English Language & Usage: Multi-Layered Discourse Room

There's something satisfying about pulling the car over, getting the map out of the glovebox, grepping around for your current location, then picking a route to where you want to be, based on lines on the paper.

Mr. Shiny and New 安宇

My wife also loves paper. For a time I convinced her to use a PDA, but eventually she stopped using it, and has completely reverted to her old ways. I want her to get a smartphone but she refuses. She also irrationally clings to the concept of dialing a phone by pressing buttons. sigh

@DavidWallace There's also something about having the tablet on your lap, magically figuring out where you are and what direction you are facing.

David Wallace

@Mr.ShinyandNew安宇 I suppose there must be. Something I have yet to experience.

@Mr.ShinyandNew安宇 How do you dial YOUR phone?

Mr. Shiny and New 安宇

@DavidWallace normally I just tap a contact icon

the phone doesn't really have buttons

sometimes I tap graphical representation of old-school buttons

I have also, at one time, installed a dialer that simulates a rotary phone.

Cerberus

4:20 AM

@DavidWallace Somehow, speed and ease of use are more satisfying to me...strange, I know!

David Wallace

@Mr.ShinyandNew安宇 See, that would suit me. I miss the rotary phone that I grew up with.

Cerberus

@Mr.ShinyandNew安宇 Really?

I just use the T9 dialler to get to the contact I want, then press it.

David Wallace

I just type in the person's phone number.

Cerberus

That's the quickest way to find a contact, the T9 dialler.

Mr. Shiny and New 安宇

@Cerberus 99% of my outgoing calls are to three numbers. I put those numbers on one of my home screens as shortcuts.

Cerberus

4:22 AM

@Mr.ShinyandNew安宇 That is...strange.

David Wallace

Or, I just wait for other people to phone me. I don't care how they dial.

Cerberus

How many times do you call that 1 % in, say, a week?

Mr. Shiny and New 安宇

@Cerberus not really. I don't make many calls.

Cerberus

@DavidWallace Your phone has no list of contacts?

David Wallace

It has a list of contacts.

Cerberus

4:23 AM

@Mr.ShinyandNew安宇 How about messages, then?

@DavidWallace So you don't type the phone number, right?

Mr. Shiny and New 安宇

In the last week I called 6 numbers not in my top 4.

David Wallace

If I want to phone somebody, I often don't remember whether I've added them to my list of contacts. So it's easier just to type their phone number, than to search for them and possibly have to type the number anyway.

Mr. Shiny and New 安宇

@Cerberus It's the same: I text two people regularly and maybe 4 others occaisionally.

Cerberus

Odd.

Mr. Shiny and New 安宇

The messages app sorts the history by most-recently contacted.

Cerberus

4:25 AM

Yes.

Mr. Shiny and New 安宇

So I open the app, and bingo, they're right there.

B! I! NGO! and Bingo was his name-o

Cerberus

@DavidWallace So where do you find this phone number? You learn it by heart? You have it in some kind of booklet?

@Mr.ShinyandNew安宇 I suppose Bingo sounds Asian.

I knew your wife was Asian.

David Wallace

Sounds like a dog.

Cerberus

I just didn't know it was an actual name, Bingo.

Mr. Shiny and New 安宇

@Cerberus I don't think it's asian. It's a word.

Cerberus

4:26 AM

@DavidWallace You are mistaken: that is a dingo.

Mr. Shiny and New 安宇

It's from a song

David Wallace

There was a farmer had a dog and Bingo was his name-o

B I NGO

Cerberus

@Mr.ShinyandNew安宇 Then why did her parents call her that—they thought it was fun?

Mr. Shiny and New 安宇

"There was a man who had a dog/ and Bingo was his name-o/ B! I! N-G-O! / B! I! N-G-O! /B! I! N-G-O!/ And Bingo was his name-o

David Wallace

B I NGO,

Mr. Shiny and New 安宇

4:27 AM

@Cerberus It's also a word you can exclaim when you find something

David Wallace

B I NGO and Bingo was his name-o!

