## Search found 458 matches

- Thu May 25, 2017 8:30 pm UTC
- Forum: Coding
- Topic: Neighbors of a cluster: What is this called?
- Replies:
**8** - Views:
**6463**

### Neighbors of a cluster: What is this called?

Probably a pretty straightforward question, but I'm just blanking on it. Any help is appreciated. Hopefully, I can set this up in a non-confusing way: I have a cubic box in a three-dimensional Euclidean space. (let's say 0 <= x,y,z <= 100) I have a large number of points of interest inside this box....

- Thu May 18, 2017 6:49 pm UTC
- Forum: News & Articles
- Topic: Where Aren't They Now (Obituaries)
- Replies:
**321** - Views:
**89147**

### Re: Where Aren't They Now (Obituaries)

Chris Cornell, singer and front man for numerous bands, including Soundgarden and Audioslave, dies at age 52 hours after a concert in Detroit. BBC article claims police are investigating as a possible suicide.

### Re: Free Will

Probably true, but I read it as though the context was how people in the AI community view the status of Alan Turing - i.e., this isn't a question of who is the most popular pop scientist that your Aunt Ethel knows about, but rather an evaluation by people who work in the field for a living.

### Re: Free Will

I like this post here, and the parts about Turing's moral heroism give me goosebumps. This is greatness. http://www.scottaaronson.com/blog/?p=63 Thanks for that - an excellent read. I have to admit, I laughed out loud at the "Jews cheat" anecdote. I also enjoyed the article. An aside: Som...

- Tue May 16, 2017 9:09 pm UTC
- Forum: News & Articles
- Topic: Where Aren't They Now (Obituaries)
- Replies:
**321** - Views:
**89147**

### Re: Where Aren't They Now (Obituaries)

Actor Powers Boothe , who played Jim Jones in a TV movie, appeared as Lt. Col. Andrew Tanner in "Red Dawn" and may be more well known recently as Gideon Malick from "The Avengers" and "Agents of S.H.I.E.L.D." passed away at 68. Ian Brady , one of the perpetrators of the...

- Thu May 11, 2017 9:39 pm UTC
- Forum: News & Articles
- Topic: In other news... (humorous news items)
- Replies:
**15108** - Views:
**2523273**

### Re: In other news... (humorous news items)

CorruptUser wrote:So... obese people are more likely than average to have better sense of taste/smell? I'm now imagining the "gargle with novacain" diet.

Benzocaine, not novocaine. And they made it in candy form, so it was bound to be a hit with fat people! Something about that name, though ...

- Thu May 04, 2017 8:37 pm UTC
- Forum: News & Articles
- Topic: Trump presidency
- Replies:
**8423** - Views:
**739894**

### Re: Trump presidency

sardia wrote:This means Trump is serious about repealing healthcare. Given how lackluster attempt last time,I didn't think he cared about the aca promise.

PS, news forum seems dead, has everyone fled to faid?

FaiD also seems quite slow. Guess we're all just in a slump.

- Thu May 04, 2017 8:12 pm UTC
- Forum: News & Articles
- Topic: Trump presidency
- Replies:
**8423** - Views:
**739894**

### Re: Trump presidency

sardia wrote:Democrats are panicking as House Speaker Ryan surprises everyone with vote Thursday. They have the votes to get approval in the House, sparing Trump from a humiliating loss.With $8 Billion Deal on Health Bill, House G.O.P. Leader Says ‘We Have Enough Votes’

By the skin of their teeth.

- Wed May 03, 2017 3:13 pm UTC
- Forum: News & Articles
- Topic: In other news... (humorous news items)
- Replies:
**15108** - Views:
**2523273**

### Re: In other news... (humorous news items)

Acting like you've already won is definitely in the 'massive gaffe' territory. Is he really doing that? Celebrating having reached the 2nd round doesn't seem that weird to me. Sports teams will generally celebrate reaching the finals too. I admit I'm not following the French election as closely as ...

