Search found 97 matches

by gfauxpas
Tue Apr 16, 2013 1:13 pm UTC
Forum: Mathematics
Topic: When should I stop sampling?
Replies: 6
Views: 1907

Re: When should I stop sampling?

Complex meaning X is a subset of C? Or something else? I'm assuming Y is a subset of R?

Edit: is X finite?
by gfauxpas
Tue Jan 22, 2013 8:56 pm UTC
Forum: Mathematics
Topic: A question about Pi
Replies: 6
Views: 2046

Re: A question about Pi

by gfauxpas
Tue Jan 01, 2013 8:49 pm UTC
Forum: Mathematics
Topic: Pokemon probability: Catching Feebas
Replies: 8
Views: 3901

Pokemon probability: Catching Feebas

ITT I think about video games. Background information: In the Pokemon games, there are various areas where you can search for certain creatures ("Pokemon") and then, once encountered, other stuff happens not relevant to the question. In the game ("Pokemon: Platinum edition"), the...
by gfauxpas
Tue Nov 13, 2012 4:05 pm UTC
Forum: Mathematics
Topic: Stupid Question
Replies: 12
Views: 2901

Re: Stupid Question

How about a piecewise function?
ℤ² → ℤ:
(a,b) ↦ a + b, if a ≤ b
(a,b) ↦ a + b + 1, if a > b

edit: oh, right, I don't know why I thought it was :/
by gfauxpas
Fri Oct 12, 2012 3:37 pm UTC
Forum: Mathematics
Topic: Induction with arithmetic mean
Replies: 5
Views: 2106

Re: Induction with arithmetic mean

Even if you could, I'm not sure why you'd do it. The proof for the example you gave is basically trivial and too easy to fall on when trying induction. Well that was just an example, I was asking about any theorem involving the arithmetic mean. Σ(x-μ)², characterizations of sample/population varian...
by gfauxpas
Thu Oct 11, 2012 4:59 pm UTC
Forum: Mathematics
Topic: Induction with arithmetic mean
Replies: 5
Views: 2106

Induction with arithmetic mean

Hello xkcd friends, There are theorems showing equivalence between various ways of computing expressions involving the arithmetic mean. The proofs, as far as I can figure out, just involve algebraically manipulating one expression into another. But I was wondering if they can be proven with inductio...
by gfauxpas
Thu Oct 04, 2012 9:19 pm UTC
Forum: Mathematics
Topic: Equivalent Statements and Negations
Replies: 2
Views: 1619

Re: Equivalent Statements and Negations

Be careful to make sure that what you're calling the negation is really the negation. For b), the negation of "has only the trivial solution" is "does not have only the trivial solution". In this situation you're okay, though, because null spaces are never empty.
by gfauxpas
Wed Oct 03, 2012 12:04 pm UTC
Forum: Mathematics
Topic: On pi being unkowable
Replies: 15
Views: 3701

Re: On pi being unkowable

If you don't mind working with some limits, then you can talk about bounding a circle (or whatever) with appropriate polygons. Archimedes was perfectly happy computing pi as being bounded between the perimeter of an n-gon inside the circle, and the perimeter of an n-gon outside the circle. Obviousl...
by gfauxpas
Wed Oct 03, 2012 2:15 am UTC
Forum: Mathematics
Topic: On pi being unkowable
Replies: 15
Views: 3701

Re: On pi being unkowable

gmalivuk wrote:Yes, we had the concept of length down at least a couple years before the invention of calculus.


What's the definition of the length of a curved line? Is it a primitive term?

edit: aaah I meant length of a circumference, of course we know what the length of a straight line is.
by gfauxpas
Wed Oct 03, 2012 1:28 am UTC
Forum: Mathematics
Topic: On pi being unkowable
Replies: 15
Views: 3701

Re: On pi being unkowable

Is there a definition of "length of a diameter" that can be defined entirely in geometry, i.e. without √(r²+(dr/dθ)²)dθ or similar?
by gfauxpas
Tue Sep 25, 2012 2:39 am UTC
Forum: Mathematics
Topic: Complement of Infinite Union.
Replies: 7
Views: 3568

Re: Compliment of Infinite Union.