How come your words are different from mine?

Mr. Shiny and New 安宇

it's also a game

David Wallace

Although mine are oddly ungrammatical.

Cerberus

@Mr.ShinyandNew安宇 D'oh.

I am trying to be funny, but you're not biting.

Mr. Shiny and New 安宇

@Cerberus heheh "trying" is right.

Cerberus

4:28 AM

Bingo is played in every home for elderly people around the world.

And the word is uttered when one has bingo.

Mr. Shiny and New 安宇

@DavidWallace Actually, I know that variant too

David Wallace

Well, you do now anyway.

Mr. Shiny and New 安宇

No, I mean, I've sung it both ways

Cerberus

And the general exclamation, somewhat similar to "eureka!", is no doubt very common as well.

Mr. Shiny and New 安宇

In fact I was singing "farmer" in my head while my fingers were typing "a man who"

@Cerberus They couldn't make "Eureka" into a game because it has two Es in it.

David Wallace

4:30 AM

Why doesn't this chat let you say exactly the same thing twice?

Mr. Shiny and New 安宇

Doesn't it?

oops I guess not

Cerberus

@Mr.ShinyandNew安宇 Huh, isn't Bingo played with numbers?

@DavidWallace Because it sucks.

Mr. Shiny and New 安宇

@Cerberus yes but the numbers are in columns under the letters

David Wallace

I had terrible trouble typing B I NGO over and over.

Cerberus

Oh.

Mr. Shiny and New 安宇

4:31 AM

"Under the B, 5", "Under the O, 74"

Cerberus

Well, who plays Bingo anyway.

Mr. Shiny and New 安宇

at my parents' timeshare in Aruba, they have daily bingo. And the guy who used to call it had all these little quirky things he ALWAYS said for certain numbers.

eg: B11 was "Under the B: A pair of SEXY legs!"

David Wallace

@Mr.ShinyandNew安宇 You could say the same for euchre.

Cerberus

Your parents play Bingo??

Mr. Shiny and New 安宇

@Cerberus Not usually. But the bingo game was played on the patio by the pool.

Cerberus

4:33 AM

How annoying.

Mr. Shiny and New 安宇

I might play when we go this year with my daughter. She will find it fun.

ChairOTP

Hi

Mr. Shiny and New 安宇

Hi

ChairOTP

How's everyone doing?

Cerberus

We did play Bingo in French, at school.

To learn the French numbers.

Hi!

ChairOTP

4:35 AM

It's funny how you guys started talking about one thing, and ended up talking about Bingo.

Mr. Shiny and New 安宇

That's how conversations go

You're just lucky (or maybe unlucky) that we're not talking about porn, or balrogs, or balrog porn.

ChairOTP

Hahahah someone always brings up porn.

Cerberus

*balrogs

@Mr.ShinyandNew安宇 (I get the evil triangle again.)

David Wallace

@ChairOTP We always will if you wait long enough.

Mr. Shiny and New 安宇

@Cerberus maybe you've been getting it all along, but your phone is only periodically trying to do something, so periodically showing it

Cerberus

4:39 AM

Yes.

I'm busy installing stuff on my phone all the time, but not using Google services all the time.

ChairOTP

@DavidWallace I've noticed from the past two days.

Cerberus

Not that it pops up when I use Gmail or anything.

David Wallace

@ChairOTP You won't have to wait quite so long, if you want us to end up talking about phones.

And when I say "us", I mean Cerberus :-)

ChairOTP

@DavidWallace As I said, someone always brings up porn... and apparently that someone is Cerberus.

Mahnax

Hi everyone.

Mr. Shiny and New 安宇

4:44 AM

quick, hide the porn, a minor is here

2

Cerberus

hides phone

David Wallace

This has the most useful answer I've ever seen.

0

Q: Limit to a function

So I'm having trouble with the following limit: $$\lim_{x\to2}{\frac{x^2-x-2}{\sqrt{x^2+5}-3}}$$ Common factor doesn't work. Any hints on how to tackle it?