- Wed May 03, 2017 2:55 am UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

a substitute (k + 1) step, which everyone here told me isn't a step in working the problem. That's a miscommunication –I haven't followed the discussion closely enough to understand what exactly is misunderstood and by whom, but there's definitely a miscommunication in there. This is absolutely cor...

- Wed May 03, 2017 2:49 am UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

It's because your original goal, in all of this induction, is to prove that there is a nice, simple formula for finding the sum of the first n positive integers. That formula is n(n+1)/2. You're trying to prove this is true for all positive integers, right? k is just a positive integer. k+1 is just...

- Tue May 02, 2017 8:29 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

So what you have on that next-to-last line is the (k+1)-case. You connected it up from the k-case. That was what we wanted to do. But we can also get the (k+1)-case directly from the original equation: 1 + 2 + 3 + ... + n = n(n+1)/2 if we substitute (k+1) for n: 1 + 2 + 3 + ... + k + (k+1) = [(k+1)...

- Tue May 02, 2017 8:18 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

First, some terminology. You didn't "plug in" (k+1) to both sides, you added it to both sides. "Plugging in" is the same as substitution, and you don't want to substitute anything here. Now, when you added (k+1) to both sides, what you're doing is actually writing the (k+1)-case...

- Tue May 02, 2017 8:05 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

For this proof to work, the above equation needs to be equivalent to the (k+1)-case: 1 + 2 + 3 + ... + k + (k + 1) = [(k+1)((k+1)+1]/2 Well, we can see that the left hand sides of those two equations are equal. The way we prove that 1 + 2 + 3 + ... + k + (k + 1) = k(k + 1)/2 + (k + 1) is equivalent...

- Tue May 02, 2017 7:57 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

Where do you think you need to substitute (k+1) down the line? Once I relate (or incorporate, or do some math-verb) k and (k + 1) (see below) 1 + 2 + 3 + ... + k + (k + 1) = k(k + 1)/2 + (k + 1) #I added (k + 1) to the right-hand side as well because that's what algebra rules require. Beyond that, ...

- Tue May 02, 2017 7:44 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

Because you need to use the k-case (assume it is true) to get to the (k+1) case. If the sum of the first k positive integers is 1 + 2 + 3 + ... + k, what is the sum of the first (k+1) positive integers? It's the sum of the first k positive integers ... plus k+1. 1 + 2 + 3 + ... + k+1 = 1 + 2 + 3 + ...

- Tue May 02, 2017 7:35 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

Because you need to use the k-case (assume it is true) to get to the (k+1) case. If the sum of the first k positive integers is 1 + 2 + 3 + ... + k, what is the sum of the first (k+1) positive integers? It's the sum of the first k positive integers ... plus k+1. 1 + 2 + 3 + ... + k+1 = 1 + 2 + 3 + ...

- Tue May 02, 2017 7:31 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

Do not substitute k+1 for k. Doing that without knowing exactly why you're doing it will lead you to a wrong answer. So go back to this point: Start with equation 1. 1 + 2 + 3 + ... + k = k(k + 1)/2 (equation 1) Add (k+1) to both sides: Start with equation 1. 1 + 2 + 3 + ... + k + (k+1) = k(k + 1)/...

- Tue May 02, 2017 7:19 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

Do not substitute k+1 for k. Doing that without knowing exactly why you're doing it will lead you to a wrong answer. So go back to this point: Start with equation 1. 1 + 2 + 3 + ... + k = k(k + 1)/2 (equation 1) Add (k+1) to both sides: Start with equation 1. 1 + 2 + 3 + ... + k + (k+1) = k(k + 1)/2...

- Tue May 02, 2017 7:10 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

What's the difference between the k-case and the (k+1)-case? It's the same as the answer to: what is the difference between the left hand side of equation 1 and the left hand side of equation 2? Answer: (k+1) So what we need to do is use the k-case to get to the (k+1) case. That's important - the id...