Although basically an equivalent method, it can sometimes be far quicker to simply use equivalences of definitions to manipulate the two sides of the equation. That's the way I'd choose to approach this. But meh. Specifically in this case, the definitions of "union", "intersection&qu...
by gfauxpas
Wed May 09, 2012 9:40 pm UTC
Forum: Mathematics
Topic: confused with integration
Replies: 7
Views: 1821

Re: confused with integration

Yakk wrote:Dmitry, all of the math you did in this post can be done with sup and sub. Avoid using jsmath unless you need it, because it takes a long time to render in some browsers.

and I like having this on my bookmarks so I can copy and paste stuff like ℝ, ∧, ⇔, ⊢
by gfauxpas
Wed May 09, 2012 12:06 am UTC
Forum: Mathematics
Topic: Trigonometry help needed
Replies: 3
Views: 1161

Re: Trigonometry help needed

Are you given constraints? After playing around with it with a bunch of identities I gave up and looked at where there graphs intersect. There are an infinite amount of solutions and wolfram alpha doesn't suggest anything simple. Maybe you're supposed to to assume that -π/2 < x < π/2, and you're sup...
by gfauxpas
Fri May 04, 2012 10:22 pm UTC
Forum: Mathematics
Topic: Points along a rotated sine wave
Replies: 14
Views: 4719

Re: Points along a rotated sine wave

Meem, what are those horizontal lines outside your matrices, absolute value of each entry in the matrix? Never seen that notation before, but I guess it makes sense.

And whoops, I forgot about the constant rate. What exactly is rate, here? Magnitude of first derivative WRT t?
by gfauxpas
Fri May 04, 2012 1:09 pm UTC
Forum: Mathematics
Topic: Points along a rotated sine wave
Replies: 14
Views: 4719

Re: Points along a rotated sine wave

What about this? p: ℝ 4 → ℝ 2 (or a subset of either): p\left({x,y,\theta,t}\right) = \begin{bmatrix} \cos \theta & - \sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}\begin{bmatrix} x \\ y \end{bmatrix} where x = t , y = sin t , θ can be held constant if you'd like, and the ope...
by gfauxpas
Fri Apr 27, 2012 3:27 am UTC
Forum: Mathematics
Topic: Self Studying Proof-Based LinAlg
Replies: 6
Views: 1734

Re: Self Studying Proof-Based LinAlg

Try these: http://www.khanacademy.org/#linear-algebra - math videos, most by educator Sal Khan , my favorite math resource. http://www.proofwiki.org/wiki/Category:Linear_Algebra - math wiki. You can find theorems that aren't up yet and prove them, for practice. http://tutorial.math.lamar.edu/Classes...
by gfauxpas
Fri Apr 20, 2012 12:55 am UTC
Forum: Mathematics
Topic: Odd/stupid/interesting question
Replies: 4
Views: 1357

Re: Odd/stupid/interesting question

x2 + y2 = 0 for real x, y only has the solution x = y = 0
by gfauxpas
Thu Apr 19, 2012 2:39 pm UTC
Forum: Mathematics
Topic: Augmented Matrix in LaTeX
Replies: 5
Views: 6920

Re: Augmented Matrix in LaTeX

Thanks a lot. What's {ccc}, column column column?
by gfauxpas
Thu Apr 19, 2012 1:59 pm UTC
Forum: Mathematics
Topic: Augmented Matrix in LaTeX
Replies: 5
Views: 6920

Augmented Matrix in LaTeX

Is it possible to create any of these sorts of structures in LaTeX? I imagine the one in the lower right is easiest.
by gfauxpas
Wed Apr 18, 2012 7:37 pm UTC
Forum: Mathematics
Topic: Arccosine (trig function questions)
Replies: 12
Views: 2710

Re: Arccosine (trig function questions)

Another thing to watch out for, the -1 in general implies the inverse on the entire domain, f: X → Y, f -1 : Y → X. But none of the trig functions are invertible without restricting the domain. So sin -1 can imply a relation that's one-to-many, but arcsine is something more specific than "the i...
by gfauxpas
Tue Apr 10, 2012 2:05 pm UTC
Forum: Mathematics
Topic: Logarithmically growing function with finite limit at infini
Replies: 10
Views: 3198

Re: Logarithmically growing function with finite limit at in

Because look, I can do this: g(x) = ln(ax) - ln x. This clearly converges to ln a... Faster than you might think. ln(ax) - ln(x) = ln(a) + ln(x) - ln(x) = ln(a) is constant. right, which is why I'm not sure the OP would consider such a function "...
by gfauxpas
Tue Apr 10, 2012 12:09 am UTC
Forum: Mathematics
Topic: Logarithmically growing function with finite limit at infini
Replies: 10
Views: 3198

Re: Logarithmically growing function with finite limit at in

Timefly wrote:I'm thinking something along the lines of log(ax)-H_x


where x is a positive integer? Hx is the harmonic series as a function of x, right?

