## Search found 825 matches

Mon Feb 23, 2009 9:16 am UTC
Topic: 0547: "Simple"
Replies: 121
Views: 23257

### Re: "Simple" Discussion

I wanted to agree with the math professors thing, but after reading the real number article, I can't. It's wrong or misleading in every paragraph. Also funny are http://simple.wikipedia.org/wiki/Linear_algebra and http://simple.wikipedia.org/wiki/Infinity .
Thu Feb 12, 2009 8:31 pm UTC
Forum: Mathematics
Topic: Formatting the 'd' in Leibniz Notation
Replies: 10
Views: 2094

### Re: Formatting the 'd' in Leibniz Notation

Upright feels more correct, but it's ugly, more effort to write, and is almost never used, so I go with italic.
Sat Feb 07, 2009 11:13 pm UTC
Forum: Mathematics
Topic: taylor expansion of sin(x)
Replies: 15
Views: 3358

### Re: taylor expansion of sin(x)

Cycle wrote:In fact, all functions with periodic derivatives are expressible with just e^x and trig functions, not just those of order four. For example, the function exp(x/2)cos(x√3/2) is equal to it's own third derivative.

How do you prove that?
Mon Jan 26, 2009 6:49 am UTC
Forum: Mathematics
Topic: 1.0000000...1 = 1?
Replies: 19
Views: 1964

### Re: 1.0000000...1 = 1?

The "real numbers" is just a name for our common number system. There's nothing called unreal numbers. You have to define your notation to be able to ask what it equals. You might as well ask if "1.00###¤menstruationcycle#...1..." equals 1.
Mon Jan 26, 2009 6:40 am UTC
Forum: Mathematics
Topic: 1.0000000...1 = 1?
Replies: 19
Views: 1964

### Re: 1.0000000...1 = 1?

The notation 0.999... by definition means \sum_{n=1}^\infty\frac9{10^n} , which is equal to 1. 1.000...1 however is not standard notation, so you can't just ask what it is without defining it. The only sensible way I can think of to define it is by \lim_{n\to\infty}(1+\frac1{10^n}) , in whic...
Sat Jan 10, 2009 8:09 pm UTC
Forum: General
Topic: ITT: We make xkcd slightly worse.
Replies: 8668
Views: 1802073

### Re: ITT: We make xkcd slightly worse.

Vista: Well, it's better than regurgitating the same joke over and over again.
Fri Jan 09, 2009 9:23 pm UTC
Forum: Mathematics
Topic: Fractals, baby! Vote now!
Replies: 45
Views: 8427

### Re: Fractals, baby! Vote now!

^

Context Free Art looks amazing. The gallery has a lot of wallpaperable stuff.
Wed Jan 07, 2009 6:47 pm UTC
Forum: Mathematics
Topic: Conformal Mappings
Replies: 2
Views: 446

### Re: Conformal Mappings

Conformal mappings transform lines and circles to lines and circles. Focus on transforming the boundaries of your sets. So if you want to transform the area inside the circle to the upper half-plane, try to transform the circle into the straight line z=0 instead. Do it step by step, by composition o...
Sat Jan 03, 2009 11:53 am UTC
Forum: Mathematics
Topic: Prove that two curves in a square intersect
Replies: 76
Views: 6592

### Re: Prove that two curves in a square intersect

That loop deleting algorithm only works if there are finitely many self-intersections. It wouldn't work on a space-filling curve, was my point. However, Wikipedia confirms that it suffices to check simple curves in this case: It can be shown any Hausdorff space which is path-connected is also arc-co...
Sat Jan 03, 2009 9:59 am UTC
Forum: Mathematics
Topic: Prove that two curves in a square intersect
Replies: 76
Views: 6592

### Re: Prove that two curves in a square intersect

Intuitively yes, but I don't see a way to reduce a non-simple curve to a simple one. Do all continuous curves contain a simple curve with the same endpoints? What simple curve do we associate with a space-filling curve?
Sat Jan 03, 2009 9:44 am UTC
Forum: Mathematics
Topic: Prove that two curves in a square intersect
Replies: 76
Views: 6592

### Re: Prove that two curves in a square intersect

A neat topological proof would be this: suppose we've proved that d separates the unit square into at least two connected components, with the endpoints of c in different components. Suppose c and d do not intersect. Then the unit square minus d is path connected but not connected; contradiction. He...
Fri Jan 02, 2009 11:45 pm UTC
Forum: Mathematics
Topic: Prove that two curves in a square intersect
Replies: 76
Views: 6592

### Re: Prove that two curves in a square intersect

That function needn't be continuous. Let d be a staircase function, and let c be, say, the graph of y=x.
Fri Jan 02, 2009 10:33 pm UTC
Forum: Mathematics
Topic: Prove that two curves in a square intersect
Replies: 76
Views: 6592

### Prove that two curves in a square intersect

Here's a fun problem I came up with. Let c be a continuous curve in the unit square from the left edge to the right edge and let d be a continuous curve in the unit square from the bottom edge to the top edge. Prove that c and d intersect. Is there a simple proof? The statement is obvious, but provi...
Sat Dec 27, 2008 3:40 pm UTC
Forum: Mathematics
Topic: A non-analytic manifold
Replies: 10
Views: 1700