Cerberus

@DavidWallace And Mr Shiny!

Mahnax

Mm, perhaps I shouldn't reveal such things.

David Wallace

In NZ he wouldn't be.

Cerberus

4:44 AM

Don't tempt us.

ChairOTP

@DavidWallace lol

David Wallace

I suppose having found it, I should answer it. Or at least provide a hint in a comment.

Oh, that's no fun. He's changed his answer to a less amusing one now.

ChairOTP

@DavidWallace Did you get 9/2 as well?

David Wallace

But the new answer is actually a good one.

Mahnax

Oh yeah, so I handed in my two weeks' notice at work today.

David Wallace

4:49 AM

Do you have something else lined up?

Mahnax

Not at the moment, but tons of places are hiring.

All of them better than my current[?] occupation.

ChairOTP

why can't I add a comment?

Cerberus

@Mahnax Were they shocked?

Mahnax

@Cerberus Yeah.

One of my favourite co-workers is sad that I'm leaving.

Her husband is happy that I'm getting out of a crappy job.

waiwai933

@ChairOTP You need 50 rep to comment on any post; you can always comment on your own posts.

David Wallace

4:52 AM

@ChairOTP Yes, I get 9/2, using the method suggested by Amzoti. Not L'Hôpital.

ChairOTP

@waiwai933 oh thanks.

waiwai933

You can automatically get 100 rep on every site in the Stack Exchange network once any of your accounts surpass 200 rep.

ChairOTP

@DavidWallace Both work.

Cerberus

@Mahnax Aww.

David Wallace

@ChairOTP I know. Interesting how many echoes there are in that question.

Mahnax

4:53 AM

@Cerberus The manager is also sad.

Cerberus

Aww2.

But so be it.

Mahnax

Yeah. I'm happy to leave, but I'll miss a couple people.

ChairOTP

@DavidWallace Our teacher doesn't let us use L'Hopital. I just cheat and use it and check if my answer is right.

David Wallace

@Mahnax You can stay in touch with them, surely!

Mahnax

@DavidWallace Yeah, of course.

David Wallace

4:55 AM

@ChairOTP What planet is your teacher on?

Mahnax

They live close to me.

ChairOTP

@DavidWallace Well he hasn't taught us derivative, so that's why he says I can't use it.

David Wallace

He's probably scared you'll show him up.

Cerberus

@Mahnax Understandable.

David Wallace

On this particular question though, I feel that amzoti's method is superior to using L'Hôpital.

Cerberus

4:57 AM

Oh shit, it's 7 am already.

David Wallace

I wish I had thought of it first.

ChairOTP

Well today I made him doubt about 1 to the infinity power.

Using common sense you would say it's 1... but you'll be surprised what other numbers you can get from there.

Mahnax

I have nothing meaningful to add to this mathy conversation. All I know is that the derivative of x^n is equal to nx^(n-1).

David Wallace

@ChairOTP You need to define what you mean by "infinity power". The only sensible definition is "limit as n approaches infinity of nth power".

ChairOTP

@DavidWallace It is superior in some way because it's the way how it was solved before L'Hopital even existed.

Mr. Shiny and New 安宇

4:59 AM

@ChairOTP That doesn't mean it's superior.

ChairOTP

@DavidWallace limit as x approaches infinity of 1^x is 1.

Mr. Shiny and New 安宇

But it's 7am in cerb ville which means it's 1am here which means I am up too late.

ChairOTP

@DavidWallace But 1 to the infinity power is undetermined.

David Wallace

@ChairOTP But there is a sensible definition for it, as my comment suggested.

ChairOTP

@DavidWallace humour me? what do you mean by sensible?

David Wallace

5:00 AM

Well, it's like the sum to infinity of a series.

There's a question on that. Give me a moment.

math.stackexchange.com/questions/116269/… - note particularly my excellent answer :-)

Unless you're doing non-standard analysis or some fancy set theory, pretty much anything you say about "infinity" is just a shorthand for talking about some kind of limit.

