Search found 35 matches

by AllSaintsDay
Thu May 06, 2010 6:25 pm UTC
Forum: Mathematics
Topic: Need some understanding.
Replies: 13
Views: 2004

Re: Need some understanding.

Also "L'Hôspital's rule" has an circumflex on the o. Don't you mean "L'Hôpital's rule?" L'Hôpital and L'Hospital are both correct. L'Hôspital is not. The circumflex, among other uses, came into French as shorthand for "there's an s after this vowel that we don't pronounce a...
by AllSaintsDay
Wed Apr 21, 2010 3:37 am UTC
Forum: Mathematics
Topic: latex symbol
Replies: 10
Views: 4643

Re: latex symbol

I always thought of the injection arrow as being an arrow with a small subset symbol on the domain end.
by AllSaintsDay
Wed Apr 14, 2010 9:12 am UTC
Forum: Mathematics
Topic: expected number of right positions in random permutation
Replies: 7
Views: 1776

Re: expected number of right positions in random permutation

I seem to recall there being an example or two in the introductory chapter of Koshnevisan about this distribution. I think it went all the way to computing the distribution completely for a set of any size, but I could be misremembering.
by AllSaintsDay
Thu Mar 25, 2010 6:47 am UTC
Forum: Mathematics
Topic: Famous Math Quotes!
Replies: 32
Views: 8138

Re: Famous Math Quotes!

This one was at the beginning of a chapter of the Prob book I checked out (Koshnevisan): "Experimentalists think that it is a mathematical theorem, while mathematicians believe it to be an experimental fact."~Gabriel Lippman, in a discussion with J. J. Poincare about the Central Limit Theo...
by AllSaintsDay
Thu Mar 18, 2010 12:02 am UTC
Forum: Mathematics
Topic: Ideal Currency Denominations
Replies: 47
Views: 5814

Re: Ideal Currency Denominations

Is it common all over the US for prices to be [nice, round number] + [weird tax percent], or only in certain states/types of store? Is this a common method in many other countries? It's definitely common over most of the US, but there are some exceptions. Concession stands at events or on the stree...
by AllSaintsDay
Tue Mar 16, 2010 6:48 am UTC
Forum: Mathematics
Topic: A slightly logic-esque mathematic question
Replies: 12
Views: 2285

Re: A slightly logic-esque mathematic question

The question is answerable, but you need to be more specific. There are different, equally good ways to pick numbers at random, and the answer to your question depends on which of those ways you use. So it's not exactly that your question isn't well-phrased, it's that you haven't given enough inform...
by AllSaintsDay
Fri Mar 05, 2010 8:34 am UTC
Forum: Mathematics
Topic: Are integers arbitrary?
Replies: 54
Views: 4894

Re: Are integers arbitrary?

I attempted to use it, by considering the set of integers to be all numbers that can be reached by adding or taking away 1 from 0 a finite number of times, but then realised that in order to reach only the integers, that definition would have to be '...or taking away 1 from 0 a finite, *integer* nu...
by AllSaintsDay
Fri Feb 19, 2010 10:42 pm UTC
Forum: Mathematics
Topic: Infinity
Replies: 31
Views: 4145

Re: Infinity

Image
by AllSaintsDay
Mon Feb 15, 2010 7:41 pm UTC
Forum: Mathematics
Topic: Inconsistent variables in the two envelopes problem
Replies: 6
Views: 1403

Re: Inconsistent variables in the two envelopes problem

RequinB4 wrote:You could always hit the other person with a $5 wrench until she tells you which has more money.

This is only a good idea if E(larger envelope)-5 > E(envelope1) (which is also E(envelope2).
by AllSaintsDay
Wed Feb 10, 2010 5:03 am UTC
Forum: Mathematics
Topic: What is the error in this 2=1 "proof"?
Replies: 22
Views: 3561

Re: What is the error in this 2=1 "proof"?

It is my understanding that if something is "infinitesimally small" then it does not exist. See any .(9)=1 proof for that. I think that understanding is wrong. How can dy/dx exist if neither dy or dx exist? In standard calculus definitions, they don't. dy/dx doesn't get its meaning from &...
by AllSaintsDay
Wed Feb 10, 2010 12:53 am UTC
Forum: Mathematics
Topic: Statistics Question: Confidence Intervals
Replies: 8
Views: 1276

Re: Statistics Question: Confidence Intervals

If you took a coin you were just given as change (i.e., you a priori have no reason to think it's biased), flip it a bunch, and find that, with 95% confidence, the coin comes up heads 55+% of the time, would you feel as though the probability that your coin was weighted was 95%? That statement does...
by AllSaintsDay
Tue Feb 09, 2010 5:57 pm UTC
Forum: Mathematics
Topic: What is the error in this 2=1 "proof"?
Replies: 22
Views: 3561

Re: What is the error in this 2=1 "proof"?