### Re: A non-analytic manifold

http://mathworld.wolfram.com/SmoothManifold.html says yes - well, at least it says that there exist non-smooth manifolds in R^4 and higher. I can't give you the example though, I just accidentally stumbled upon this while preparing for a test on (among others) C^1 manifolds. Thanks. So apparently t...
Sat Dec 27, 2008 10:54 am UTC
Forum: Mathematics
Topic: A non-analytic manifold
Replies: 10
Views: 1700

### A non-analytic manifold

I'd like an example of a manifold that isn't analytic (or differentiable). A silly example is the real line with the two charts \varphi(x)=x, \psi(x)=2x if x>0, x otherwise.. Then \varphi^{-1}\circ \psi isn't differentiable at 0. But this can easily be turned into an analytic manifol...
Thu Dec 25, 2008 12:10 am UTC
Forum: Coding
Topic: Python anagram solver
Replies: 34
Views: 7441

### Re: Python anagram solver

Berengal wrote:I was looking for my old "everything you'll ever need in an interactive haskell session" file

Fri Dec 19, 2008 11:56 pm UTC
Forum: Mathematics
Topic: Using the graph of a polynomial to prove it has no zeroes
Replies: 6
Views: 2107

### Using the graph of a polynomial to prove it has no zeroes

I have a degree 12 polynomial, and I want to prove it has no zeroes in the interval [0,1]. Plotting it in this region, I can plainly see this, and I wonder if this can be turned into a rigorous proof somehow. For an arbitrary function, you of course can't draw any conclusions from a computer generat...
Mon Dec 15, 2008 10:09 pm UTC
Forum: Mathematics
Topic: Subsets vs Proper Subsets
Replies: 16
Views: 3590

### Re: Subsets vs Proper Subsets

Cleverbeans wrote:
Tac-Tics wrote:There are many cases in mathematics where definitions do not parallel every day language.

Don't get me started on open and closed sets.....
Could you get started a little? What's wrong about calling sets open and closed?
Mon Dec 15, 2008 6:55 pm UTC
Forum: Mathematics
Topic: Subsets vs Proper Subsets
Replies: 16
Views: 3590

### Re: Subsets vs Proper Subsets

And what's with the misleading "subset" name? Subset seems to imply one is a smaller set than the other. Typically, "subset", "less than", "smaller", "inequality", "positive" etc are used even when there might be equality, for convenience....
Sun Dec 14, 2008 2:42 pm UTC
Forum: Mathematics
Topic: Proving that the integers are countable (constructively)
Replies: 14
Views: 5075

### Re: Proving that the integers are countable (constructively)

You don't need to define it with a formula. It's perfectly acceptable to define the bijection f by saying it maps 1,2,3,4,5,.... to 0,1,-1,2,-2,.... respectively. It's what any mathematician would write. That is, "define f(1)=0, f(2)=1, f(3)=-1, f(4)=2, f(5)=-2, and so on.". If you want to...
Wed Dec 10, 2008 6:35 pm UTC
Forum: Mathematics
Topic: Putnam A2, revised
Replies: 14
Views: 2065

### Re: Putnam A2, revised

Alan has a winning strategy for the 3x3 case by only placing zeroes. I'm not going to write it out, but there aren't that many cases to consider. It seems like this doesn't work for the 4x4 case though. One thing I tried was for Alan to place three zeroes in a row so he will only need to worry about...
Tue Dec 09, 2008 8:48 pm UTC
Forum: Mathematics
Topic: Mathematical sequences/equations
Replies: 3
Views: 593

### Re: Mathematical sequences/equations

The sequence goes 3, 3*2, 3*2*3, 3*2*3*4, ... So the nth term is 3*(1*2*...*n)=3*n! (that is, n factorial).
Sun Dec 07, 2008 11:26 am UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 485707

++$_ wrote:if you add up all the prime numbers, you get minus an eighth. Is that a real series? I couldn't find it by googling. Fri Dec 05, 2008 9:32 am UTC Forum: General Topic: Tabbed browsing. Replies: 38 Views: 3375 ### Re: Tabbed browsing. I'm a stacker. I used to be queuer, but it frequently happened that I eventually arrived at a tab that I have no recollection of opening, nor any idea of why I would want to look at it. The danger with stacking though is that you risk never completing your browsing since each tab is likely to spawn ... Fri Dec 05, 2008 9:23 am UTC Forum: Mathematics Topic: Favorite math jokes Replies: 1452 Views: 485707 ### Re: Favorite math jokes A mathematician walks into a bar where they have$3 for a beer and orders a beer, a second mathematician orders two, a third orders three, before the fourth orders his the bartenders throws them a quarter. I was wondering when someone was going to make this joke. I had the same idea, but couldn't t...
Tue Dec 02, 2008 11:59 pm UTC
Forum: Mathematics
Topic: Limits question : (
Replies: 6
Views: 922

### Re: Limits question : (

Now, if reading is your talent, you would have noticed that in the proof question you are asked to find the delta. So if you had solved that problem, you would have solved this one.
Tue Dec 02, 2008 11:29 pm UTC
Forum: Mathematics
Topic: Limits question : (
Replies: 6
Views: 922

### Re: Limits question : (

You'll get even greater chances of someone helping you if you create a third identical thread. Third time's the charm!
Tue Dec 02, 2008 8:40 am UTC
Forum: Mathematics
Topic: decent graphing calculator
Replies: 7
Views: 1139

### Re: decent graphing calculator

qinwamascot wrote:If you're looking at the TI-83+, I'd recommend even a step down from that to the TI-82.

