Search found 501 matches

by Dark Avorian
Mon Mar 18, 2013 10:35 pm UTC
Forum: Mathematics
Topic: derivative of x^x^x^x^...
Replies: 5
Views: 2685

Re: derivative of x^x^x^x^...

Well, supposing it exists and is differentiable, we observe that f(x) = x ^ f(x) = e^(ln(x)f(x)) applying the chain rule f'(x) = [e^(ln(x)f(x))]* [f(x)/x + f'(x)ln(x)] f'(x) [ 1 - f&#...
by Dark Avorian
Mon Mar 18, 2013 7:11 pm UTC
Forum: Mathematics
Topic: Beautiful proofs/mathematical properties
Replies: 16
Views: 3906

Re: Beautiful proofs/mathematical properties

I especially like the look of this one: 2+2=2*2=2 2 = 2 2= 2 2=2 2 =... But I have to admit I don't understand the later ones completely. For example I read 2 2 as "2 in base 2" and that just doesn't make sense at all, so I suppose I've missed something? Also, does the ... indicate that t...
by Dark Avorian
Sun Mar 17, 2013 11:28 pm UTC
Forum: Science
Topic: Neat and tidy charges - An unanswered question or not?
Replies: 27
Views: 5657

Re: Neat and tidy charges - An unanswered question or not?

To be honest, given the strength of the electric field, it's pretty obvious that charge has to be fundamentally quantized. I remember hearing somewhere that a minuscule shift in the balance of electron to proton charge ratio (from 1 to say 1.00000000001) could cause attractive/repulsive forces on th...
by Dark Avorian
Sat Mar 16, 2013 7:32 pm UTC
Forum: News & Articles
Topic: Protests in New York over teen shot by police
Replies: 9
Views: 2270

Re: Protests in New York over teen shot by police

Yeah, seriously. I live on the east coast in a sheltered neighborhood and I've heard of the Rodney King riots.
by Dark Avorian
Thu Mar 14, 2013 9:41 pm UTC
Forum: School
Topic: How to make teachers friendlier and easier to talk to?
Replies: 16
Views: 14398

Re: How to make teachers friendlier and easier to talk to?

I'm still trying to figure out how to do this in university. I was never very close to any of my teachers in high school, excepting perhaps one science teacher. I've always tried to make myself friendlier and more open to teachers/professors and I've found it's easier at the university level. Maybe...
by Dark Avorian
Thu Mar 14, 2013 9:38 pm UTC
Forum: School
Topic: American school system
Replies: 22
Views: 17752

Re: American school system

I had different schedules every day in both high school and university- it really depends on the school. But yes, the American system is very different from the one in Europe in that on both levels you are sort of expected to be a well-rounded scholar through the requirements- later on you can of c...
by Dark Avorian
Mon Mar 11, 2013 9:49 pm UTC
Forum: Mathematics
Topic: forth dimension
Replies: 13
Views: 2242

Re: forth dimension

I've always thought of time as the best aid in visualising 4 dimensions for me.
by Dark Avorian
Thu Mar 07, 2013 7:16 pm UTC
Forum: Mathematics
Topic: A->A^(-1) is continuous (A. Calc)
Replies: 8
Views: 1635

Re: A->A^(-1) is continuous (A. Calc)

Yeah we can consider linear operators as matrices as just nm-dimensional vectors. Since that space is finite dimensional, norms are all equivalent, so we can consider them simply under a euclidean or max norm (for general linear transforms, we would have to consider the operator norm)
by Dark Avorian
Thu Mar 07, 2013 6:15 pm UTC
Forum: News & Articles
Topic: The Global Growth of Drone Warfare
Replies: 272
Views: 43051

Re: The Global Growth of Drone Warfare

Or ya know, a Cartel kingpin in vaguely arguably isolated location. I could totally see the US hitting that guy with a drone strike.
by Dark Avorian
Thu Mar 07, 2013 3:37 am UTC
Forum: Mathematics
Topic: A->A^(-1) is continuous (A. Calc)
Replies: 8
Views: 1635