- Tue May 02, 2017 6:58 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

No, you're only trying to show the last part: 1 + 2 + 3 + ... (k + 1) = (k +1)((k + 1) + 1)/2 The preceding equations are not what you're trying to show. Moreover, they are false: for example, the sum of 1 through k is certainly not equal to the sum of 1 through k+1. It seems like you might be usin...

- Tue May 02, 2017 4:38 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

As promised, here's what I've got so far in using pen and paper and working back through the original problem in light of everyone's help. I want to show the following: 1 + 2 + 3 + ... + n = n(n + 1)/2 First, I'll perform a check using 1 as a base case, to create the first "rung" on the l...

- Mon May 01, 2017 6:34 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

The statement you're ultimately trying to prove is "The sum of the first n positive integers, P(n), is given by [n(n+1)]/2". What you want to recognize is that the left-hand side of the quoted portion above ("1 + 2 + 3 + ... + n + (n+1)") is the sum of the first (n+1) positive i...

- Mon May 01, 2017 6:25 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

Some progress; see below When I want to prove that the (n + 1) case is true (where I've already proved that the whole thing holds for some n; in this case, I used 4), I add (n + 1) to both sides, as below: [Started with] 1 + 2 + 3 + ... + n = n(n + 1)/2 [Add (n + 1) to both sides] 1 + 2 +3 + ... + ...

- Mon May 01, 2017 4:20 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

1 + 2 + 3 + 4 + ... + (m+1) = [(m+1)(m+1+1)]/2 = [(m+1)(m+2)]/2 (Call this the proof equation) But what is 1 + 2 + 3 + 4 + ... + m+1? It's 1 + 2 + 3 + 4 + ... + m + (m+1). But we already know what 1 + 2 + 3 + 4 + ... + m is, it comes from the "prior equation", and so we know 1 + 2 + 3 + 4...

- Mon May 01, 2017 4:15 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

The "proof equation" isn't derived formally here. We hypothesized it, and now we're going to prove it. We can plug it in because at that point, we are proving "If it's true for n, then it's true for n+1." So we get to assume it's true for n, and then try to prove it for n+1. We ...

- Mon May 01, 2017 3:45 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

What is it that you don't understand? I can be more helpful if I know specifically what is wrong.

- Mon May 01, 2017 3:17 pm UTC
- Forum: Mathematics
- Topic: Mathematical Induction - Introductory Question
- Replies:
**257** - Views:
**42145**

### Re: Mathematical Induction - Introductory Question

So, your statement to be proven is: 1 + 2 + 3 + 4 + ... + n = n*(n+1)/2 The first step, involving the base case, is just to show that your statement is true for some value of n . In your case, you started with a base case of 4. Showing that the statement is true in this case (where n = 4 is pretty e...

- Wed Apr 26, 2017 5:40 pm UTC
- Forum: News & Articles
- Topic: Where Aren't They Now (Obituaries)
- Replies:
**321** - Views:
**89147**

### Re: Where Aren't They Now (Obituaries)

Jonathan Demme, director of "The Silence of the Lambs" and "Philadelphia," dead at age 73. Personally, I really liked "Stop Making Sense," although it's been a long time since I've seen it.

- Wed Apr 26, 2017 4:56 pm UTC
- Forum: News & Articles
- Topic: Trump presidency
- Replies:
**8423** - Views:
**739894**

### Re: Trump presidency

I should have known. ObsessoMom seems to be a reasonable and caring person based on my meager sampling of her posts. It occurred to me that at least in some respects her father must be the same. I ascribe to the adage that the fruit doesn't fall far from the tree. So I supposed that he might be dis...

- Wed Apr 26, 2017 4:47 pm UTC
- Forum: News & Articles
- Topic: Trump presidency
- Replies:
**8423** - Views:
**739894**

### Re: Trump presidency

I should have known. ObsessoMom seems to be a reasonable and caring person based on my meager sampling of her posts. It occurred to me that at least in some respects her father must be the same. I ascribe to the adage that the fruit doesn't fall far from the tree. So I supposed that he might be dis...

