## Search found 555 matches

Sun Jul 28, 2013 3:12 pm UTC
Forum: Mathematics
Topic: How to convince a friend the equivalence of infinite sets
Replies: 32
Views: 8209

### Re: How to convince a friend the equivalence of infinite set

Seemingly reasonable premise #1: The whole is always strictly greater than the part. Seemingly reasonable premise #2: Two sets have the same "size" if their elements can be put into one-to-one correspondence. Those premises both seem plausible, and as far as I'm aware, I think that before ...
Fri May 31, 2013 1:04 pm UTC
Forum: Mathematics
Topic: Seeking quick proof of a trig inequality
Replies: 11
Views: 3721

### Re: Seeking quick proof of a trig inequality

Very nice. That's exactly the type of thing I was hoping for, that uses trig identities cleverly until you get to something that's "obviously" negative due to the quadrants that certain angles are in.
Fri May 31, 2013 1:24 am UTC
Forum: Language/Linguistics
Topic: Obscure Language Game
Replies: 305
Views: 133800

### Re: Obscure Language Game

The best guess I can make is "something related to Polish".
Thu May 30, 2013 10:38 pm UTC
Forum: Mathematics
Topic: Seeking quick proof of a trig inequality
Replies: 11
Views: 3721

### Re: Seeking quick proof of a trig inequality

Everything you say is true, but what I was hoping for (ideally) was a more analytic proof, completely free of any statements such as "look at the picture". (Although of course, in some contexts, "look at the picture" would be a good enough proof.) It's possible that there isn't a...
Thu May 30, 2013 8:03 pm UTC
Forum: Mathematics
Topic: Seeking quick proof of a trig inequality
Replies: 11
Views: 3721

### Seeking quick proof of a trig inequality

This isn't homework and I'm not a student. I've been looking at the following function of two variables: f(x,y) = cos(x) + cos(y) + cos(x+y) One can use Wolfram Alpha to get a picture of the behavior of this function: http://www.wolframalpha.com/input/?i=cos%28x%29%2Bcos%28y%29%2Bcos%28x%2By%29 Supp...
Fri Apr 26, 2013 8:35 pm UTC
Forum: Mathematics
Topic: Silly geometry question
Replies: 6
Views: 1596

### Re: Silly geometry question

In any right triangle where both the hypotenuse and one of the legs (call it "A" of A²+B²=C²) are whole numbers, is it possible for B² to be an even number that is not divisible by 4? The answer looks pretty simple. If B is even A and C are odd. B^2=C^2-A^2=(C+A)(C-A) Sum and difference i...
Fri Apr 19, 2013 8:02 pm UTC
Topic: 1201: "Integration by parts"
Replies: 81
Views: 25870

### Re: 1201: "Integration by parts"

It's been a while since I've done integration, but isn't the formula x^n = x^(n+1)/(n+1) + c? This may seem pedantic, but I believe it to be important. You don't literally mean what you typed. If you think about it, what you typed is a gross misuse of the equals sign. (I'm a university math instruc...
Wed Apr 03, 2013 12:32 am UTC
Forum: Language/Linguistics
Topic: Obscure Language Game
Replies: 305
Views: 133800

### Re: Obscure Language Game

Fa vor i ir i chimeri; helleut ir i nam thite. Gilla cosdum thite cumma. Veya thine mota vara gort o yurn sinna gort i chimeri. Gav vus da on da dalight brow vora. Firgive vus sinna vora sin vee firgive sindara mutha vus. Lyv vus ye i temtation, min delivra vus fro olt ilt. If this is Germanic but ...
Tue Mar 19, 2013 9:39 pm UTC
Forum: Mathematics
Topic: Number of days between consecutive Easters
Replies: 2
Views: 1733

### Number of days between consecutive Easters

I was procrastinating today and I was playing around with the number of days between consecutive Easters. Usually, that number is 350, 357, or 385. This makes sense, because Easter has to happen shortly after a full moon, so the number of days between consecutive Easters has to be close to an intege...
Fri Mar 15, 2013 11:06 am UTC
Forum: Language/Linguistics
Topic: Obscure Language Game
Replies: 305
Views: 133800