One pretty awful difference is that A/BC evaluates to A/(B*C) with the TI-82, but to (A/B)*C with the TI-83+. A/B*C evalutes to (A/B)*C with both.
Thu Nov 27, 2008 11:11 pm UTC
Forum: Mathematics
Replies: 11
Views: 1460

Looks like garbage. What tips it off are the arbitrary constants thrown in, like 82 and pi.
Wed Nov 26, 2008 8:20 pm UTC
Forum: Mathematics
Topic: Need help with integration problem
Replies: 7
Views: 1040

### Re: Need help with integration problem

One thing that's for sure is that you won't find the value of that integral by finding an anti-derivative to the integrand. The most famous function that doesn't have an elementary antiderivative is e^{-x^2} , and you can transform your integrand to that one by a change of variables. Pretty much the...
Wed Nov 26, 2008 5:26 pm UTC
Forum: Mathematics
Topic: Induction - A true form of proof?
Replies: 70
Views: 6361

### Re: Induction - A true form of proof?

The second step is not assuming it is true for all k. It is assuming it is true for some k. You already know it's true for at least one k, namely k=1. The induction step (step three) then proves that it is true for k+1, i.e. for k=2. So now you know it's true for k=1 and k=2. Now the induction step ...
Mon Nov 24, 2008 5:23 pm UTC
Forum: General
Topic: Have you ever been Banned? (here or anywhere)
Replies: 125
Views: 10805

### Re: Have you ever been Banned?

I was permanently banned from the #hugs irc channel (I don't remember which network) immediately upon joining it and declaring I wanted a hug. I bet they couldn't imagine I actually use the Hugs Haskell compiler, which is what I later found out the channel was actually about.
Sat Nov 15, 2008 8:20 am UTC
Forum: Mathematics
Topic: Number of checkmate positions
Replies: 27
Views: 4301

### Re: Number of checkmate positions

qinwamascot wrote:Although the latter is finite if you account for the 50 move rule. I did that calculation quite a while back of what the longest possible chess game is.
An exact calculation? What is it? Is 50*32 moves possible?

Edit: Typo. Changed 40 to 32.
Sat Nov 15, 2008 8:07 am UTC
Forum: Logic Puzzles
Topic: Tetris Puzzle
Replies: 13
Views: 3805

### Re: Tetris Puzzle

That strategy assumes that instead of each piece being independently randomly chosen, you instead get one of each piece every seven pieces. As such, it doesn't apply to many tetris games. I'm not a Tetris expert, but that seems to be the most common way that the pieces are generated. (Mathematicall...
Thu Nov 13, 2008 9:21 pm UTC
Forum: Mathematics
Topic: Minimum bit string (shortest common superstrings)
Replies: 20
Views: 2313

### Re: Minimum bit string

I remember a similar problem from my Discrete Maths course. There's a code lock to a door with the buttons 0-9, and if the correct four buttons are pressed in the right order (regardless of what digits had been pressed earlier), then the door will open. What's the shortest sequence of button presses...
Thu Nov 13, 2008 5:45 am UTC
Forum: Mathematics
Topic: Which is bigger?
Replies: 35
Views: 3482

### Re: Which is bigger?

doogly wrote:Graham's number is computable, so there are definitely bigger numbers. I like the discussion here: http://scottaaronson.com/writings/bignumbers.html

QFT! This is a great article if you're fascinated by large numbers.
Tue Nov 11, 2008 11:38 am UTC
Forum: Mathematics
Topic: MATLAB sucks...
Replies: 27
Views: 6054

### Re: MATLAB sucks...

A related problem: how do you place exactly n points on a sphere as evenly as possible (meaning the minimal distance between any two points on the sphere is maximized)? Is there a nice and easy algorithm for it? The geodesic sphere thing seems nice, but it doesn't work for all n. The perfect way to ...
Tue Nov 11, 2008 1:30 am UTC
Forum: General
Topic: Cannot remember the comic's name
Replies: 2
Views: 557

### Re: Cannot remember the comic's name

wulffmorgenthaler?
Mon Nov 10, 2008 4:49 pm UTC
Forum: Mathematics
Topic: Help an Aussie engineer pass his Numerical Analysis Exam!
Replies: 3
Views: 909

### Re: Help an Aussie engineer pass his Numerical Analysis Exam!

My mistake, I used "linear" instead of "first-order".
Mon Nov 10, 2008 2:39 pm UTC
Forum: General