Mr.Persona

Or, perhaps, do you agree with my belief that it'll merely convert the group of capable students from a normal distribution into a more concentrated one? I.e., the middle will be split and the stupider will get stupider and the smarter smart.

My reasoning being that, the lack of having busy work at school would result in the smarter kids actually making proper use of their time and learning more than school ever could. In contrast, the more apathetic kids, no longer force fed knowledge to barely squeeze by, will instead waste their time and learn nothing.

Your thoughts? I also question if YA! StackOverflow, etc. had an uptick in questions as a result of the latter group.

Thought this would be a fun question to post.

Anyone know why, under my answers, my responses to "Math question, please help?" and "Need help with these three college math intermediate problems on functions and graphing?" were ghosted? If you click "show more" on my "My Answers" page, you should be able to read it all. As a result, you can see I don't have links there, nor is my IP a foreign IP which has the possibility of being banned.

It sucks to waste points on this. This has happened before, but it sucks that, when I'm logged in the answers are there & they disappear only once I've logged out (even clicking edit & then submit again doesn't make them get posted).

So, suppose we define the complex numbers as (a, b).

We can prove this representation is equivalent to a + bi.

And that makes sense, we are showing two representations are equivalent.

But what is the purpose in provign something like:

a + bi = a' + bi' forces a = a' and b = b'?

It just seems odd for this not to be the case.

Is this just to prove that two complex numbers are only equvilant if their real and imaginary parts are the same?

If so, regardless, what is the purpose in proving things like this?

Also, in Ahlfors:

They consider F which is a super set of R and has a solution for x^2 + 1 = 0.

They let C be the subset of all elements of the form a + bi. [first, I don't see how they can let that be so, because how do we know elements in F are even of that form?]

They then state C is a subfield of F, and that makes sense via some mechanical proofs for a field.

They then prove the structure of C is independent of F.

They consider F' which is another superset of R and a root i' being the solution to x^2 + 1 =0.

The corresponding C' is formed by all elements a + b i' .

They show there is a bijection and consequent isomorphism, but what does it mean for the structure to be independent of F?

I have been roaming the internet attempting to find stuff on symmetric polynomials, and it all seems to start with a level of knowledge I am unfamiliar with.

Josh Swanson gave me a great recommendation for generating functions which is very readable, and I'm hoping to find just as readable an introduction to symmetric polynomials.

(I do understand proofs to sufficient level of Alhfors and Rudin part 1).

I know kids who go to MOPs (or whatever the abbreviation is) for the USAMO/IMO stuff go through a ton of material/problems in a short amount of time.

I wish to go through the IMO Compendium on my own.

There are 166 thereoms I'd have to internalize. Any thoughts as to how to do this effectively?

Likewise, if xyzzy reads this, please look back at my Riemann question and elaborate based on my comments.

Does anyone here know a good explanatory text for the Riemann-Stieltjes integral? I sort of get how there is a funcion alpha which we are using in place of the x-axis, and partitioning it instead, and somewhere it said it was like a density, but I don't understand it in full. Also, any text on applications to help differentiate it from the standard Riemann integral would be helpful.

I've recently finished a course in real analysis (i.e. Baby Rudin first 6 chapters).

I did pretty well in the class, but should I work through all the problems before moving on to studying the second half (of baby rudin)?

So, I am given a metric space. I have to prove it is complete. I know complete means that every cauchy sequence is convergent.

So you let {x_n} be a sequence of elements in the space and prove it converges.

My issue is, to prove convergence you state:

for every epsilon > 0, there exists N such that for every n >= N, d(x_n, x) < epsilon.

But how do I prove the existence of such an x? (a limit point?)

I think that is my only issue because once I construct the limit point, I should be able to prove the given cauchy sequence is convergent.

(also, since one is trying to prove d(x_n, x) < epsilon, I thought you might be able to do:

d(x_n, x) <= d(x_n, x_m) + d(x_m, p)

and then since cauchy you know:

d(x_n, x) < (epsilon/2) + d(x_m, p)

but then you are just back where you started since now you have to prove d(x_m, p) < epsilon/2 which is the same as proving d(x_n, x) < epsilon.

So, once one has a limit point, which is part of my question since I don't know how to construct one, does being cauchy play a role in proving convergence? (the latter question stemming from the above).

Why is it that women, and men who like anime/Japanese culture, tend to use emoticons so much?

Likewise, why do women in particular tend to use the acronym "lol" and "LOL"?

Especially in unfunny situations, and places where it is just out of place.

I'll cease writing here else I might attempt to answer my own question and deter different answers.

If at all possible I request detailed answers an non-ranting answers.

In group theory, as well as ring theory, one can construct new objects from old ones with the notion of a factor group, i.e.:

Z/nZ or R/Z.