### Re: Obscure Language Game

Kulturit pisoqaanersaasut nunami innutaalersut ataatsimut taaguuserlugit [...] kulturiinik taaneqartarput, tamarmillu amerikkap avannarliup nunavittaata issittortaanit sorlaqarlutik. I edited out a word that would have likely given it away too easily. I'm going to guess that this is one of the abor...
Mon Feb 25, 2013 8:08 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 421105

### Re: My write-up of the "Blue Eyes" solution (SPOILER A

I do not understand why I would consider the 1 person case at any point Let's say there are 17 blue-eyed people on the island, and four of them are named Alice, Bob, Carol, and Doug. If I'm looking at the island from the outside, I know there are 17 blue-eyed people. I don't have to seriously consi...
Mon Feb 25, 2013 2:51 am UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 157367

### Re: A very interesting Mathematical Paradox

Ok, so conclusion: We can define some arbitrary axioms such that the sum is 1. We can also define some natural axioms such that the sum is less then 1. What are the "natural axioms" that imply that 0.999... is less than 1? I mean, yes, I'm sure it's possible to write down some axioms that...
Sun Feb 24, 2013 9:56 pm UTC
Forum: Mathematics
Topic: Average number of legs of a person
Replies: 2
Views: 5600

### Re: Average number of legs of a person

I will now alter my guess of "nearest power of ten" to be 1 in 1000, as opposed to my earlier stated 1 in 10,000. The figure of 1 in 200 is higher than I expected, but as you point out, that includes all amputations, not just legs. Furthermore, it might include cases where just a hand or f...
Sun Feb 24, 2013 2:44 pm UTC
Forum: Mathematics
Topic: Average number of legs of a person
Replies: 2
Views: 5600

### Average number of legs of a person

This isn't pure math. I hope I'm posting in the right place. Probably a lot of us here have heard the saying "Most people have an above average number of legs." And probably most of us have a sense of why it's true. I was wondering, though, what do you think the average number of legs of a...
Fri Feb 22, 2013 3:55 pm UTC
Forum: Mathematics
Topic: Homework help: Mathematical problem solving-number theory
Replies: 8
Views: 1636

### Re: Homework help: Mathematical problem solving-number theo

Following the hints of jedelmania, I have another family of solutions. Idea: Since one solution is x=y=z=2, we try looking for solutions satisfying x=y=2^k, where k is yet to be determined. This gives (2^k)^n + (2^k)^n = z^(n+1) 2 * 2^(kn) = z^(n+1) 2^(kn+...
Wed Feb 20, 2013 8:03 pm UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 157367

### Re: A very interesting Mathematical Paradox

There is no such thing as a sum of an infinite series. There is, if we define things that way. AND, there are ways to define the "sum" of an infinite series that are reasonably natural. AND, that's what mathematicians standardly do. ...its just meaningless arbitrarily defined symbol manip...
Wed Feb 20, 2013 3:45 pm UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 157367

### Re: A very interesting Mathematical Paradox

eulerIV is correct that the answer *ultimately* comes down to definitions. (However, that doesn't necessarily mean the entire discussion is pointless.) We can either directly define 0.999... to be 1, or we can define 0.999... in some other way, and then prove that it equals 1 as a consequence of oth...
Wed Feb 20, 2013 3:31 pm UTC
Forum: Language/Linguistics
Topic: Annoying words, and Words You Hate
Replies: 1991
Views: 487412

### Re: Annoying words, and Words You Hate

Exactly. Dictionaries describe. They describe the language as it is currently used. That could include describing some words as nonstandard or informal or offensive, if those words are considered nonstandard or informal or offensive by many/most speakers and/or by the compilers of the dictionary. An...
Sat Feb 16, 2013 9:29 pm UTC
Forum: Language/Linguistics
Topic: Obscure Language Game
Replies: 305
Views: 133800

### Re: Obscure Language Game

gmalivuk wrote:The last one, if you skim through it, looks Italian. You say it's not Romance, so I'm going to guess it might be a language that got its orthography from Italian, if there are any like that?

Possibly Maltese??
Sat Feb 16, 2013 9:28 pm UTC
Forum: Language/Linguistics
Topic: Obscure Language Game
Replies: 305
Views: 133800

### Re: Obscure Language Game

I'm also going to guess that the second one is a less-obvious Celtic language. It resembles Welsh a little bit, but I don't think it's Welsh.