But I don't know if the OP would call that logarithmic growth. Because look, I can do this: g(x) = ln(ax) - ln x. This clearly converges to ln a...
by gfauxpas
Mon Apr 09, 2012 11:47 pm UTC
Forum: Mathematics
Topic: Logarithmically growing function with finite limit at infini
Replies: 10
Views: 3198

Re: Logarithmically growing function with finite limit at in

What do you mean by f(+∞)? Do you mean f(x) as x→+ ∞? And by f(0)=0, do you mean f(1) = 0? If by "grows logarithmically" you mean "of the form f:ℝ _{>0} \to ℝ, x \mapsto \lambda \log_a x where λ is some non-zero constant and a is some positive constant, then no, because \log_a x = \df...
by gfauxpas
Wed Apr 04, 2012 8:59 pm UTC
Forum: Mathematics
Topic: Simplify
Replies: 15
Views: 4516

Re: Simplify

Qaanol wrote:In one line, here is the condition which, if met, renders the original form undefined:

x5y = y5x


Hey neat, how'd you combine all the restraints into one equation like that?
by gfauxpas
Mon Apr 02, 2012 9:50 am UTC
Forum: Mathematics
Topic: Improper integral question
Replies: 14
Views: 3968

Re: Improper integral question

\int \frac{f'(x)}{f(x)} dx = \ln f(x) Sorry, you lose a point. The correct answer is \int \frac{f'(x)}{f(x)} dx = \ln f(x) + C Well if you want to play that game: \displaystyle \int \frac{f'(x)}{f(x)} dx = \ln|f(x)|...
by gfauxpas
Thu Mar 22, 2012 8:15 pm UTC
Forum: Mathematics
Topic: Triangle Inequality for Vectors - Equality iff Parallel
Replies: 6
Views: 3430

Re: Triangle Inequality for Vectors - Equality iff Parallel

We didn't learn inner products yet :( We use: Let v = (v 1 , v 2 , ..., v n ) in ℝ n , v i in ℝ. \displaystyle \Vert \mathbf v \Vert = \sqrt{\sum_{i=1}^n v_i^2} edit: when you say the relationship between inner products and norm, do you mean things like \mathbf v \cdot \mathbf v = \Vert \mathbf v \V...
by gfauxpas
Thu Mar 22, 2012 7:52 pm UTC
Forum: Mathematics
Topic: Triangle Inequality for Vectors - Equality iff Parallel
Replies: 6
Views: 3430

Re: Triangle Inequality for Vectors - Equality iff Parallel

Can you please explain a bit more what you mean when you say I have flexibility picking u?
by gfauxpas
Thu Mar 22, 2012 1:11 pm UTC
Forum: Mathematics
Topic: Triangle Inequality for Vectors - Equality iff Parallel
Replies: 6
Views: 3430

Re: Triangle Inequality for Vectors - Equality iff Parallel

Well this is for undergrad linear algebra, but such investigation is for my own sake. My prof. only holds us responsible to know the proof of the main part of the triangle inequality because we have a lot of stuff to memorize. Thanks for the starting point!
by gfauxpas
Thu Mar 22, 2012 12:41 pm UTC
Forum: Mathematics
Topic: Being Fast At Calculation
Replies: 14
Views: 3241

Re: Being Fast At Calculation

Do you mean at arithmetic? If you're allowed calculators on exams, there's a ton of stuff that you can do on calculators, a lot more than just addition/subtraction/multiplication/division. So if you get familiar with your calculator you can save a ton of time. What subject is this in? And can you gi...
by gfauxpas
Thu Mar 22, 2012 12:25 pm UTC
Forum: Mathematics
Topic: Triangle Inequality for Vectors - Equality iff Parallel
Replies: 6
Views: 3430

Triangle Inequality for Vectors - Equality iff Parallel

Hello friends. I'm having trouble with the second part of the triangle inequality for vectors: || v + w || = || v || + ||w|| iff v = c w , c ≥ 0. The "if" part I understand the proof and have the intuition, geometric intuition (in ℝ 1 or ℝ 2 or ℝ 3 , at least): if the vectors are parallel,...
by gfauxpas
Wed Mar 07, 2012 8:21 pm UTC
Forum: Mathematics
Topic: Quick question on basic calculus.
Replies: 50
Views: 6826

Re: Quick question on basic calculus.

