Search found 882 matches

by NathanielJ
Thu Oct 23, 2014 7:26 pm UTC
Forum: Mathematics
Topic: How many ways can you prove x + 1/x >= 2?
Replies: 23
Views: 14315

Re: How many ways can you prove x + 1/x >= 2?

Had I done a proof where I made use of the fact that -1 <= cos(x) <= 1, would you expect a proof of this statement? Well this would most likely depend on what definition of cos(x) you were using and what you were trying to prove with it. If the question was to come up with a proof of the fact that ...
by NathanielJ
Thu Oct 23, 2014 12:40 am UTC
Forum: Mathematics
Topic: How many ways can you prove x + 1/x >= 2?
Replies: 23
Views: 14315

Re: How many ways can you prove x + 1/x >= 2?

By contradiction. Assume x > 0 and x + 1/x < 2. Then x^2 +1 < 2x and thus x^2-2x+1 < 0 but x^2 -2x + 1 = (x-1)^2 and since it is a square it must be positive, and we have the contradiction. I'm never really a fan of "contradiction" proofs that can easily be written backwards as direct pro...
by NathanielJ
Sat Jan 11, 2014 4:13 am UTC
Forum: Mathematics
Topic: P and NP proof attempt
Replies: 15
Views: 2977

Re: P and NP proof attempt

Ice cream is flamingo and purple monkey dishwasher. Therefore P != NP.

Ok now tell me why my proof is wrong.
by NathanielJ
Mon Dec 16, 2013 3:54 pm UTC
Forum: Mathematics
Topic: Idea for using pi approximations to get close to 1
Replies: 24
Views: 5757

Re: Idea for using pi approximations to get close to 1

There is no geometry where the circumference:diameter ratio is constant but not equal to the usual value. Yes there is. There are geometries that aren't hyperbolic, eulcidean, or elliptic. For example the 1-norm on R 2 gives pi = 4. Right you are. I forgot a word in that statement. "Smooth&quo...
by NathanielJ
Sun Nov 24, 2013 5:11 am UTC
Forum: Mathematics
Topic: Check result-condition number
Replies: 6
Views: 1714

Re: Check result-condition number

Yes. More specifically, it's 4885477064818389638136352610039211133217/52164587258011922567975512864675399397.
by NathanielJ
Wed May 01, 2013 10:05 pm UTC
Forum: Mathematics
Topic: Is Who wants to be a millionaire just a game of luck?
Replies: 21
Views: 6625

Re: Is Who wants to be a millionaire just a game of luck?

Finally, 50-50 will remove 2 wrong answers, so you have 1 right answer and 1 wrong answer, so you basically know the answer. Question 15: 100% <--- 50-50 Ignoring all of the other mathematical mistakes, I'm having trouble understanding how someone could think that if you're randomly guessing betwee...
by NathanielJ
Sun Nov 18, 2012 8:31 pm UTC
Forum: Mathematics
Topic: Can all numbers be represented by (a^n) +/- (b^m)?
Replies: 12
Views: 1983

Re: Can all numbers be represented by (a^n) +/- (b^m)?

This question is still open as far as I am aware, and generally thought to be fairly difficult. Heck, the problem of whether or not the solution to a^n +/- b^m = 1 is unique took over 150 years to solve . Here is a brief discussion of this (and closely-related questions) . The gist is this: no, we d...
by NathanielJ
Sat Oct 27, 2012 2:47 am UTC
Forum: Mathematics
Topic: Problem Generating Infinitely Many Endless Bitstrings
Replies: 10
Views: 2929

Re: Problem Generating Infinitely Many Endless Bitstrings

As far as I can tell, you haven't generated any infinite bitstrings, only all finite bitstrings. If you generated an infinite bitstring, you should be able to answer the question "at what step did I add this bitstring?", which you can't, because no step in your procedure turns a finite bit...
by NathanielJ
Mon Oct 01, 2012 5:06 pm UTC
Forum: Mathematics
Topic: Exponent of a two-by-two matrix
Replies: 3
Views: 2577

