Search found 825 matches

by Torn Apart By Dingos
Thu Aug 14, 2008 6:50 am UTC
Forum: Mathematics
Topic: More about xkcd number and other big numbers
Replies: 92
Views: 17651

Re: More about xkcd number and other big numbers

So assuming Henkin semantics is consistent, we're done! No, because you can do a Godel-attack on Henkin semantics. There is no way to formally say {0,1,2,...} and pin down what you mean exactly. Any and all attempts to do so, even if they look like they are doing it, have a leak. What's the leak? P...
by Torn Apart By Dingos
Thu Aug 14, 2008 6:42 am UTC
Forum: Mathematics
Topic: Something I've been wondering since 7th grade
Replies: 22
Views: 4424

Re: Something I've been wondering since 7th grade

phlip wrote:
Torn Apart By Dingos wrote:[...] exponentiation has [...] associativity, commutativity [...]

What type of crazy exponentiation are you using?

Way to butcher that quote, you might have a future in politics. ;) It also isn't continuous. I said "some of the nice properties", but I agree it was badly phrased.
by Torn Apart By Dingos
Wed Aug 13, 2008 10:54 pm UTC
Forum: Gaming
Topic: How old is your brain OR Is there a subform for flash games?
Replies: 24
Views: 2489

Re: How old is your brain OR Is there a subform for flash games?

I have a 26-year old brain? I didn't come here to be insulted!
by Torn Apart By Dingos
Wed Aug 13, 2008 10:13 pm UTC
Forum: Mathematics
Topic: Relative Sizes of Infinite Sets
Replies: 25
Views: 2590

Re: Relative Sizes of Infinite Sets

VolatileStorm wrote:Finite and infinite is pretty obvious why not, but why can't you do it with the integers and the reals?

This is proved with the famous Cantor's diagonal argument (the same method is used to prove that the reals and the real-valued functions are different sizes).
by Torn Apart By Dingos
Wed Aug 13, 2008 10:09 pm UTC
Forum: Mathematics
Topic: Relative Sizes of Infinite Sets
Replies: 25
Views: 2590

Re: Relative Sizes of Infinite Sets

There's no one-to-one correspondence between a finite and an infinite set.
There's no one-to-one correspondence between the integers and the reals.
There's no one-to-one correspondence between the reals and the set of functions from R to R.
by Torn Apart By Dingos
Wed Aug 13, 2008 10:07 pm UTC
Forum: Mathematics
Topic: More about xkcd number and other big numbers
Replies: 92
Views: 17651

Re: More about xkcd number and other big numbers

[quote=Torn]Why wouldn't it stop? What do you mean by pin down N? Do you mean ZFC` does not know that N in ZFC is equal to {0,1,2,...}? Again, I don't know how ZFC` is constructed so I can't tell what's possible in it. Express my proof in whatever system (second-order logic?) is needed to make it f...
by Torn Apart By Dingos
Wed Aug 13, 2008 9:02 pm UTC
Forum: Mathematics
Topic: More about xkcd number and other big numbers
Replies: 92
Views: 17651

Re: More about xkcd number and other big numbers

Your assumption -- "assume M halts" -- is not an axiom. If you make it an axiom, then yes, it can have arbitrary effects on what other symbols mean. Remember: the elements that are in N are described by the axioms. Can you please give a concrete example with a concrete axiom Y added and a...
by Torn Apart By Dingos
Wed Aug 13, 2008 8:30 pm UTC
Forum: Mathematics
Topic: tileings
Replies: 4
Views: 2336

Re: tileings

by Torn Apart By Dingos
Wed Aug 13, 2008 8:22 pm UTC
Forum: Mathematics
Topic: More about xkcd number and other big numbers
Replies: 92
Views: 17651

Re: More about xkcd number and other big numbers

The N is part of your system of axioms from ZFC. Under some ZFC+X, N has more elements than you might think. That sounds suspect. Why should N change rather than a myriad of other structures involved in the definition of BB? And doesn't it also depend on the definition of N? But please expand on th...
by Torn Apart By Dingos
Wed Aug 13, 2008 7:03 pm UTC
Forum: Mathematics
Topic: Something I've been wondering since 7th grade
Replies: 22
Views: 4424