Re: A->A^(-1) is continuous (A. Calc)

Do you know the most common way to determine (cough cough) whether a transform is invertible? If you do, think about why its pretty immediate that the set of non-invertible transforms is closed. Also, remember you can view every transform as a matrix, and that we can consider a metric on these matri...
by Dark Avorian
Mon Mar 04, 2013 9:59 pm UTC
Forum: News & Articles
Topic: Gay cures AIDS
Replies: 39
Views: 8040

Re: Child with HIV cured

And you'd have to be a match to one of them to recieve it.
by Dark Avorian
Mon Mar 04, 2013 9:16 pm UTC
Forum: Books
Topic: Wheel of Time (Split from Geeky/Nerdy Kids Books)
Replies: 228
Views: 129905

Re: Wheel of Time (Split from Geeky/Nerdy Kids Books)

I loved that. I think after watching the entire cosmological battle in total detail, it's worthwhile to leave a mystery.
by Dark Avorian
Mon Mar 04, 2013 8:18 pm UTC
Forum: News & Articles
Topic: Gay cures AIDS
Replies: 39
Views: 8040

Re: Child with HIV cured

Sizik wrote:Better headline:
Gay cures AIDS


Where's your god now!?
EDIT: He's being awesome and screwing with bigots actually.
by Dark Avorian
Sun Mar 03, 2013 8:50 pm UTC
Forum: Serious Business
Topic: Teaching Kids to Code
Replies: 90
Views: 31331

Re: Teaching Kids to Code

I'm sorry, but teaching kids to code in a large scale school setting seems just as likely to involve rote memorisation and regurgitation as teaching grammar, history, math, science. Every subject can be taught in this way, and as long as that is the most efficient way given our evaluation system for...
by Dark Avorian
Sat Mar 02, 2013 9:24 pm UTC
Forum: Serious Business
Topic: Teaching Kids to Code
Replies: 90
Views: 31331

Re: Teaching Kids to Code

This is contradictory. Syntax almost by definition comes about according to the capricious whimsy of whoever designed the language. I didn't say it didn't. I just said you use it all the time, while solving problems you actually understand, and it's not a lot to memorise. Then I submit that your ma...
by Dark Avorian
Thu Feb 28, 2013 9:43 pm UTC
Forum: Mathematics
Topic: Help with Principles of Mathematical Analysis
Replies: 11
Views: 3142

Re: Help with Principles of Mathematical Analysis

About the Schwarz inequality, a more natural proof perhaps comes from the notion of an inner product. Particularly, for any pair of n-tuples of complex numbers we can define an inner product as follows (a_1, ..., a_n) * (b_1, ..., b_n) = sum{i=1 to n} a_i conj(b_i) Where conj() is the complex conjug...
by Dark Avorian
Thu Feb 28, 2013 9:04 pm UTC
Forum: Mathematics
Topic: Infinite Sets
Replies: 18
Views: 3534

Re: Infinite Sets

Ah I see. Basically, if there is a set which contains itself, then there is a set which contains only itself (by the axiom of paring, apparently), and then that set violates regularity. So my set effectively violates the axiom of pairing in conjunction with the axiom of regularity. So 'c' was the c...
by Dark Avorian
Thu Feb 28, 2013 3:24 pm UTC
Forum: News & Articles
Topic: Wanted: Middle-aged couple for trip to Mars
Replies: 43
Views: 6255

Re: Wanted: Middle-aged couple for trip to Mars

Wait. Do we have the ability to take off from mars if we send someone there?
by Dark Avorian
Thu Feb 21, 2013 10:46 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1176: "Those Not Present"
Replies: 139
Views: 26755

Re: 1176: "Those Not Present"