Re: Exponent of a two-by-two matrix

Some formulas for the matrix exponential of a 2-by-2 matrix are given in this paper. It seems like you want either Corollary 2.3 or 2.4.
by NathanielJ
Wed Sep 26, 2012 12:37 am UTC
Forum: Mathematics
Topic: MD5 Hash in the file you are hashing
Replies: 11
Views: 3570

Re: MD5 Hash in the file you are hashing

An MD5 key is what, 128 bits? Make a file with 128*2^128 bits, containing every possible sequence of 128 bits. Then you're guaranteed it contains its own MD5 hash :) By using the de Bruijn sequence approach, you can reduce the size of the file to 2^128 + 127 bits and still contain every possible se...
by NathanielJ
Sun Sep 23, 2012 6:28 am UTC
Forum: Mathematics
Topic: Linear algebra question
Replies: 4
Views: 2040

Re: Linear algebra question

Do you also have by any chance a reference for the proof at hand? Use the formula a \times b = \|a\| \|b\| \sin(\theta) n , where \theta is the angle between a and b, and n is the unit vector perpendicular to a and b (chosen according to the right-hand rule). Multiplying a and b by R won't ...
by NathanielJ
Fri Aug 24, 2012 2:14 am UTC
Forum: Mathematics
Topic: Conway's Game of Life: Collapsing Lines
Replies: 8
Views: 3003

Re: Conway's Game of Life: Collapsing Lines

All lines after some (reasonably small, less than 1000 for sure, and probably about 50 or so) length spit out a glider and thus don't collapse to nothing.

Also, many questions like this are discussed and answered on the (shameless plug) ConwayLife.com forums.
by NathanielJ
Thu Aug 09, 2012 11:03 am UTC
Forum: Mathematics
Topic: The Shortest String Containing all Permutations of n Symbols
Replies: 29
Views: 19865

Re: The Shortest String Containing all Permutations of n Sym

Be careful when assuming that the optimal string *must* have a certain form based on the optimal strings in the n = 1, 2, 3, 4 cases. While there are indeed exactly (n-1)! instances of the digit n for those cases, and there is tons of symmetry to be found, that breaks down for n >= 5. When n = 5, I ...
by NathanielJ
Sat Jul 07, 2012 4:19 am UTC
Forum: Mathematics
Topic: Can you have matricies inside of matricies?
Replies: 11
Views: 3998

Re: Can you have matricies inside of matricies?

Related topic that may be of interest to the original poster: Kronecker product.
by NathanielJ
Thu May 24, 2012 5:30 pm UTC
Forum: Mathematics
Topic: Linear-time arithmetic prime test yields factors
Replies: 13
Views: 4328

Re: Linear-time arithmetic prime test yields factors

It depends on what you mean by "linear time". If you mean that it takes O(n) time to determine primality of the integer n, then it's not a big deal because we have many algorithms that are much faster (and I expect this is what you mean, since you say you discovered the algorithm in 5th gr...
by NathanielJ
Thu Apr 05, 2012 2:31 pm UTC
Forum: Mathematics
Topic: chi² and wolfram alpha
Replies: 9
Views: 3212

Re: chi² and wolfram alpha

For most problems like this, you could use this tool. However, the p-value is so small it just spits out 0.

Heck, even MATLAB spits out 0 in this case, meaning that the probability is smaller than 10^-16 (and I would guess that it's actually in the ballpark of 10^-35).
by NathanielJ
Mon Mar 12, 2012 1:58 pm UTC
Forum: Mathematics
Topic: Show us your articles! Or what's your Erdos number?
Replies: 185
Views: 252229

Re: Show us your articles! Or what's your Erdos fish?

Talith wrote:Your article got a mention in a weekly maths podcast if you're interested. http://pulse-project.org/node/417 time - 41:30.


Awesome, thanks for the link :)
by NathanielJ
Fri Mar 09, 2012 3:01 am UTC
Forum: Mathematics
Topic: Show us your articles! Or what's your Erdos number?
Replies: 185
Views: 252229

Re: Show us your articles! Or what's your Erdos number?

My most recent paper (well, preprint) is arXiv:1203.1633 [cs.CC], which is by far the most fun paper I've written. My Erdos number is 3, through this paper with Man-Duen Choi.
by NathanielJ
Fri Mar 02, 2012 5:36 am UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 461368

Re: Favorite math jokes

Eebster the Great wrote:
Qaanol wrote:Commute with a joint.

