## Search found 69 matches

- Sun Jul 17, 2011 9:23 pm UTC
- Forum: Mathematics
- Topic: Why does a Taylor series work?
- Replies:
**45** - Views:
**12414**

### Re: Why does a Taylor series work?

If its clear what's going on, then that's fine, but saying that the atomic polynomials span the continuous functions is wrong, even saying that atomic polynomials span smooth functions is wrong, which was the original context that skep was responding to. Oh, you're right. I misread cleverbeans's po...

- Sun Jul 17, 2011 9:03 pm UTC
- Forum: Mathematics
- Topic: Why does a Taylor series work?
- Replies:
**45** - Views:
**12414**

### Re: Why does a Taylor series work?

This is just false. Continuous functions are an infinite dimensional vector space, true, but there is no basis consisting of polynomials, not every function can be written as a linear combination of polynomials, and a Taylor series is not a way of writing a function as a linear combination of polyn...

- Sun Jul 17, 2011 6:33 pm UTC
- Forum: Mathematics
- Topic: Why does a Taylor series work?
- Replies:
**45** - Views:
**12414**

### Re: Why does a Taylor series work?

This is just false. Continuous functions are an infinite dimensional vector space, true, but there is no basis consisting of polynomials, not every function can be written as a linear combination of polynomials, and a Taylor series is not a way of writing a function as a linear combination of polyn...

- Wed Jul 13, 2011 12:49 am UTC
- Forum: School
- Topic: Reactions to your Major
- Replies:
**344** - Views:
**55598**

### Re: Reactions to your Major

I went in this week for jury duty, but wasn't called to serve on a trial. I was sitting there when someone taps me on the shoulder and asks... "What are you majoring in or what did you major in, if you are out of college?" My reply- "Chemistry with a minor in Mathematics and possibly...

- Mon Jul 11, 2011 7:20 am UTC
- Forum: Mathematics
- Topic: Wrong on the Internet II: Norman J. Wildberger
- Replies:
**85** - Views:
**48105**

### Re: Wrong on the Internet II: Norman J. Wildberger

I read one of the articles on this website, and he made a lot of good points and a lot of bad points. I more or less agreed with his point that the foundations of math are really messy and most students of mathematics (and probably some professional mathematicians as well) don't really think about t...

- Wed Feb 16, 2011 8:15 pm UTC
- Forum: Mathematics
- Topic: Is this a meaningless math question?
- Replies:
**24** - Views:
**2518**

### Re: Is this a meaningless math question?

or perhaps I am mistaken in assuming that 0 probability means an occurrence is impossible? That is a mistake, yes. Choose a random integer, and the probability you'll pick 10697 is 0 because there are infinitely many integers to choose from. But it's not impossible for you to choose 10697. Ummm...n...

- Thu Nov 11, 2010 11:08 am UTC
- Forum: Mathematics
- Topic: Can (PI) exist?
- Replies:
**24** - Views:
**4456**

### Re: Can (PI) exist?

It just so happens that PI ends up converging to a constant so that it can be approximated This is yet another problem with this post. Every nondecreasing sequence of real numbers that is bounded above converges. So if I have some number of the form r + \sum_{i=1}^{\infty} \frac{x_i}{10^i} where ea...

- Tue Nov 09, 2010 9:32 am UTC
- Forum: Mathematics
- Topic: Can (PI) exist?
- Replies:
**24** - Views:
**4456**

### Re: Can (PI) exist?

Concerning the proof of Pi: It uses a bunch of symmetrical polygons inscribed into a circle, right? What do you mean "proof of pi?" Do you mean the calculation of the ratio of the circumference of a circle to its diameter? Are you trying to argue that this number does not exist or that it...

- Sat Oct 30, 2010 11:05 pm UTC
- Forum: Mathematics
- Topic: limit question
- Replies:
**13** - Views:
**1505**

### Re: limit question

keeperofdakeys wrote:L'hopital's rule?

I'm really not a fan of using L'hopital's rule on this limit, because the derivatives for sine and cosine are usually obtained by using that limit.

- Wed Oct 06, 2010 7:12 pm UTC
- Forum: Mathematics
- Topic: Sufficiently large values of 2 such that 2+2=5
- Replies:
**5** - Views:
**2792**

### Re: Sufficiently large values of 2 such that 2+2=5

This is where it comes out that I don't understand 4D mathematics. I had assumed that if a 3-sphere is the boundary of a 4-ball, it must be in 4-space or else the ball it is defining doesn't exist. When people say that the 3-sphere is the boundary of a 4-ball, that just means that they have the sam...