I know that the definition of the elemnents are the left cosets for every a in the group placed in the 'denominator', but I don't know what the actual elements in the resulting groups/quotient rings(?), are.

i.e., what are the elements of R/Z? How does one figure them out?

And, I guess in general, how does one come about figuring out the elements in a group or ring of the Form G/N or R/W?

Reading through the Yahoo Answer section and reviewing the part on how Yahoo Answers is community moderated and all that, since higher execs. aren't going to come here and get our feedback: is there any way to make suggestions that actually reach someone who isn't just a member of the community?

E.g. Restore a no answers check box under justification that the point of this site is to be informative and respond to users questions.

E.g. Provide some compatibility with free software such as LaTeX like on Art of Problem Solving, at least for the Science and Mathematics sections so that questions can be easily stated without ambiguity, and answers can be clearly given.

By definition, a mapping or function states that each element in a set S has a unique element in the destination set, call it set T.

A mapping is one to one if f(x) = f(y) implies x = y.

My question then is, isn't every function, therefore, one-to-one?

If so, what is the point of defining the specific type of mapping known as one-to-one maps if, in order to be a mapping, this property must be satisfied.

A question asks how many ways to get 2 pair, such that there isn't a 4 of a kind.

My thoughts are there are two cases.

case 1:

you get a full house, e.g. Ace, Ace, Ace, Duece, Duece

Case 2: You get 2 pair, and then a rank differing from both pairs. e.g. Ace, Ace, Duece, Duece, five

For the first case I did:

[(13 choose 1)*(4 choose 3)]*[(12 choose 1)*(4 choose 2)]

since I pick 3 cards of the same rank and then two others which are of a different rank.

I get that to equal 3744.

But, since the order in which I choose either the set of 3 or the set of 2 doesn't matter, I divide by 2!. giving me 1872

For the second case I got:

[(13 choose 1)*(4 choose 2)]*[(12 choose 1)*(4 choose 2)]*[(11 choose 1) * (4 choose 1)]

= 247104

But since the order in which I choose these 3 sets doesn't matter, I divide by 3!

= 41184

Adding the cases I get: 43056 ways to get 2 pair such that it is not 4 of a kind.

Please, someone tell me if I am correct, and if I am wrong, please tell me where I went wrong and what my misconception was.

My problem is that I get confused with the different names and, I don't know enough about each subject to determine if whatever they are talking about in the syllabus is relavent.

For example, I know in the UK Analysis is just Calculus, but in the U.S. Analysis is its own set of courses post Multi. Var.

Does anyone know an easy way to find equivalent courses and what would be considered Analysis in the UK?

I have a set of headphones with a broken ear piece. That set has its own volume control (analog style were you can just adjust it).

I have another set of headphones that arn't broken, but they do not have that volume control piece.

Is it possible for me to cut out the volume control from the broken headphones, merge it with the wires in the new one, and for it to still work?

I remember having watched a movie which was in black and white.

The movie's plot centered around a man who went to visit a house, yet feels as if he has been there before.

I forget if murders occurs.

At the end of the film it is revealed it had been a dream.

If anyone knows the film's name I'd be most grateful to be reminded.

My PC has, since 2 am this morning, had this problem where, after a while the screen goes black and this weird buzzing noise iminates from the speakers (not the tower unit, i think).

I looked around and cleaned out the dust, but then I also wondered if my motherboard temperatures could be causing it, therefore, if possible, could someone tell me if the temperatures are all good?

Here are the temps:

http://img818.imageshack.us/img818/38/efx.png

Just an odd curiosity:

What is the best wine/expensive wine/epicist wine.

The most I know about wine is that it needs time to settle to be at the peak of flavor, but besides that I don't know anything.

First of all, i'd like to ask if you can refer to any sites with geometric proof problems and solutions so that i can practice.

second am i correct?:

Given: line CP is perpendicular bisector of segment AB

Prove: CA = CB

..................C

................/..|..\

............../....|....\

............/......|......\

........A/____.|.____\B

...................P

Note: it should show that there's a right angle at CPB and that AP = PB

Now my proof:

1) given: line CP is perpendicular bisector of segment AB

2) def of Perpendicular bisector: <APC = <CPB

3) reflexive Prop: segment PC = Segment PC

4) SAS prostulate: Triange ACP is congruent to triange CPB

5) corresponding parts of triangle: CA = CB

...........B

.......... /|\

........../.|.\

........./..|..\

....... /...|...\

A ----D---- C

given. triangle ABC is isoceles, segment BD bisects angle <B

prove: triange ABD = traingle CBD

---

My proof:

Given: segment BD bisects <B

reflexive Property of Congruence: segment BD = segment BD

def. of midpoint: point D is the midpoint

def of midpoint: segment AD = segment DC

def of perpendicular lines: segment BD is perpendicular to segment AC

def of right angles: <ADB , <BDC are right angles

SAS Postulate: triangle ABD = triange CBD