomized theory is enumberale, but why these axioms? are they consistent? are they... true? 3. not all theorems are equal, human obviously have a way to focus on "interesting" ones, that's not what a mechanized list can satisfy. 4. enumerability is just theoretical, there is no efficient algorithm at all.
It does not work that way. It's up to the experts to pick the arbitrary anecdotal events that supports the theory sentimentally. If you do it, you are just a stupid whore of big oil companies who doesn't know anything about scientific methods.
Global Warming is unfalsifiable. No matter what happens, the experts will find it supporting global warming. Can they give us ONE possible event that can falsify Global Warming? Nope. Can you imagine any event that could convince the experts to drop their theory? Nope.
Of course, it's the damn free market and evil big corporations. It's not like government has done anything wrong in this case... our governments obviously still don't have enough power to shape the contents on internet.
Dictatorship is the most efficient system in decision making.
And politicians in a 'democratic' system knows this as well. It's not unusual to delegate one person(I'm even not talking about an elected one) the sole decision making power on extremely important issues.
And I recommend Ruby on Rails. Its developer community has been growing exponentially, from 5 guys in 2006 to 10 guys in 2007. If you are extra conservative, you can try Groovy on Rails. It's just like Java, but better.
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Neonderthals are STILL ALIVE! They're just called Neocons today. See Dick Cheney.
No, Cheney is just a cousin.
Sure you can construct a Turing Machine with bounded tape, as long as you can prove that the tape is long enough. If you are really picky about words - this machine with bounded tape is exactly equivalent to a "true" Turing Machine with unbounded tape, thus, for all senses and purposes, is a Turing Machine.
without EU, France would have forced this law across Europe.
does anyone know why they have to implement it with cookies and redirects? (according to wikipedia)
couldn't they have done this silently and leave users completely unaware of it?
Has AP banned all photos originated from Iran? No, that would be very retarded.
You quote the information, and you give the source, that's all.
"This is the promo shot of the new General provided by DoD" - what's the problem?
This country is becoming more queer everyday.
that is a fucking stupid made up word.
basically it's like cavity search for the internet.
Next smallest and most regular syntax for a useful language is probably smalltalk
What?! You are saying that Turing Machine Language is not a useful language?
Is it Grammar Nazi, or Grammar Nazis?
Gov should mandate people to work during night time, then you'll get all the day lights to yourself.
You have just described Godel's theorems perfectly according to http://uncyclopedia.wikia.com/wiki/Incompleteness_Theorem
can human brain be simulated by a Turing machine? It's plausible that human brain obey physics - but is physics Turing computable?
Of course we can create physical machines that's the same as human brains - million of of them everyday:)
and most mathematicians probably have a strong expectation that it doesn't matter whether you pick some other foundation, Wiles' proof will still be valid.
what do you mean by a proof being valid in another set of axioms? that there is a simple way to translate the proof into the 2nd system and it'll be true then?
the set of all statements is countable, so is the subset of all true statements. however, it doesn't mean you can count it:) There "exists" a way to count it, but nobody knows how. (Some people think that's just B.S. and reject such mathematics)
proof implies finite steps. "proof in finite steps" is just to reassure the readers.
that sounds good, except ... true?
1. number theory is not axiomizable, its truth is not effectively enumerable.
2. an axiomized theory is enumberale, but why these axioms? are they consistent? are they
3. not all theorems are equal, human obviously have a way to focus on "interesting" ones, that's not what a mechanized list can satisfy.
4. enumerability is just theoretical, there is no efficient algorithm at all.
I'm not a mathematician.
Without humans, there is no "good" or "bad". Unless there's some overlord above humans that defines moral standards.
It does not work that way. It's up to the experts to pick the arbitrary anecdotal events that supports the theory sentimentally. If you do it, you are just a stupid whore of big oil companies who doesn't know anything about scientific methods.
Nice try, kid. A 10-year cooling won't disprove Global Warming either.
http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2008/04/30/eaclimate130.xml
Global Warming is unfalsifiable. No matter what happens, the experts will find it supporting global warming. Can they give us ONE possible event that can falsify Global Warming? Nope. Can you imagine any event that could convince the experts to drop their theory? Nope.
Of course, it's the damn free market and evil big corporations. It's not like government has done anything wrong in this case... our governments obviously still don't have enough power to shape the contents on internet.
Dictatorship is the most efficient system in decision making.
And politicians in a 'democratic' system knows this as well. It's not unusual to delegate one person(I'm even not talking about an elected one) the sole decision making power on extremely important issues.
I have no idea what you are saying.
This has nothing to do with the conclusion of the experiment. It is about the methodology. The math is either right, or wrong.
And I recommend Ruby on Rails. Its developer community has been growing exponentially, from 5 guys in 2006 to 10 guys in 2007. If you are extra conservative, you can try Groovy on Rails. It's just like Java, but better.