- Sun Oct 03, 2010 11:39 am UTC
- Forum: Mathematics
- Topic: Good counter-examples for compactness
- Replies:
**7** - Views:
**2097**

### Re: Good counter-examples for compactness

I think I'm gonna make some enemies with this example, but: (0,1) is closed in the space (0,1) with the usual metric. Furthermore, (0,1) is (totally) bounded. However, (0,1) is not compact. The problem with "closed" is that it's a property of the metric space you're inside of, and not the ...

- Thu Sep 30, 2010 10:09 pm UTC
- Forum: General
- Topic: Whiteness and Masculinity Club (Good or Bad?)
- Replies:
**332** - Views:
**24223**

### Re: Whiteness and Masculinity Club (Good or Bad?)

Supremum: the argument against has been made I think a few times in this thread. Maybe at least two or three times, I dunno, I certainly haven't read all eight pages. If you have some questions about any of the two or three arguments already made that were unclear, maybe someone from the opposition...

- Thu Sep 30, 2010 9:58 pm UTC
- Forum: General
- Topic: Whiteness and Masculinity Club (Good or Bad?)
- Replies:
**332** - Views:
**24223**

### Re: Whiteness and Masculinity Club (Good or Bad?)

Ok, I see why people would have a problem with the Whiteness and Masculinity Club as described in the OP- the club just exists to be contrary while a black womens' club serves a real purpose. I also admit that white men are privileged over pretty much every other social group (at least in the US). H...

- Mon Sep 27, 2010 6:00 pm UTC
- Forum: Mathematics
- Topic: Really basic stuff that was never proven in class
- Replies:
**83** - Views:
**10338**

### Re: Really basic stuff that was never proven in class

Back in 6th grade my "Honors Math" teacher was a big Number Theory freak. Prime numbers were his favorite topic to discuss with us. He told us that there were infinitely many. Being in 6th grade, none of us questioned him, but thinking back I don't think he ever proved it to us. That's pr...

- Mon Sep 27, 2010 2:54 pm UTC
- Forum: Mathematics
- Topic: Really basic stuff that was never proven in class
- Replies:
**83** - Views:
**10338**

### Re: Really basic stuff that was never proven in class

Doraki wrote:If p is a prime divisor of n²+1, then p is a gaussian prime.

No, that's not true at all:

(2 + i)(2-i) = 5

(4-i)(4+i) = 17

In general, if n^2 +1 is a prime, then it is congruent to 1 mod 4 and therefore factors over the gaussian integers.

- Sun Sep 26, 2010 1:16 pm UTC
- Forum: General
- Topic: Blistering blue barnacles
- Replies:
**28528** - Views:
**3099243**

### Re: Rant Thread (to balance Awesome Thread)

I'm now doing degree level chemistry and am really disappointed to see the fear of the evil mathematics still remains and can't be offered as an alternative explanation or mentioned without fear of upsetting the students. Wait, really? That's actually a pretty serious problem. However, I still don'...

- Sun Sep 26, 2010 12:45 pm UTC
- Forum: General
- Topic: Blistering blue barnacles
- Replies:
**28528** - Views:
**3099243**

### Re: Rant Thread (to balance Awesome Thread)

Of course, there's also a middle ground: openly state that the Bohr model (or whichever model of whichever subject) is outdated and overly simplistic, and that it is sufficient for the time being, but should not be taken as an accurate representation of the atom (or whichever subject). That's a goo...

- Sun Sep 26, 2010 11:11 am UTC
- Forum: Mathematics
- Topic: Really basic stuff that was never proven in class
- Replies:
**83** - Views:
**10338**

### Re: Really basic stuff that was never proven in class

I've never gotten a decent, easy proof that there are infinite Gaussian Primes. I'm assuming we're not allowed to take for granted that there are infinitely many primes that are congruent to 3 (mod 4)? Edit: Actually, scratch that, it's easy to show even without that fact. it's not super hard to sh...

- Sun Sep 26, 2010 10:14 am UTC
- Forum: General
- Topic: Blistering blue barnacles
- Replies:
**28528** - Views:
**3099243**

### Re: Rant Thread (to balance Awesome Thread)

I was so pissed when I found out that Bohr's model of the atom wasn't correct and no one had told me. I was in eighth grade and flipping through next year's textbook when I happened upon this thing about atoms. WHAT THE HELL. I HAVE BEEN TAUGHT ABOUT ATOMS SINCE FOREVER AND NOT ONCE HAS ANYONE MENT...