Isn't there a Celtic language historically spoken in Brittany in France? Maybe it's that one.
Mon Feb 11, 2013 2:12 am UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 157367

### Re: A very interesting Mathematical Paradox

As a math educator, the *pedagogical* question of how best to convince people is interesting to me. I mean, in a very real sense, the answer is "Point nine repeating is exactly one, as a consequence of various conventions and definitions that mathematicians use." And while it's true that t...
Sat Feb 09, 2013 5:27 pm UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 157367

### Re: A very interesting Mathematical Paradox

When talking about "point nine repeating", I too have encountered the attitude that 1/3 isn't "really" equal to 0.333..., I guess because the person is imagining 0.333... as a kind of "process" that "gets closer" to 1/3 but "never gets there". To a c...
Wed Jan 16, 2013 4:02 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 421105

### Re: My write-up of the "Blue Eyes" solution (SPOILER A

Although there are already many people chiming in, I hope that the following comments of mine are helpful. Each of the following statements is different. In fact, for the moment, let's not even worry about the truth or falsity of the statements -- just note that each statement in the list, be it tru...
Wed Dec 05, 2012 2:48 am UTC
Forum: Language/Linguistics
Topic: You keep using that word...
Replies: 39
Views: 13691

### Re: You keep using that word...

Sloppy use of "exponential" bugs me too. And in fairness, for *some* of these vocabulary things that people complain about, I think that the complaining is silly. It's a case by case thing and we may disagree on some specifics, but there are some instances when informal language is just in...
Sun Nov 25, 2012 3:35 am UTC
Forum: Language/Linguistics
Topic: English as She Is Spoke [English practice]
Replies: 338
Views: 159640

### Re: English as She Is Spoke [English practice]

This native speaker thinks both are perfectly acceptable, and sound almost identical in terms of formality, etc. "Kill all the mice" vs "kill all of the mice" "Eat all the pies" vs "eat all of the pies" They both sound perfectly natural and correct to me. Poss...
Mon Nov 12, 2012 5:44 pm UTC
Forum: Language/Linguistics
Topic: English as She Is Spoke [English practice]
Replies: 338
Views: 159640

### Re: English as She Is Spoke [English practice]

Both "I talk how I want" and "I talk like I want" sound reasonably natural to this native speaker as far as informal spoken language goes. "I talk how I want" sounds a little more natural to me. "I talk the way I want to" sounds pretty natural to me as well, a...
Wed Oct 31, 2012 7:24 pm UTC
Forum: Mathematics
Topic: Combination Problem
Replies: 10
Views: 2789

### Re: Combination Problem

What do you mean when you say "there is at least two gaps between the numbers"? Can you perhaps rephrase in a different way? I assume you mean some kind of variation on the original problem. In the original problem, we were choosing 6 numbers from 1 to 40, and we weren't allowed consecutiv...
Wed Oct 31, 2012 2:44 am UTC
Forum: Mathematics
Topic: Probability exercise: limit of sequence using definition
Replies: 7
Views: 1523

### Re: Probability exercise: limit of sequence using definition

As for the purely "intuitive" part of the question:

When n gets big, -1 + 1/n gets close to -1, but 1 + 1/n gets close to 1.

Speaking purely informally, if you care about large values of n, then 1 + 1/n is close to 1, not 2.
Wed Oct 17, 2012 2:57 pm UTC
Topic: 1122: "Electoral Precedent"
Replies: 167
Views: 45931

### Re: 1122: "Electoral Precedent"

Every time the Giants defeat the Patriots in the Super Bowl, it's followed nine months later by Barack Obama being elected President.

Of course, that's only happened once so far. But people seem to think there's more than a 50% chance of that trend continuing.
Mon Oct 15, 2012 2:33 pm UTC
Forum: Language/Linguistics
Topic: Comparative phrase...
Replies: 9
Views: 4273

### Re: Comparative phrase...

bobsbarricades wrote:Person 1: ""[x] is useful at nothing so much as [y]" is a common comparative phrase, and its meaning is completely different from "useful at nothing".

Discuss.

I have evidence that it's not a common comparative phrase.