Re: Something I've been wondering since 7th grade

The interesting question here, in my opinion, is how should x$y be defined so that x+y=x$x$...$x (repeated y times), and $ gets some of the nice properties that addition, multiplication and exponentiation has (associativity, commutativity, continuity?).
by Torn Apart By Dingos
Wed Aug 13, 2008 6:57 pm UTC
Forum: Mathematics
Topic: More about xkcd number and other big numbers
Replies: 92
Views: 17651

Re: More about xkcd number and other big numbers

The N is part of your system of axioms from ZFC. Under some ZFC+X, N has more elements than you might think. That sounds suspect. Why should N change rather than a myriad of other structures involved in the definition of BB? And doesn't it also depend on the definition of N? But please expand on th...
by Torn Apart By Dingos
Wed Aug 13, 2008 4:27 pm UTC
Forum: Mathematics
Topic: More about xkcd number and other big numbers
Replies: 92
Views: 17651

Re: More about xkcd number and other big numbers

So.. in a frivolous attempt to cheat and use an idea already sort of suggested.... (factorials for emphasis! (and size)) (1+1+...+1+1)!!! How big is it? How big do you want it to be? = (−½)!!! Or, if !!! denotes the triple factorial, the answer is (-1/2)!!!= \displaystyle \frac{3^{\frac{x+2}{3}} \G...
by Torn Apart By Dingos
Wed Aug 13, 2008 3:53 pm UTC
Forum: Mathematics
Topic: More about xkcd number and other big numbers
Replies: 92
Views: 17651

Re: More about xkcd number and other big numbers

To be clear, you usually end up proving "it cannot be proven that T halts in ZFC, and it cannot be proven that T ~halts in ZFC". What do you mean by "You usually end up proving"? Where, why? I didn't say that that was being proven, it was an antecedent. Besides, there are lots s...
by Torn Apart By Dingos
Wed Aug 13, 2008 2:48 pm UTC
Forum: Mathematics
Topic: More about xkcd number and other big numbers
Replies: 92
Views: 17651

Re: More about xkcd number and other big numbers

Can you be more explicit? What exactly in my proof is wrong? I'm getting confused about which systems all the statements are in. My proof that there's a contradiction is in some system outside ZFC, but I don't know what it is - I'm not using any alien logic, so I guess I'm implicitly encoding statem...
by Torn Apart By Dingos
Wed Aug 13, 2008 2:30 pm UTC
Forum: Coding
Topic: Noob question about arrays
Replies: 34
Views: 4642

Re: Noob question about arrays

Are you using C/C++? If you're declaring it as follows, it all ends up on the stack, which is rather limited in size.
Object array[1000000];
You want to put the array on the heap instead, thusly:
Object * array = new Object[1000000];
Don't forget to delete it when you're done, thisly:
delete [] array;
by Torn Apart By Dingos
Wed Aug 13, 2008 12:28 pm UTC
Forum: Mathematics
Topic: More about xkcd number and other big numbers
Replies: 92
Views: 17651

Re: More about xkcd number and other big numbers

You have brought up a very subtle point. When you talk about a Turing machine, you have in your mind a very concrete object. Probably an actual tape with maybe a person with a pencil and instructions or something. But this is not actually what a Turing machine is. It is actually a formal descriptio...
by Torn Apart By Dingos
Mon Aug 11, 2008 11:51 pm UTC
Forum: Mathematics
Topic: A little thing I've written
Replies: 11
Views: 2388

Re: A little thing I've written

It's perfectly well defined if you don't assume friendship is commutative. John could consider Bob his friend even if Bob does not consider John his friend.
by Torn Apart By Dingos
Mon Aug 11, 2008 2:51 pm UTC
Forum: General
Topic: Future Technology Mega Poll!
Replies: 29
Views: 2944

Re: Future Technology Mega Poll!

Not in such a short time. Take the first one. For a millionfold improvement in 20 years, processing power will have to double every year (2^20 ~ 1000^2). A doubling every year seems to be pushing it, and even then, I don't believe exponential growth can be sustained for 20 more years. Umm, you are ...
by Torn Apart By Dingos
Mon Aug 11, 2008 12:24 pm UTC
Forum: General
Topic: Future Technology Mega Poll!
Replies: 29
Views: 2944

Re: Future Technology Mega Poll!