Hey, look, it's the warning my differential geometry professor gave us the first day of class! Now if only I could find my notes to see what exactly it was he said about it.
by AllSaintsDay
Tue Feb 09, 2010 5:44 pm UTC
Forum: Mathematics
Topic: Statistics Question: Confidence Intervals
Replies: 8
Views: 1276

Re: Statistics Question: Confidence Intervals

If you took a coin you were just given as change (i.e., you a priori have no reason to think it's biased), flip it a bunch, and find that, with 95% confidence, the coin comes up heads 55+% of the time, would you feel as though the probability that your coin was weighted was 95%?
by AllSaintsDay
Fri Feb 05, 2010 5:58 am UTC
Forum: Mathematics
Topic: Infinity
Replies: 31
Views: 4145

Re: Infinity

Paradoxes only happen if you think of infinity as a number. It's much more satisfying, and much more relevant to modern mathematics, to think of infinity as a place. Different functions get there at different speeds. Why is that concept difficult to swallow? Hey guys. Party... be there. Where? Why ...
by AllSaintsDay
Sat Jan 23, 2010 7:23 am UTC
Forum: Mathematics
Topic: Very Big Numbers
Replies: 14
Views: 1751

Re: Very Big Numbers

scikidus wrote:Obligatory link to FG thread where we made gob-smackingly huge numbers:

Is it bad that I read this as a link to a finitely generated thread, before my brain kicked in?
by AllSaintsDay
Fri Jan 08, 2010 7:04 am UTC
Forum: Mathematics
Topic: Bad at math
Replies: 15
Views: 2068

Re: Bad at math

They have the same dimensions. Typically, torque is a pound-foot, but occasionally a foot-pound. Always, to my knowledge, energy is a foot-pound. Metrically, a newton-meter of energy is a joule, and only referred to as a newton-meter while doing dimensional analysis and such(though technically, it s...
by AllSaintsDay
Tue Oct 20, 2009 11:41 am UTC
Forum: Mathematics
Topic: Second Ace Paradox
Replies: 66
Views: 8412

Re: Second Ace Paradox

So, some two-cents-ing: First, a way to think of the question that's more explicit about assumptions: Alice and Sam are sitting in front of you, each with a deck of cards. Alice is going to deal herself a hand of thirteen, and then tell you whether or not that hand has an ace in it. Sam is going to ...
by AllSaintsDay
Wed Oct 14, 2009 5:07 pm UTC
Forum: Mathematics
Topic: Has Fermats Last Theorem been solved?
Replies: 25
Views: 4623

Re: Has Fermats Last Theorem been solved?

Just to prevent misinformation, it was the proof of Wiles (Wiles' proof), not the proof of Wile (Wile's proof).
by AllSaintsDay
Sat Oct 10, 2009 12:26 am UTC
Forum: Mathematics
Topic: Help with Adjugate matrix method
Replies: 6
Views: 1186

Re: Help with Adjugate matrix method

Yeah, I was aware of all this, but I had never heard, or perhaps did not remember, the name of the inverse times the determinant. I've always just heard it called the adjoint or classical adjoint (as WP says). Other than easy 2x2 inverses, I don't think it's really all that useful until you start d...
by AllSaintsDay
Sun Oct 04, 2009 7:11 am UTC
Forum: Mathematics
Topic: integrating sin(x^-1)
Replies: 31
Views: 4304

Re: integrating sin(x^-1)

ok so i didnt understand any of this once again sorry for being difficult :oops: The statement "only continuous functions are integrable" isn't normally the definition of integrable. Riemann's actual definition involves upper and lower approximations of the function and taking limits. Thi...
by AllSaintsDay
Wed Sep 23, 2009 9:20 pm UTC
Forum: Mathematics
Topic: What's the coolest thing you've ever learned in math class?
Replies: 58
Views: 6788

Re: What is...

skeptical scientist wrote:Why does it feel like a partial order to you?

Basically, if you take two maps f,g:[0,1]->[0,1], it feels to me like the periods of points under f and those under g shouldn't be comparable under set inclusion in general. But they are.
by AllSaintsDay
Wed Sep 23, 2009 6:15 am UTC
Forum: Mathematics
Topic: What's the coolest thing you've ever learned in math class?
Replies: 58
Views: 6788

Re: What is...

Sharkovsky's Theorem. Putting the naturals in the order
3,5,7,9,11,13,15,...
6,10,14,18,22,30,...
12,20,28,36,44,60,...
24,40,56,72,88,120,...
...
...,32,16,8,4,2,1
should not be useful. But it somehow is. And it's a total order on something that feels like it should be a partial order.
by AllSaintsDay
Fri Aug 14, 2009 9:45 pm UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 434
Views: 161279

Re: Math: Fleeting Thoughts

Just use whatever notation is best for getting the job done. If that job is to teach students, consistency is a good thing. If not, then whatever works. Eh, there isn't really a job to get done. Just something that made me go "Huh." I won't bring this up while teaching periodic functions....
by AllSaintsDay
Thu Aug 13, 2009 7:16 pm UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 434
Views: 161279

Re: Math: Fleeting Thoughts

stephentyrone wrote:
AllSaintsDay wrote:Is [imath]\chi_\mathbb{Q}[/imath] (i.e., the characteristic function of the rationals) periodic? If so, what is its period?