Results of Google search for that exact phrase
Wed Oct 10, 2012 2:26 pm UTC
Forum: Mathematics
Topic: Homework Looks like partial integration, but isnt?
Replies: 4
Views: 2086

### Re: Homework Looks like partial integration, but isnt?

just an update on what i've done: I've used u = root(4-x^2) and used that in the equation where du = -2x * dx . so the remaning dx we had is -(1/2)du = dx, so our new integral is: -(1/2) integral( root(u) du ) Careful. I believe what you meant to type was u = 4-x^2 not u = root(4-x^2). If we choose...
Wed Oct 10, 2012 11:10 am UTC
Forum: Mathematics
Topic: What is wrong with this inference?
Replies: 2
Views: 1738

### Re: What is wrong with this inference?

If your premises imply a tautology, that doesn't mean the conjunction of your premises is a tautology. If your premises imply a statement known to be true, that doesn't mean your premises are true.
Thu Sep 20, 2012 8:29 pm UTC
Forum: Language/Linguistics
Topic: Annoying words, and Words You Hate
Replies: 1991
Views: 487412

### Re: Annoying words, and Words You Hate

I'm aware that many people maintain a distinction between acronyms and initialisms. They say that acronyms are things like NATO, FIFA, and FUBAR, which we pronounce as though they were words. (We say "fee-fah", not "eff eye eff eh".) And they say that initialisms are things like ...
Thu Sep 20, 2012 8:17 pm UTC
Forum: Mathematics
Topic: Lottery Problem: "All or Nothing"
Replies: 8
Views: 7736

### Re: Lottery Problem: "All or Nothing"

(I was ninja'd, so some of what I typed is redundant. But I'm keeping it, since sometimes a little redundancy is good for pedagogical purposes.) With most lotteries, order doesn't matter. You're just picking a set of numbers. So, like option 1 in the original post, not option 2. For illustrative pur...
Wed Sep 19, 2012 2:31 pm UTC
Forum: Language/Linguistics
Topic: The Oxford Comma
Replies: 26
Views: 15397

### Re: The Oxford Comma

I will add that to me personally (and probably others), the picture of "eggs, toast and orange juice" accurately captures my aesthetic reasons for preferring the Oxford comma. As I mentioned above, my subjective impression is that writing "Matthew, Mark, Luke and John" makes it l...
Tue Sep 18, 2012 9:19 pm UTC
Forum: Mathematics
Topic: Help with a Chernoff bound
Replies: 3
Views: 1018

### Re: Help with a Chernoff bound

Glad I could help. My thesis actually mentions Chernoff bounds for sums of independent +1/-1 random variables, so your question caught my eye.
Tue Sep 18, 2012 9:12 pm UTC
Forum: Logic Puzzles
Topic: Seventeen "Blue Eyes" Objections and Responses [SPOILER]
Replies: 73
Views: 41351

### Re: Seventeen "Blue Eyes" Objections and Responses [SPOILER]

I must confess that I'm not a big fan of using words like "optimization" or "strategy" or "treat night 1 as night 99" when talking about this puzzle. The islanders aren't "trying" to leave the island, and they're not trying not to leave the island. I'm pretty ...
Tue Sep 18, 2012 7:18 pm UTC
Forum: Mathematics
Topic: Help with a Chernoff bound
Replies: 3
Views: 1018

### Re: Help with a Chernoff bound

What is the result or theorem that you are quoting or relying on? Is it \Pr[T\geq (1+\varepsilon) \mu] \leq \exp(-\mu \varepsilon^2 / 3) i.e. is this what you "know" to be true? And are you trying to "force" the probability to be at most 1/N^2? Then, if I'm unders...
Mon Sep 17, 2012 9:54 pm UTC
Forum: Mathematics
Topic: The uses of log10
Replies: 17
Views: 4052

### Re: The uses of log10

Yes. When you teach beginning students about logarithms, it unfortunately would tend to distract if you use a number approximately equal to 2.718. It's a lot more intuitive to say "The logarithm of 100 is 2, the logarithm of 1000 is 3, the logarithm of 10000 is 4, and so on -- but we can also f...
Sun Sep 16, 2012 12:05 pm UTC
Forum: Language/Linguistics
Topic: Using who/whom in passive voice.
Replies: 16
Views: 15083

### Re: Using who/whom in passive voice.

Exactly. It's like "I was talked about by Fiona" "He was talked about by Fiona" "Fiona talked about me" "Fiona talked about him" Grammatically speaking, "I" and "he" are the subjects in the first two sentences, and "me" and "...