ChairOTP

@DavidWallace So you mean that talking about infinity implies talking about a limit, right?

David Wallace

Well, if you and the person that you're talking to accept that it's a shorthand.

I would argue that you shouldn't say things like "1 to the power of infinity" until both sides agree that this actually means "limit as n approaches infinity of 1 to the power of n".

ChairOTP

So basically you couldn't raise an integer to the infinite power (not talking about limits) because infinity is not a number.

@DavidWallace but no, leaving aside limits, 1 to the power of infinity.

David Wallace

@ChairOTP Correct.

ChairOTP

yet you still can prove 2 to the power of infinity is infinity.

David Wallace

5:06 AM

Arithmetic operations are defined for certain types of numbers.

@ChairOTP You can do no such thing.

ChairOTP

@DavidWallace I could, but then I would have to think of infinity as a number, which is incorrect.

Mr. Shiny and New 安宇

wow, reading that math site has just revealed to me how much math I have forgotten.

ChairOTP

@DavidWallace because I'd be making arithmetic operations with infinity, when infinity is not included in arithmetic.

Mr. Shiny and New 安宇

anyway, I must be off. bye!

David Wallace

If you don't accept that "2 to the power of infinity" means "limit as n approaches infinity of 2 to the power of n", then you don't have a definition for "2 to the power of infinity". If you don't have a definition, then you can't meaningfully assert that it's equal to anything. Much less prove anything.

Bye, Mr S&N.

Mahnax

5:08 AM

@Mr.ShinyandNew安宇 Bye!

ChairOTP

@DavidWallace So, "2 to the power of infinity" is indetermined when thinking of infinity as a number. But when we talk about limits, it does 'exist'.

David Wallace

Of course, you could define "to the power of" in terms of cardinality of cross products of sets. But then you get into problems about what "infinity" means.

@ChairOTP Umm, I would say that it CAN be defined in terms of limits.

But it doesn't go without saying that you should use that definition just because it exists.

ChairOTP

Yet, I wonder why the limit as n approaches infinity of 1 to the n power is 1, but when I evaluate limit as n approaches infinity of (1+r/n) to the tn power, where r,t are both real numbers, isn't 1. And it's in the 1 to the infinity power form.

David Wallace

OK, so think of two forces - one pushing the value towards 1 and the other pushing the value towards infinity. Together, they manage to push it to a value in between.

Err, I mean e^(tr) I think

ChairOTP

Yep, the second one.

Then, I would have to say the limit as n approaches infinity of 1 to the n power is undetermined, because I can get infinity answers.

David Wallace

5:15 AM

I read your fraction as 1/rn the first time, for some reason.

@ChairOTP Then you would be incorrect.

ChairOTP

It's like 0/0, it has lots of answers, that's why is undefined.

David Wallace

1 is not the same thing as 1+r/n.

ChairOTP

@DavidWallace as n approaches infinity, it is, or not?

David Wallace

If you write y = 1^n and watch what happens to y as n goes to infinity - well, it never changes. It starts at 1 and stays at 1.

You can't go around replacing terms in a limit expression with their limits and expect everything to stay the same.

ChairOTP

Then (1+r/n) to the tn power, is not in the 1 to the infinity power form?

@DavidWallace Then I must say one finds plethora of garbage in Internet.

3

David Wallace

5:20 AM

@ChairOTP That is indeed true.

@ChairOTP When you're taking a limit, you can't take the limits of different parts of your expression separately. Your example is the perfect illustration of why.

ChairOTP

@DavidWallace Because all those examples I've evaluated in which they replace terms so the new expression is in the 1 to the infinity power you get infinity of numbers.

@DavidWallace What if we take, different functions?

David Wallace

For example?

ChairOTP

f(x) to the power of g(x)

and make f(x)= (1+r/n) and g(x)=tn

evaluate those limits when n approaches infinity

David Wallace

@ChairOTP You can't apply the limits separately to the two parts of the expression.