The example of the exponential function was intended to further illustrate this, its actually really hard to prove that the derivative comes out to be exp(t) without first proving the power rule and applying that to the series (unless you're comfortable differentiating across limits (not something ...
by gfauxpas
Wed Mar 07, 2012 7:55 pm UTC
Forum: Mathematics
Topic: Quick question on basic calculus.
Replies: 50
Views: 6826

Re: Quick question on basic calculus.

\frac{d^2y}{dx^2} is just shorthand for \frac{d(\frac{dy}{dx})}{dx} , no? If that's true then d\frac{dy}{dx} is the same thing as, say, dw , i.e., just as meaningful as any other differential. Then however you want to define dy, (which I'm not offering up a definition for), d^2y isn't bette...
by gfauxpas
Tue Mar 06, 2012 4:03 pm UTC
Forum: Mathematics
Topic: Quick question on basic calculus.
Replies: 50
Views: 6826

Re: Quick question on basic calculus.

Considering dx is normally thought of as a very small quantity, i'm not sure that I would accept that as being an inequality in the limit as dx->0. The only examples I know of where treating a derivative as a fraction causes problems is in the partial differentiation case. Except if I know what lim...
by gfauxpas
Tue Mar 06, 2012 3:08 pm UTC
Forum: Mathematics
Topic: Quick question on basic calculus.
Replies: 50
Views: 6826

Re: Quick question on basic calculus.

In that case is there an explanation why \frac{dy}{dx}dx=dy that a highschooler can understand, or do you advise me to simply take it as it is? The best I can give you what I learned from here , that at any particular point the derivative can be treated as the slope m of a straight line, m= \dfrac ...
by gfauxpas
Tue Mar 06, 2012 2:34 pm UTC
Forum: Mathematics
Topic: Quick question on basic calculus.
Replies: 50
Views: 6826

Re: Quick question on basic calculus.

Exactly what kind of problems can I expect to encounter if I treat derivation as a fraction of differentials? Well, that's a very reasonable question! \displaystyle \frac {\mathrm d}{\mathrm dx}x^2 = \frac {(x + \mathrm dx)^2 - x^2}{\mathrm dx} = \displaystyle \frac {x^2 + 2x \cdot \mathrm ...
by gfauxpas
Sun Mar 04, 2012 2:51 am UTC
Forum: Mathematics
Topic: Quick question on basic calculus.
Replies: 50
Views: 6826

Re: Quick question on basic calculus.

I'm not the only one that cancelled the derivatives, khanacademy apparently did the same thing. Khan is using a mnemonic device to help you remember integration by substitution - he alludes to his informality once in a while in the videos. In my Calc I classes, we were discouraged from thinking abo...
by gfauxpas
Thu Mar 01, 2012 7:56 pm UTC
Forum: Mathematics
Topic: Quick question on basic calculus.
Replies: 50
Views: 6826

Re: Quick question on basic calculus.

This would actually be completely legitimate: \int x^2 2x \ \mathrm dx = \int x^2 \frac {\mathrm d x^2}{\mathrm d x} \ \mathrm dx which makes it easy to remember the theorem of integration by substitution, even if the /real/ reason isnt because the fractions cancel out. But yeah, your suggested way ...
by gfauxpas
Tue Feb 28, 2012 9:48 pm UTC
Forum: Mathematics
Topic: Funny mathematical terms and statements
Replies: 21
Views: 8436

Re: Funny mathematical terms and statements

The window question can be answered "yes" whether or not it's an excusive or or not. He's not asking "is the windows open or closed" He's asking "do you want the window open or closed?" Answer version 1: yes, I would like the window open ∨ closed Answer version 2: yes, ...
by gfauxpas
Tue Feb 28, 2012 1:44 pm UTC
Forum: Mathematics
Topic: Funny mathematical terms and statements
Replies: 21
Views: 8436

Re: Funny mathematical terms and statements

Inductive reasoning - statements that are "probably true". They're not based on the deductive method and therefore are about as strong as a "wild guess" in math. Induction - a form of mathematical proof about the properties of natural numbers. It is an example of deductive reason...
by gfauxpas
Wed Feb 22, 2012 10:35 am UTC
Forum: Mathematics
Topic: Nonstandard proofs for simple theorems
Replies: 34
Views: 7331

Re: Nonstandard proofs for simple theorems

This is possibly a circular proof, because fermat's last theorem could rely on this It almost certainly does not. Though I'm pretty sure it uses the fact that the integers are integrally closed, which immediately implies nth roots of 2 are irrational. Maybe Fermat's proof relied on it (if he had on...

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