Guys can we stop talking about how people who gossip are terrible when they aren't here, and talk about squids?
by Dark Avorian
Thu Feb 21, 2013 2:07 pm UTC
Forum: Mathematics
Topic: Let's All Help Carlington Learn Maths! Today: Induction
Replies: 13
Views: 2693

Re: Let's All Help Carlington Learn Maths! Today: Induction

The proposition is not the formula. P(10) is not 56. P(10) is the statement that ten lines, not concurrent, not parallel, will divide the plane into 56 segments. Further, in this example, the formula (k^2 + k +2)/2 = 1 + (sum of first k integers) Is only one part of what you have to prove. Seeing pa...
by Dark Avorian
Thu Feb 21, 2013 7:48 am UTC
Forum: Mathematics
Topic: I discovered a formula for the nth term of any sequence of
Replies: 16
Views: 2328

Re: I discovered a formula for the nth term of any sequence

You do realize that for any finite number of terms there is a unique n-1 degree polynomial p(x) such that for any integer k in the set {1,2,...,n}

p(k) = u_k
by Dark Avorian
Thu Feb 21, 2013 4:20 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1176: "Those Not Present"
Replies: 139
Views: 26755

Re: 1176: "Those Not Present"

Can I just scoot in response to every conversation?
by Dark Avorian
Thu Feb 21, 2013 3:23 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1176: "Those Not Present"
Replies: 139
Views: 26755

Re: 1176: "Those Not Present"

I would never talk about a friend in that venting way to anyone except a mutual friend I trust. I realize I'm still potentially harming them, but eh. I suppose we're really talking about different levels of gossip, although you should know your points have actually struck home for me. I guess I'm a ...
by Dark Avorian
Thu Feb 21, 2013 3:12 am UTC
Forum: Mathematics
Topic: new methods to check existence of limit
Replies: 4
Views: 1582

Re: new methods to check existence of limit

If you want something more formulaically defined:

f(x,y) = (xy^2)/(x^2 +y^6), (x,y) =\= (0,0)
f(0,0) = 0

Obviously it gives a real value everywhere. and, if x=0 then f(x,y) =0. Now suppose y = kx, as a function of x it should be continuous.
by Dark Avorian
Thu Feb 21, 2013 3:08 am UTC
Forum: Mathematics
Topic: Let's All Help Carlington Learn Maths! Today: Induction
Replies: 13
Views: 2693

Re: Let's All Help Carlington Learn Maths! Today: Induction

Yeah, P(n) is not really a function (well, if it is, it's a function from the space of natural numbers to the set of all mathematical statements. P(n) is similar to a function in that it allows us to compress and compactly express information. There are two layers of abstraction. The first is that w...
by Dark Avorian
Thu Feb 21, 2013 2:57 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1176: "Those Not Present"
Replies: 139
Views: 26755

Re: 1176: "Those Not Present"

-snip- Okay, just as a first point, anecdotal evidence is not the demon that you make it out to be. I suppose I could just have easily have framed it as a hypothetical, but concrete examples I know the details of are easier to talk about. Of course, you make a damn good point. Gossip can be used as...
by Dark Avorian
Wed Feb 20, 2013 11:42 pm UTC
Forum: General
Topic: Hifaleetin' thoughts
Replies: 90225
Views: 9397433

Re: Screechings of the Great Unwashed (Meander to the Morgue

OMNOMNOMNOM FRUIT SALAD.

Or for the more refined moment, a light salad with olive oil dressing, panko breaded warm baked goat cheese and crumbled bacon with some little crumbled peanuts
by Dark Avorian
Wed Feb 20, 2013 8:43 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1176: "Those Not Present"
Replies: 139
Views: 26755

Re: 1176: "Those Not Present"

A lot of people say that you should face someone face to face. I have to ask a question. Do you really, really want everything other people dislike about you to be told to you? Really? Frankly I would much rather everyone else talk about me. Maybe I'm wierd. I once knew this one person who was on a ...
by Dark Avorian
Wed Feb 20, 2013 6:14 pm UTC
Forum: Mathematics
Topic: new methods to check existence of limit
Replies: 4
Views: 1582