- Fri Sep 24, 2010 8:44 pm UTC
- Forum: General
- Topic: Whiteness and Masculinity Club (Good or Bad?)
- Replies:
**332** - Views:
**24223**

### Re: Whiteness and Masculinity Club (Good or Bad?)

stuff Yes. Which is why being white carries certain privileges and being male carries certain privileges. Of course. The entire point of my series of comments was that laserguy said that the heirs to the legacy of wealth and power were white males, and I was just saying that (modern!) white females...

- Fri Sep 24, 2010 8:22 pm UTC
- Forum: General
- Topic: Whiteness and Masculinity Club (Good or Bad?)
- Replies:
**332** - Views:
**24223**

### Re: Whiteness and Masculinity Club (Good or Bad?)

Because of this, they were more likely to aggregate wealth, be more educated, enter more positions of power, etc. Many of these advantages they were able, directly or indirectly, to transfer to their children. The playing field was decidedly tipped in the favour of white males, and they also create...

- Thu Sep 23, 2010 6:14 pm UTC
- Forum: General
- Topic: Whiteness and Masculinity Club (Good or Bad?)
- Replies:
**332** - Views:
**24223**

### Re: Whiteness and Masculinity Club (Good or Bad?)

Because of this, they were more likely to aggregate wealth, be more educated, enter more positions of power, etc. Many of these advantages they were able, directly or indirectly, to transfer to their children. The playing field was decidedly tipped in the favour of white males, and they also create...

- Mon Sep 20, 2010 10:05 pm UTC
- Forum: School
- Topic: Hard work vs. Smartishness
- Replies:
**247** - Views:
**36350**

### Re: Hard work vs. Smartishness

I know this is a really trite story, but I can't resist the urge to tell it anyway... I was one of those people in high school who didn't have to work hard to understand things...and you know what? I had a real wake up call no later than my first semester at college. Having been one those people who...

- Fri Sep 03, 2010 10:34 pm UTC
- Forum: School
- Topic: Quadruple majoring
- Replies:
**42** - Views:
**7555**

### Re: Quadruple majoring

I'm gonna jump on the bandwagon here. Seriously, don't even try to do this. One of my close friends (and one of the smartest people I know) is struggling to finish her math/ee double major in 4 years, and she came in with about as much AP credit as you did. She says she "lives" in the circ...

- Mon Aug 23, 2010 8:32 pm UTC
- Forum: School
- Topic: Reactions to your Major
- Replies:
**344** - Views:
**55598**

### Re: Reactions to your Major

Well I did maths, and one of the common reactions I got was "so you're going to be a maths teacher then?" Because as we all know, the only use for maths is to teach it to children. As a math major, I have never heard this one before. Usually I get something along the lines of "so, do...

- Fri Aug 13, 2010 5:20 am UTC
- Forum: Mathematics
- Topic: Revised Simple Proof of Beal's Conjecture
- Replies:
**29** - Views:
**3782**

### Re: Revised Simple Proof of Beal's Conjecture

It isn’t difficult to see that the 1st product + the 2nd product = the 3rd product if and only if the left hand side of the equation can be factorised, i.e. rewritten in the form P(Q + R) where P,Q and R are positive integers. This statement is wrong. And if it isn't wrong, please be more clear abo...

- Wed Jul 21, 2010 8:41 pm UTC
- Forum: Mathematics
- Topic: Math discovered or invented?
- Replies:
**110** - Views:
**15755**

### Re: Math discovered or invented?

I disagree. There is lots of perfectly valid math out there that doesn't obviously correspond to anything in the universe at all. False, math is in the universe, and there is no perfectly valid math that doesn't relate to other math. :lol: Oops, sorry, bad word choice on my part. When I said "...

- Wed Jul 21, 2010 3:06 am UTC
- Forum: Mathematics
- Topic: Math discovered or invented?
- Replies:
**110** - Views:
**15755**

### Re: Math discovered or invented?

black_hat_guy wrote:Math is based off of what we have observed the Universe to be.

I disagree. There is lots of perfectly valid math out there that doesn't obviously correspond to anything in the universe at all.

- Sun Jul 18, 2010 4:43 pm UTC
- Forum: Mathematics
- Topic: Usages of calculus.
- Replies:
**16** - Views:
**2230**

### Re: Usages of calculus.

One neat use of calculus that I don't think has been expressed yet is that integrals can be used to find bounds on sums. In particular, if you notice that a certain sum you're looking at happens to be a lower riemann sum for some function, then you can bound your sum by the integral of the function....