ChairOTP

@DavidWallace then go backwards, you have f(c) and g(x), you evaluate the limit in each one, and then you evaluate the limit when f(x) to the g(x) power.

wait

But I guess that you mean that when evaluating lim g(x) individually is not the same as evaluating it when being the power of, in this case, another function.

David Wallace

5:28 AM

Any of those expressions, you can evaluate at different values of x, and see what happens as x goes to c, right?

ChairOTP

@DavidWallace I suppose.

David Wallace

There's a theorem that says that if f(x) and g(x) have finite limits as x goes to c, then those expressions do what you expect them to do.

But as soon as one or both of them go to infinity, or if somewhere you end up dividing by zero, then that theorem doesn't apply.

ChairOTP

@DavidWallace so what's said up there is wrong?

John Junior

The mean value theorem?

David Wallace

@ChairOTP Err, no. Looks OK.

ChairOTP

5:31 AM

@DavidWallace Could we think of f(x) to the g(x) power as f(x), g(x) times?

Yousui

Hello fellas

Anyone here?

David Wallace

@ChairOTP Yes, we could.

Yousui

I want to know what does this thing called in English: hdlighting.com/catalog/images/ALP%20KDS1%20strip%20image1.bmp

Is it a strip light?

ChairOTP

@DavidWallace then it would be a multiplication what we would be doing, f(x)*f(x)... etc, g(x) times.

Yousui

or it's a "strip lamp"?

David Wallace

5:33 AM

@Yousui I call it a "fluorescent light".

ChairOTP

Isn't that a fluorescent lamp?

David Wallace

@ChairOTP What happens if g(x) is not an integer?

Cerberus

@Mr.ShinyandNew安宇 Ahhh my GN won't boot!

Wtf?

Yousui

OK, thanks guys!

David Wallace

@Cerberus I'll swap you for pen and paper.

ChairOTP

5:34 AM

@DavidWallace But you said we could consider the idea of infinity in this case when talking about limits.

John Junior

@Yousui A fluorescent tube.

Cerberus

It keeps repeating the Jelly Bean boot animation, the glowing, coloured cross.

Yousui

Thanks John.

ChairOTP

so we could multiply f(x) as g(x) approaches infinity

Yousui

Are there anything called "strip light" or "strip lamp"?

David Wallace

5:35 AM

How do you do f(x) . f(x) . f(x) g(x) times over if g(x) is not a positive integer?

ChairOTP

It's not a positive integer, but is the idea of a really really big amount, so we could say f(x) lots of times.

David Wallace

Striplight

A striplight is a multi-circuit stage lighting instrument. Striplights are one of the most basic types of lighting fixtures available. They usually consist of row of lamps. A single striplight is usually wired internally into either 3 or 4 circuits. Each internal circuit consists of several lamps evenly spaced within the unit. Often, a lighting designer will use roundels (colored glass lenses) or gels to make these lights different colors. The unit can then be wired into several different circuits, allowing each bank of colored lights to be controlled by a separate dimmer on the light...

John Junior

@Yousui For lights that are long like a strip.

ChairOTP

and evaluating its limit as f(x) is repeatedly multiplied by f(x) as many times as we could.

David Wallace

@ChairOTP Could we?

Yousui

5:37 AM

um, I think i get it. Thanks all!

ChairOTP

@DavidWallace an endless amount of times.

Yousui

This is really a wonderful community.

You guys are always ready to help.

Thanks.

John Junior

np

David Wallace

@ChairOTP Can you see how that is not a particularly rigorous definition?

ChairOTP

@DavidWallace If we go strictly into the definition of infinity, we could never do such operating, not even limits, because we'd never be approaching such thing as infinity.

David Wallace

5:41 AM

Non-standard analysis?

ChairOTP

@DavidWallace An standard analysis would require a higher knowledge in the matter which I don't have, and probably won't in a long time.

In fact I was going to ask my high school maths teacher about this so he could clear up this mess I have, he's one of the smartest people I've met.

David Wallace

Nice to have such a teacher.

Mahnax

My social studies teacher is ridiculously intelligent.

All of my teachers say he is literally the smartest man they have ever met.