Not in such a short time. Take the first one. For a millionfold improvement in 20 years, processing power will have to double every year (2^20 ~ 1000^2). A doubling every year seems to be pushing it, and even then, I don't believe exponential growth can be sustained for 20 more years. Some of the id...
by Torn Apart By Dingos
Mon Aug 11, 2008 11:08 am UTC
Forum: General
Topic: Future Technology Mega Poll!
Replies: 29
Views: 2944

Re: Future Technology Mega Poll!

I voted no to everything (I stopped and thought about them all). I don't think it's realistic to expect such dramatic changes in just 20 years. Replace it with 50 or 100 years, and we'll talk. Think about what the world looked like 20 years ago, it's essentially the same. We don't have flying cars, ...
by Torn Apart By Dingos
Sun Aug 10, 2008 3:26 pm UTC
Forum: Mathematics
Topic: Algebra and Non-Real Sets
Replies: 8
Views: 1578

Re: Algebra and Non-Real Sets

I don't know your background, so the following may or may not be helpful. The structure you're describing (two operations "addition" and "multiplication" on an arbitrary set, where the latter needn't be commutative) seems to be a ring . Topology is a sort of "calculus" ...
by Torn Apart By Dingos
Tue Aug 05, 2008 11:02 pm UTC
Forum: Mathematics
Topic: A summation question
Replies: 18
Views: 2151

Re: A summation question

Hey, where did that post go that was here before? Did the author discover a mistake and deleted it?

Token wrote:
btilly wrote:as [math]k -> \infty[/math]

You're looking for \rightarrow, I think. Oh, and the [imath] tags are quite nice, too. :wink:

I use \to.
by Torn Apart By Dingos
Fri Aug 01, 2008 9:20 am UTC
Forum: General
Topic: "idiot test" aka "read everything before doing anything"
Replies: 88
Views: 67957

Re: "idiot test" aka "read everything before doing anything"

I got this test in third grade. It was made out to be a contest (whoever got first would win), so I of course ignored the first step and raced through the rest of the steps and was proud to be the first to finish the test, upon which I was treated with a few condescending stares. Fuckers. Comic 169,...
by Torn Apart By Dingos
Thu Jul 31, 2008 10:50 pm UTC
Forum: Mathematics
Topic: weird question
Replies: 5
Views: 1274

Re: weird question

gorcee wrote:4.0/3.0
- 1.0
* 3.0
- 1.0
Is the point that it will end up at about 1e-16 because of floating point inaccuracies?

Something cooler is the Excel 2007 bug: Type =77.1*850 and =77.1*850+2 into two cells. The first displays 100000, the second displays 65537.
by Torn Apart By Dingos
Thu Jul 31, 2008 3:32 pm UTC
Forum: Mathematics
Topic: imaginary number signs?
Replies: 17
Views: 3321

Re: imaginary number signs?

Yesila's ordering is a total order on C, but it doesn't make C an ordered field.
by Torn Apart By Dingos
Thu Jul 31, 2008 12:29 pm UTC
Forum: General
Topic: Find me a hat. (Please.)
Replies: 38
Views: 4340

Re: Find me a hat. (Please.)

by Torn Apart By Dingos
Wed Jul 30, 2008 10:18 am UTC
Forum: Mathematics
Topic: Percentage of numbers that are prime
Replies: 37
Views: 11913

Re: Percentage of numbers that are prime

Edit: I have since remembered that being convergent to a number in no way means it will ever attain that value. That's not what's going on here. That's totally what's going on here. The limit of the percentage of the first n numbers which are prime is 0, but the percentage never actually becomes 0 ...
by Torn Apart By Dingos
Tue Jul 29, 2008 10:21 pm UTC
Forum: Mathematics
Topic: Percentage of numbers that are prime
Replies: 37
Views: 11913

Re: Percentage of numbers that are prime

Edit: I have since remembered that being convergent to a number in no way means it will ever attain that value. That's not what's going on here. The percentage of primes is 0 because there are so few primes that they wouldn't make up some percentage x of the natural numbers for any x>0. For example...
by Torn Apart By Dingos
Tue Jul 29, 2008 12:38 pm UTC
Forum: Mathematics
Topic: Calculating Odds?
Replies: 25
Views: 3623

Re: Calculating Odds?