Wait, I still don't get it. Is a "joint" like a "join"?


Presumably it's "a joint" like "adjoint". A normal operator is one that commutes with its adjoint. Hence, the joke. You may now slap your knee.
by NathanielJ
Wed Feb 22, 2012 5:23 pm UTC
Forum: Mathematics
Topic: Quesion about addition of inverses of odd positive integers
Replies: 20
Views: 4360

Re: Quesion about addition of inverses of odd positive integ

Afif_D wrote:But i still believe nobody can produce a 2.


Even though Nitrodon provided an explicit example that does exactly this?
by NathanielJ
Mon Feb 20, 2012 3:54 pm UTC
Forum: Mathematics
Topic: Quesion about addition of inverses of odd positive integers
Replies: 20
Views: 4360

Re: Quesion about addition of inverses of odd positive integ

I don't have an explicit example, but yes, this can be done. See this wiki page, and take x = 2, y = 1.
by NathanielJ
Sat Feb 18, 2012 6:35 am UTC
Forum: Mathematics
Topic: A Most Amazing Number
Replies: 33
Views: 16441

Re: A Most Amazing Number

Where are we drawing the line here? Maybe zero has an infinite number of decimal representations: 0, 0.0, 0.00, 0.000, ...
by NathanielJ
Thu Feb 09, 2012 9:23 pm UTC
Forum: Mathematics
Topic: Largest 3 consecutive semi-primes?
Replies: 19
Views: 5720

Re: Largest 3 consecutive semi-primes?

It's worth having a look at the OEIS's A056809, which has a list of 10000 triplets of semiprimes, the largest of which is <5991157, 5991158, 5991159>. Finiteness seems unlikely (but unproven).
by NathanielJ
Thu Dec 29, 2011 8:24 pm UTC
Forum: Mathematics
Topic: f(f(x))=exp(x) and extensions to noninteger numbers of f.
Replies: 9
Views: 3392

Re: f(f(x))=exp(x) and extensions to noninteger numbers of f

An article about the function e1/2 can be found here, and the fact that such an article exists suggests that the function exists. Unfortunately, however, I don't read German, so that's about all I can say.
by NathanielJ
Wed Dec 07, 2011 6:25 pm UTC
Forum: Mathematics
Topic: Help!
Replies: 6
Views: 1195

Re: Help!

lukesawyer wrote:Why is there a j instead of an n ?


Because xn refers to the nth (i.e., the last) entry of the n-tuple. xj refers to a general entry of the n-tuple (i.e., j can by any value between 1 and n).
by NathanielJ
Sat Oct 15, 2011 3:01 pm UTC
Forum: Mathematics
Topic: Pixels in a circle of radius (r)
Replies: 11
Views: 3720

Re: Pixels in a circle of radius (r)

This sequence appears to be 4*A022846. In other words, the number in jaap's post appears to be [imath]4\sqrt{2} = 5.65685...[/imath]

As far as a proof goes though, I have no idea.
by NathanielJ
Tue Aug 09, 2011 2:34 am UTC
Forum: Mathematics
Topic: General Addition
Replies: 7
Views: 1297

Re: General Addition

My intuition tells me that the only time your \sqrt{x}+\sqrt{y}=\sqrt{x^2+y^2+2\sqrt{xy}} formula would be "useful" would be if the inner most radical was of a perfect square... which happens exactly when x=y. It happens plenty of other times too (e.g., x = 3, y = 12), though one of them ...
by NathanielJ
Thu Jun 30, 2011 6:47 am UTC
Forum: Mathematics
Topic: Math Websites
Replies: 125
Views: 163488

Re: Math Websites

Dason wrote:Is there a reason you don't allow non-integer degrees of freedom for the t-distribution (or the other distributions for that matter)?