- Sun Jul 18, 2010 3:10 am UTC
- Forum: School
- Topic: School makes me hate math
- Replies:
**54** - Views:
**8464**

### Re: School makes me hate math

The biggest point about this pdf is the "proofs". Why we must see THIS in order to understand limits? I can read it, I can understand how it makes his way. But that just can't be the first thing we see for understanding "limit". You shouldn't, and if that's the first thing they ...

- Fri Jul 16, 2010 2:50 am UTC
- Forum: Mathematics
- Topic: Rational^irrational can yield irrational
- Replies:
**27** - Views:
**8082**

### Re: Rational^irrational can yield irrational

Here's a solution to the OP's problem that just uses the irrationality of \sqrt2 . We want x rational and y irrational such that x^y is irrational. Let a=2^{1/\sqrt2} . Consider two cases. Case 1: a is irrational. Then we have a solution x=2 , y=1/\sqrt2 . Case 2: a is rational. Then we have a solu...

- Mon Jun 14, 2010 1:18 am UTC
- Forum: Mathematics
- Topic: Math Books
- Replies:
**378** - Views:
**248959**

### Re: Math Books

Can someone recommend a book where vector calculus is built up in a coordinate-free setting? I really wish I knew more about differential forms, etc.

- Sun Jun 13, 2010 3:49 pm UTC
- Forum: Mathematics
- Topic: Determinants
- Replies:
**17** - Views:
**2160**

### Re: Determinants

Sorry, I'm going to go on a bit of a tangent here. Looking back, the way they teach matrices in high school is really annoying. At least in my high school algebra II class, we learned about matrices far before we learned about vectors. And even though they're not really the same concepts, it seems e...

- Sun Jun 06, 2010 2:16 pm UTC
- Forum: Mathematics
- Topic: Wish I had seen/understood this comic sooner...
- Replies:
**36** - Views:
**4411**

### Re: Wish I had seen/understood this comic sooner...

That be rational/get real comic has always been a pet peeve of mine. i isn't a rational number.

- Wed Jun 02, 2010 3:44 am UTC
- Forum: Mathematics
- Topic: Math discovered or invented?
- Replies:
**110** - Views:
**15755**

### Re: Math discovered or invented?

Is it safe to say the axioms are invented and the theorems and proofs are discovered? I dunno, the standard for what constitutes an acceptable proof is a social phenomenon, I'm not sure it exists outside the human experience. We can always reduce everything to the formal string games, which are ver...

- Mon May 31, 2010 8:31 pm UTC
- Forum: School
- Topic: Before you graduated
- Replies:
**18** - Views:
**2770**

### Re: Before you graduated

I haven't quite graduated yet, but I'm three years into a math degree... Don't compare yourself to other people. When I first entered college, I had this awful way of thinking where I kept saying things like "I'll never be as good at math as this person." I was getting poor grades in both ...

- Mon May 31, 2010 3:42 pm UTC
- Forum: Mathematics
- Topic: Math discovered or invented?
- Replies:
**110** - Views:
**15755**

### Re: Math discovered or invented?

I've seen some people arguing that the Pythagorean theorem does not reflect the truth of the real world. It only approximates it. But I ask, so what? That merely means we discovered something to approximate the world. Just like in science, we started with some basic observations. From what we saw, ...

- Mon May 31, 2010 1:09 am UTC
- Forum: Mathematics
- Topic: "Special" four digit number
- Replies:
**26** - Views:
**7317**

### Re: "Special" four digit number

1729. It's interesting because it's a Carmichael number, and it's the smallest number that can be expressed as the sum of two cubes in two different ways. However, it also has historical importance:

http://en.wikipedia.org/wiki/Ramanujan# ... umber_1729

http://en.wikipedia.org/wiki/Ramanujan# ... umber_1729

- Mon May 31, 2010 12:34 am UTC
- Forum: Mathematics
- Topic: Math discovered or invented?
- Replies:
**110** - Views:
**15755**

### Re: Math discovered or invented?

Math is discovered. Based on a certain set of rules, definitions, and assumptions, certain mathematical facts are true. They are true if no one knows them or if everyone knows them, because they have to follow logically from the assumptions and definitions. Now, notation may be invented, but in ord...

- Sun May 30, 2010 8:24 pm UTC
- Forum: Mathematics
- Topic: Math discovered or invented?
- Replies:
**110** - Views:
**15755**

### Re: Math discovered or invented?

We humans have attached a particular meaning to the word integer. We could have attached this meaning to any word we wanted - we could have called integers "Intagars" or "Triffids" if we wanted, as long as they had the same properties we'd still be talking about the same things....