Re: new methods to check existence of limit

yeah, that doesn't work. As you said, it just restricts consideration to a straight line. There's an example given in Rudin's "Principles of Mathematical Analysis" of an f(x,y) which is unbounded in any neighborhood of (0,0) but which is continuous when restricted to any straight line.
by Dark Avorian
Wed Feb 20, 2013 2:09 pm UTC
Forum: Mathematics
Topic: Help with Principles of Mathematical Analysis
Replies: 11
Views: 3142

Re: Help with Principles of Mathematical Analysis

I think it's using the well-ordering principle for integers there
by Dark Avorian
Tue Feb 19, 2013 3:23 am UTC
Forum: Mathematics
Topic: Let's All Help Carlington Learn Maths! Today: Induction
Replies: 13
Views: 2693

Re: Let's All Help Carlington Learn Maths! Today: Induction

Theres a bit of a question as to how much you need to/can formalize something, and how much a pretty clear, but not necessarily rigorously symbolically encoded argument can be used. Also, realize that the notation, P(n), or whatever you've seen doesn't necessarily mean it's gonna look much like a fu...
by Dark Avorian
Thu Feb 14, 2013 2:32 pm UTC
Forum: Science
Topic: Why do some people believe the universe is infinite?
Replies: 91
Views: 14664

Re: Why do some people believe the universe is infinite?

Density wouldn't necessarily be indeterminate. Again, an infinite chessboard has infinite area, and infinite black area, but the density is definitely 50%, we just take a limit.
by Dark Avorian
Mon Feb 11, 2013 12:34 am UTC
Forum: News & Articles
Topic: Police misbehavior thread
Replies: 7005
Views: 1166982

Re: Police misbehavior thread

I'll admit I'm privileged and naive, but deep in my heart I'd rather trust cops with the disgression to kill when threatened than try and restrict them.
by Dark Avorian
Sun Feb 10, 2013 3:40 am UTC
Forum: Mathematics
Topic: A Thread for scratch123's Random Math Questions
Replies: 71
Views: 16819

Re: A Thread for scratch123's Random Math Questions

Stickman wrote:
doogly wrote:The math doesn't lie.


Except for differential geometry.


That was painful.
by Dark Avorian
Fri Feb 08, 2013 9:13 pm UTC
Forum: Mathematics
Topic: Mathematics - a new basis
Replies: 36
Views: 7418

Re: Mathematics - a new basis

Day 2: The disease has infected another member of the forum. Immediate quarantine protocols are recommended.
by Dark Avorian
Thu Feb 07, 2013 3:10 pm UTC
Forum: General
Topic: Hifaleetin' thoughts
Replies: 90225
Views: 9397433

Re: Screechings of the Great Unwashed (Meander to the Morgue

Never had a nosebleed last this long before... 32 minutes and counting. I had nosebleeds this long multiple times in a few days after moving to a cold place for college and right after a nasty head cold with lots of nasal congestion and noseblowing. I went to see a doctor who advised using some Afr...
by Dark Avorian
Wed Feb 06, 2013 1:01 pm UTC
Forum: Mathematics
Topic: Mathematics - a new basis
Replies: 36
Views: 7418

Re: Mathematics - a new basis

Henry Lebag?

I'm gonna go out on a limb and say you mean Henri Lesbesgue.
by Dark Avorian
Tue Feb 05, 2013 4:33 am UTC
Forum: Mathematics
Topic: Why do we need infinite sets again?
Replies: 20
Views: 3121

Re: Why do we need infinite sets again?

]And I maintain that from there you can define rational numbers and their arithmetic(though again not as a set), and from there you can define limits, and with them, computable numbers and calculus. Ummm...like http://en.wikipedia.org/wiki/Construction_of_the_real_numbers#Construction_from_Cauchy_s...

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