Quite honestly I'd just never thought about it, since I've never had a need for non-integer degrees of freedom myself. I'll add it to the list ;)
by NathanielJ
Wed Jun 29, 2011 8:22 pm UTC
Forum: Mathematics
Topic: Math Websites
Replies: 125
Views: 163488

Re: Math Websites

I made a stat distribution calculator a little while ago (for computing p-value, z-values, t-values, f-values, etc):

http://www.statdistributions.com
by NathanielJ
Sun Jun 12, 2011 2:23 pm UTC
Forum: Mathematics
Topic: PhD in hand
Replies: 43
Views: 5308

Re: PhD in hand

Brilliant, congrats!
by NathanielJ
Tue May 10, 2011 11:06 pm UTC
Forum: Mathematics
Topic: Disguised forms of 2
Replies: 114
Views: 11672

Re: Disguised forms of 2

skeptical scientist wrote:From this, the actual value is somewhere between 1.94146112352 and 1.94146112389. links go to Mathematica and Rick Astley, respectively.


More decimal places can be found here, by the way.
by NathanielJ
Sat Apr 30, 2011 2:01 am UTC
Forum: Mathematics
Topic: Solve this 4x4 matrix using Cramer's rule
Replies: 6
Views: 7793

Re: Solve this 4x4 matrix using Cramer's rule

There are faster stuff out there than just straight forward Gaussian elimination, for example to calculate something like the LU decomposition using Straussen (nobody uses Coppersmith–Winograd), and using that to compute both the determinant and to solve linear systems. IIRC the Big-O for determina...
by NathanielJ
Thu Apr 28, 2011 4:32 pm UTC
Forum: Mathematics
Topic: Solve this 4x4 matrix using Cramer's rule
Replies: 6
Views: 7793

Re: Solve this 4x4 matrix using Cramer's rule

However, suppose you have a fairly large linear system, and for some reason, you want to find the value of only one of the variables. Can Cramer's rule be a good thing to use in that case? Not really, no, unless the matrix has very specific sparsity properties that make the related determinants col...
by NathanielJ
Thu Apr 28, 2011 3:14 pm UTC
Forum: Mathematics
Topic: Übernions
Replies: 3
Views: 1307

Re: Übernions

I know I'm fascinated by quaternions and octonions and such. Here's my question: does an algebra system exist for any dimension 2^n where n is a positive integer? You can create "an algebra system" in any dimension -- the question is just what rules do and do not break in that dimension. ...
by NathanielJ
Thu Apr 21, 2011 9:04 pm UTC
Forum: Mathematics
Topic: Help with a non-integer exponent
Replies: 7
Views: 2022

Re: Help with a non-integer exponent

Is D rational? If I remember right, a rational base to an irrational power is transcendental (unless f is 0 or 1, but this can be checked easily), so if B and C are algebraic and D is irrational, we have B*f^D is transcendental, so (1-Bf^D)/C is as well, so f^2 would have to be, so f would have to ...
by NathanielJ
Thu Apr 21, 2011 6:08 am UTC
Forum: Mathematics
Topic: The Shortest String Containing all Permutations of n Symbols
Replies: 29
Views: 19865

Re: The Shortest String Containing all Permutations of n Sym

I along with my math professor Dan Ashlock... Oh wow that's weird -- what a small world, Dan is a professor at my university (U of Guelph). I had no idea that he had worked on this problem! We also found algorithms for deriving the shortest strings, but we couldn't prove that our strings were short...
by NathanielJ
Fri Feb 18, 2011 3:41 am UTC
Forum: Mathematics
Topic: The Shortest String Containing all Permutations of n Symbols
Replies: 29
Views: 19865

Re: The Shortest String Containing all Permutations of n Sym

How did I know that one of the first replies would be to the Wikipedia article on de Bruijn sequences? The de Bruijn diagram approach doesn't work because there is no way to concatenate all of the permutations next to each other with overlap n-1 each. After you use n of the permutations, you run out...
by NathanielJ
Thu Feb 17, 2011 8:10 pm UTC
Forum: Mathematics
Topic: The Shortest String Containing all Permutations of n Symbols
Replies: 29
Views: 19865

Re: The Shortest String Containing all Permutations of n Sym

Hm. What properties could we expect this minimal string to have? Should we expect it to have no repetitions of length n? It *cannot* satisfy the rule that each substring of length n has every character, since then it would just be repetitions of one template. Can we find some rule governing how man...

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