David Wallace

And he teaches social studies?

Mahnax

Yes.

He also teaches World History 35 and Theory of Knowledge though.

ChairOTP

5:46 AM

@DavidWallace I really look up to him because he taught us in one year what we're supposed to learn in maybe 3 years of our course in university.

David Wallace

Yes, I'm impressed that someone your age knows L'Hôpital's rule.

Mahnax

My maths teacher said that my social teacher could easily teach us quadratics just as well as he could.

Not that they're difficult, but still.

David Wallace

Any well educated adult with a teaching qualification should be able to teach quadratics.

John Junior

@Mahnax What do you think makes him such an excellent teacher?

Mahnax

@DavidWallace I disagree.

ChairOTP

5:49 AM

@DavidWallace I'm actually grateful because my high school wasn't a really big high school nor a private one, it was really cheap, like I mean really really cheap, yet I got more than most of other students from more privileged high schools got.

Mahnax

How many English teachers have cared to remember quadratics?

ChairOTP

@Mahnax or P.E teachers.

Mahnax

@ChairOTP Right. Or French, or Social Studies, or Foods, etc.

David Wallace

@Mahnax Inexcusable.

You will notice, however, that my comment contained the word "should".

ChairOTP

@DavidWallace Taking into account that some teachers shouldn't be called teachers.

Mahnax

5:51 AM

@DavidWallace Right—I still disagree. An English teacher has no obligation to remember quadratics.

David Wallace

Ownership of a brain?

Mahnax

:6218566 He's intelligent, articulate, and can still actually teach.

ChairOTP

:6218566 I think the answer might be, he doesn't teach, he makes us think. I'm a self-taught student, so it was easier for me to approve his class.

David Wallace

@Mahnax Do you feel that quadratics should be taught to every student?

Mahnax

@DavidWallace Yes.

David Wallace

5:52 AM

Even those who will become English teachers?

Mahnax

Sure.

David Wallace

But why? If they're not expected to remember them?

ChairOTP

@Mahnax I don't really agree.

Mahnax

@DavidWallace Maybe they'll want to switch careers later on, change their major, or something.

ChairOTP

They had to learn it at some point (high school) but then they just decided to major in an specific area that didn't imply the use of qudratics.

Mahnax

5:54 AM

But it's unreasonable to expect an elderly English teacher to know quadratics inside out and backwards.

David Wallace

I feel that everything I learnt in high school should be something I am able to teach. Otherwise, how can I say that I learnt it?

However, I couldn't teach PE if my life depended on it.

Mahnax

Some people forget things if they don't use them.

ChairOTP

@DavidWallace Then maybe you didn't learn but memorized.

David Wallace

@ChairOTP hah! If you knew me, you wouldn't say such things.

ChairOTP

@DavidWallace well, then speaking in general terms.

David Wallace

5:55 AM

@Mahnax Some people own books, or have internet access.

John Junior

Education is what is left when you forget everything you learned in school.

Mahnax

If I understand you correctly, you're saying a teacher should be able to teach any subject they learned.

ChairOTP

@Mahnax Plus, as far as I know, teachers do study before they teach students, so they basically don't really know it inside out and backwards.

David Wallace

@Mahnax I think you understand me correctly.

ChairOTP

@Mahnax "any subject they learned".

Mahnax

5:58 AM

@DavidWallace So my Physics teacher should be able to explain the inner workings of photosynthesis and cell resp. to me?

My Maths teacher should be able to teach me how to write commentaries?

Cerberus

@Mr.ShinyandNew安宇 Okay, I can boot into recovery mode, thank God.

David Wallace

@Mahnax Have they learnt the inner workings of photosynthesis and cell respiration?

Mahnax

@DavidWallace Probably. It's in the curriculum, and has been for quite some time here.

David Wallace

@Mahnax Absolutely, they should.

ChairOTP

Exactly my point, they might have taken Biology or English, but if they didn't learn, how come they're supposed to teach you.

Transcript for

English Language & Usage: Multi-Layer…