Chances of you meeting that specific famous person, in that exact pub, in that year: Assume both you (meaning the original poster) and Morello visit the bar at discrete one hour intervals, chosen randomly with equal probability from the 4380 hours. The probability that your ten hours will overlap w...
by Torn Apart By Dingos
Sun Jul 27, 2008 7:13 pm UTC
Forum: Mathematics
Topic: fourth degree polynomials with variable coefficients
Replies: 3
Views: 1235

Re: fourth degree polynomials with variable coefficients

There is a closed form solution for quartic equations, but it's huge (completely written out, it fills out a whole paper). Since your coefficients vary, it's doubtful it would simplify to something short. If you can get away with it, use numerical approximations instead. http://en.wikipedia.org/wiki...
by Torn Apart By Dingos
Sat Jul 26, 2008 8:14 pm UTC
Forum: Mathematics
Topic: Sum of cosines
Replies: 19
Views: 2124

Re: Sum of cosines

If you divide each term by n, you might get something like what you wanted, because the harmonic series [imath]\sum_1^\infty\frac1n[/imath] diverges, but as soon as you change some signs it's likely to converge (such as [imath]\sum_1^\infty(-1)^n\frac1n[/imath]).
by Torn Apart By Dingos
Thu Jul 24, 2008 9:52 pm UTC
Forum: Mathematics
Topic: HELP!
Replies: 6
Views: 1302

Re: HELP!

What's W? Write down all the steps, then it will be easy for you to spot any errors you've made.
by Torn Apart By Dingos
Thu Jul 24, 2008 8:10 pm UTC
Forum: Mathematics
Topic: HELP!
Replies: 6
Views: 1302

Re: HELP!

I assume all variables are real, except for J, which is the imaginary unit? Since the imaginary part is zero, you have an equation 2/omegaC - 1/omega^3LC^2 = 0. Use that equation to simplify the value of R/omega^4L^2C^2 (for example by solving for omega, then substituting it into the latter). Simpli...
by Torn Apart By Dingos
Thu Jul 24, 2008 7:58 pm UTC
Forum: Mathematics
Topic: The identification topology of a union
Replies: 5
Views: 1617

Re: The identification topology of a union

The example the book gives is the following. Take the family of "closed intervals" in the plane given by \{0\}\times[0,1], [0,1]\times\{1\}, \{1\}\times[0,1], [1/n,1/(n+1)]\times\{0\} for n=1,2,3,... . The subspace topology on their union is homeomorphic to the circle (because the ...
by Torn Apart By Dingos
Thu Jul 24, 2008 4:47 pm UTC
Forum: Mathematics
Topic: The identification topology of a union
Replies: 5
Views: 1617

Re: The identification topology of a union

I don't see what you're getting at, jestingrabbit. I understand identification maps and identification spaces, and how they are totally different from the subspace topology, but not what the author means by the identification topology of a union. What subsets of the plane would you use whose union i...
by Torn Apart By Dingos
Thu Jul 24, 2008 3:53 pm UTC
Forum: Mathematics
Topic: The identification topology of a union
Replies: 5
Views: 1617

The identification topology of a union

I'm reading M A Armstrong's Basic Topology, and I'm confused by what the identification topology of a union is supposed to be. Let X_a,a\in A be a family of subsets of a topological space and give each X_a , and the union \bigcup X_a the induced topology. ... Let \bigoplus X_a denote the disjoint un...
by Torn Apart By Dingos
Thu Jul 24, 2008 12:27 pm UTC
Forum: Mathematics
Topic: Small calculus question - squared delta function
Replies: 21
Views: 9399

Re: Small calculus question - squared delta function

The integral of a function that is zero everywhere except on a discrete set is zero. You need to give us the definition of the delta function that your book or source is using for us to be able to determine if your integral is even well defined.
by Torn Apart By Dingos
Thu Jul 24, 2008 10:49 am UTC
Forum: Mathematics
Topic: Small calculus question - squared delta function
Replies: 21
Views: 9399

Re: Small calculus question - squared delta function

What's your definition of delta? If you really mean the Kronecker delta, i.e. \delta(x)=\begin{cases}1, x=0\\0, x\neq 0\end{cases} , then, yes, (\delta(x))^2=\delta(x) and \left(\sum_n \delta(x-nT)\right)^2=\sum_n \delta(x-nT) , but the whole i...

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