- Mon Apr 24, 2017 7:02 pm UTC
- Forum: Science
- Topic: Lay question about entropy
- Replies:
**29** - Views:
**6066**

### Re: Lay question about entropy

The entropy of classical empty space is 0. A classical vacuum is super boring, and you cannot avoid quantum mechanics for very long here. So, quantum mechanics in a vacuum is like Liam Neeson looking for his daughter? :D "I don't know who you are. I don't know what you want. At least not at th...

- Mon Apr 24, 2017 6:54 pm UTC
- Forum: Science
- Topic: Lay question about entropy
- Replies:
**29** - Views:
**6066**

### Re: Lay question about entropy

doogly wrote:It is probably not the worst analogy someone has tried to use for quantum mechanics.

Oh, I've certainly heard worse. Mostly from mainstream reporting on quantum mechanics. But they generally try to succeed and fail, where as I was trying to fail and succeeded. We're all winners.

- Mon Apr 24, 2017 6:46 pm UTC
- Forum: News & Articles
- Topic: In other news... (humorous news items)
- Replies:
**15108** - Views:
**2523273**

### Re: In other news... (humorous news items)

What does happen if one of the candidates gets assassinated? Does the other win by default? Does the 2nd runner up get the slot? Does the candidate's party get to nominate someone? Does the 2nd round get postponed? Does the first round get redone? It appears you return to first ballot and do it all...

- Mon Apr 24, 2017 6:21 pm UTC
- Forum: Science
- Topic: Lay question about entropy
- Replies:
**29** - Views:
**6066**

### Re: Lay question about entropy

doogly wrote:The entropy of classical empty space is 0.

A classical vacuum is super boring, and you cannot avoid quantum mechanics for very long here.

So, quantum mechanics in a vacuum is like Liam Neeson looking for his daughter?

- Thu Apr 20, 2017 6:38 pm UTC
- Forum: General
- Topic: Questions For The World
- Replies:
**2216** - Views:
**438326**

### Re: Questions For The World

Middle US (Illinois/Indiana/Ohio) - never heard anyone use "hoover" as a verb or a generic noun. Only appears in UK shows I watch (and then almost entirely), though I know Hoover vacuum cleaners as well, and remember commercials running often on TV, along with their jingle.

- Wed Apr 19, 2017 1:55 pm UTC
- Forum: Science
- Topic: Safe electrolytes for electrolysis.
- Replies:
**14** - Views:
**4009**

### Re: Safe electrolytes for electrolysis.

I was thinking of wiring up parallel batteries anyway. I had thought of using sodium bicarbonate as well, but I am wasn't sure if I might get adverse reactions from the anion such as reduction to CO or something like that, though that might not be a problem if the area is well ventilated. I'm fairl...

- Wed Apr 19, 2017 4:15 am UTC
- Forum: Science
- Topic: Safe electrolytes for electrolysis.
- Replies:
**14** - Views:
**4009**

### Re: Safe electrolytes for electrolysis.

You ruled out sodium chloride because of the possibility of chlorine-generating side reactions, but what about something like sodium bicarbonate? A sodium salt would still be a good idea if you're interested in making the electrolysis easier, and as far as I know, sodium bicarb isn't going to be cau...

- Mon Apr 17, 2017 8:12 pm UTC
- Forum: News & Articles
- Topic: Military coup attempt in Turkey? [coup fails] [skullcracking!]
- Replies:
**126** - Views:
**37466**

### Re: Military coup attempt in Turkey? [coup fails] [skullcracking!]

So ... exactly as it has been since last year's "coup"? Or like that, but to the limit?

- Fri Apr 14, 2017 6:41 pm UTC
- Forum: Gaming
- Topic: Mass Effect : Meet and Fuck
- Replies:
**277** - Views:
**84403**

### Re: Mass Effect : Meet and Fuck

Hey, it is "Mass Effect: Meet and Fuck" after all... No, it's just creepy. Although, for some reason, I got the male Ryder option when I made my character, and while he doesn't hit on Suvi, some of the other crew members talk about her accent later and how much they appreciate it, and I fo...