Yes. Every rational number is a period of [imath]\chi_\mathbb{Q}[/imath].

I meant the more common definition of period, also called fundamental period.
by AllSaintsDay
Thu Aug 13, 2009 6:35 pm UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 434
Views: 161279

Re: Math: Fleeting Thoughts

Fleeting thought I had yesterday:
Is [imath]\chi_\mathbb{Q}[/imath] (i.e., the characteristic function of the rationals) periodic? If so, what is its period?
by AllSaintsDay
Tue Jun 16, 2009 4:59 am UTC
Forum: Mathematics
Topic: Enterprising Maths
Replies: 7
Views: 1116

Re: Enterprising Maths

Off the top of my head, I believe every fraction was represented as a sum of distinct fractions of the form 1/n. (But could be misremembering.)

Edit: Never mind, Talith already said that.
by AllSaintsDay
Tue Mar 17, 2009 9:55 pm UTC
Forum: Mathematics
Topic: A little linear algebra
Replies: 9
Views: 1137

Re: A little linear algebra

Kurushimi wrote:Wait...aren't 1/3 and 2/3 both rational numbers?

Yeah, I think he meant that it fails with both rational, using (1/3,2/3) as a counterexample.

I'd be more certain if my computer would ever open up the paper.
by AllSaintsDay
Fri Mar 13, 2009 5:10 pm UTC
Forum: Mathematics
Topic: Pi Day
Replies: 49
Views: 6180

Re: Pi Day

You Americans* with your silly mm/dd/yyyy date formats. Here, where we use the infinitely more sensible dd/mm/yyyy format, celebrate Pi Day on July 22nd! And in the even more infinitely more sensible land of the yyyy/mm/dd format, plans should be in place for Pi Day on May 9th, 3141! * And other od...
by AllSaintsDay
Fri Mar 13, 2009 6:20 am UTC
Forum: Mathematics
Topic: Pi Day
Replies: 49
Views: 6180

Re: Pi Day

You Americans* with your silly mm/dd/yyyy date formats. Here, where we use the infinitely more sensible dd/mm/yyyy format, celebrate Pi Day on July 22nd! And in the even more infinitely more sensible land of the yyyy/mm/dd format, plans should be in place for Pi Day on May 9th, 3141! * And other od...
by AllSaintsDay
Sat Jan 24, 2009 12:48 am UTC
Forum: Mathematics
Topic: Fun with Weierstrass
Replies: 5
Views: 1388

Re: Fun with Weierstrass

It is pretty easy to find for the Weierstrass function. Just looking at the graph on Wikipedia gives you a good idea what it is. Specifically, though, the bounds Wikipedia gives for the Weierstrass M-test are sharp. So the maximum is the sum of those bounds. EDIT: Oh, wait, you said on an arbitrary ...
by AllSaintsDay
Wed Jan 14, 2009 6:41 am UTC
Forum: Mathematics
Topic: Beginner Stuff
Replies: 23
Views: 2469

Re: Beginner Stuff

Sets don't have repeated elements, or a set with repetitions is equivalent to one with repetitions removed? Sets don't have repeated elements. This isn't worth arguing; it's part of the formal definition of a set. Multisets have repeated elements. Any attempt to pretend otherwise is abuse of notati...
by AllSaintsDay
Wed Jan 07, 2009 2:39 am UTC
Forum: Mathematics
Topic: Boy or Girl Paradox
Replies: 126
Views: 14011

Re: Boy or Girl Paradox

I think I'd have to say that the way the question is worded, I would naturally interpret it in the way so that the answer is 50%. The phrase "one of them is a girl" would indicate to me that a specified child is female. Perhaps "the child who came up in conversation." Going on th...
by AllSaintsDay
Thu Aug 28, 2008 6:09 am UTC
Forum: Movies and TV Shows
Topic: Dumbest things said in movies
Replies: 87
Views: 10630

Re: Dumbest things said in movies

"These guys eat too much red meat."
From Commando
by AllSaintsDay
Thu Aug 28, 2008 3:45 am UTC
Forum: General
Topic: Who the dickens are you?
Replies: 10922
Views: 2412692

Re: INTRO THREAD THE THIRD

So, I'm supposed to introduce myself, eh? I'm 24, and about to start grad school (mathematics). I'm Louisiana raised, but will be on the West Coast until I get my doctorate. Other than the math(and related physics), geekinesses include: ⋅ RPGs. D&D, Exalted, MechWarrior, Shadowrun, VtM...
by AllSaintsDay
Thu Aug 28, 2008 3:07 am UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 493679

Re: Favorite math jokes

Rough transcript of an exchange I had in discussing a lecture... Me:"And that's true by the CMT. Which means the Contraction Mapping Theorem, not Country Music Television." Her:"Oh, I'm glad you told me, or I would have thought that math involved Carrie Underwood destroying her cheati...

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