Mathematics - 2014-04-27 (page 1 of 3)

user127001

00:00

Over my head

Chris's sis

And as W|A shows , this can be expressed the sum of these 2 integrals is actually $\pi\ln\frac34-\Im\operatorname{Li}_2\frac{3i}4$ as Cleo showed.

(or using the inverse tangent integral as sos440 showed)

That's all.

I kill the first integral from one single shot if I introduce the variable $a$, as $\log(1+a x)$, and then differentiate with respect to $a$.

Okay, my POTD tomorrow will be the original question from which these 2 integrals come from.

I need some sleep now.

user127001

Ok

Good night @Chris'ssis

Ram

01:16

Hi, any one in here?

user127001

I am @Ram

Ram

Hi, do you know any thing about Intersection pairing?

user127001

@Ram No, I don't know much math

Ram

hmmm

Pedro Tamaroff

02:19

@FernandoMartin Jacobson is sneaky.

TechMaster100

How do you find the area of a general quadrilateral, given only the side lengths of the quadrilaterals?

I would prefer if you used an example as well.

Mike

@TechMaster100 You don't.

Ram

@Mike, can you help in understanding Intersection Pairing?

I am trying to construct intersection pairing matrix (simple case S1 x S1).

at H1 x H1 to Z

Goos

@TechMaster100 It's a good question, but a quadrilateral is not determined by the length of its sides. Related.

Mike

02:35

@Ram I wish I could help! I don't know intersection pairings.

Ram

@Mike :-(

nerdy

Can i ask for recommendation of books in math.stack exchange

or do i need to ask for it in wiki community

or something

Ram

02:51

@nerdy, you can ask under soft questions tag

at math.stackexchange

nerdy

thanks!

Ted Shifrin

@Ram, usually that's done on $4n$-dimensional manifolds so that the matrix will be symmetric. Do you know Poincaré duality so that you can understand it geometrically?

Hi @Mike

user127001

Hi @Ted

Ram

@TedShifrin, thanks for reply. I am trying to construct an example. I did it on S1 x S1.

But ok, lets take S1x S1 x S1 xS1 and H2 x H2.

Ted Shifrin

Better, do $S^2\times S^2$ or $\Bbb CP^2$. So you know cup product?

Ram

02:57

So, this is exterior algebra generated by 4 elements, say p,q,r,s. So H2 will be generated by wedge sum of two elements (so 6). Now I am getting 6 x 6 matrix

Ted Shifrin

No exterior algebra !

Hi @user127001

Ram

Yes, I know cup product.

Ted Shifrin

Why are you doing exterior alg? You want the cohomology ring.

Ram

Yes, but for n torus, the cohomology ring is exterior algebra generated by n elements right?

Ted Shifrin

You can represent cohomology by diff forms, which I adore, but no exterior algebra of vector spaces here.

Ram

03:00

I don't know diff forms :-(

Ted Shifrin

Ah ... Do my two examples before tori.

user127001

@Ted I think we are completely skipping rings in our algebra class. Last class we spent it on interesting symmetries (kaleidoscopes, gyrations, etc.) and the class before that, game theory

Ram

I got [1, -1, 1, 1, -1, 1 ] in the reverse diagonal positions and wedge of p,q,r,s.

Ted Shifrin

This sounds just as crazy as Conway, @user127001.

Ram

@TedShifrin, I am having difficult time with exterior algebra. So, trying to learn it :-) with hatcher...

user127001

03:02

@Ted during the game theory class, he bet a student $20 in a game of dots and boxes and he lost lol

Ram

But, I dont know what I have to do with p \wedge q \wedge r \wedge s in the matrix.

Ted Shifrin

You should learn differential forms on manifolds , @Ram :) forget torus and do my examples, please.

Ram

Sure, let me start

Ted Shifrin

@Ram: That's the generator of $H^4$.

Ram

yes, but H2 x H2 should be mapped into Z right?

Ted Shifrin

03:05

In some ways, @user127001, rings are more fundamental than groups.

Yes.

Ram

but why I got H4 generator? Where I did the mistake?

Ted Shifrin

That is the generator of the $\Bbb Z$.

Ram

So, it seems my calculation is alright?

Pedro Tamaroff

Ah, lhfs.

robjohn

Ha! I just noticed that I have a MetaStackExchange account and that one of my MSO answers was migrated there. I love the comments to the answer.

Ted Shifrin

03:08

You need a 6x6 matrix for that torus. Hence the reason I told you to do the other ones.

robjohn

Real on-topic comments.

user127001

@robjohn you have not changed your profile picture for how many years?

Ted Shifrin

Hi @Pedro

@Pedro: The friend I had dinner with in ATL was suggesting we visit BA:)

robjohn

@user127001 Since it was suggested. I created it that day.

2

Ted Shifrin

@robjohn doesn't age ...

user127001

03:11

Wow

How did you decide on the color @robjohn

Pedro Tamaroff

@tedshifrin well ill be waiting at Ezeiza =]

robjohn

@user127001 it seemed a mean color.

user127001

I think red might look pretty mean

robjohn

@user127001 but I don't think it is as nice for an avatar.

user127001

But I thought you wanted it to be mean for an avatar

Ram

03:15

@TedShifrin, okay I calculated Ring of CP2that is $mathbb Z[x]/x^3$. So, I have to start with H2 x H2 -> Z right

Ted Shifrin

But your $x$ is in degree 2, @Ram, right?

Ram

yes. x is in degree 2

Ted Shifrin

Do you understand what's going on geometrically?

Ram

Nope.

I couldnt find material to read more about it..

Ted Shifrin

sigh. Too much fancy stuff and not enough understanding. The generator corresponds to a projective line in the projective plane. And a line intersects another line in ....

robjohn

03:19

wow... I just got an upvote on an answer from 2011.

talk about digging up old questions

Ted Shifrin

What are you waiting for, @Pedro? :D

Ram

@TedShifrin, Hatcher din't gave any geometric interpretation :-(. I dont know any better book to Hatcher. Can you suggest some thing for this?

Ted Shifrin

Surely he does when he discusses Poincaré duality?

Ram

yes

Mike

Hi @Ted

Ram

03:29

he gives this as connection between cup and cap products

Ted Shifrin

Griffiths and Harris discuss all this in chapter 0 of their algebraic geometry book.

Sadly, alg top books don't do a good job of providing insight. One needs professors for that :(

user127001

Really

Ted Shifrin

Some of us do, you know, @user127001 :D

user127001

lol

Wow this Griffiths & Harris book costs $116.39

Mike

Anyone have much experience with Mathematica?

Ted Shifrin

03:31

Yes, @Mike

Ram

OK, great I will find that. And I have another question,

Ted Shifrin

Griffiths and Harris, despite dozens of errors, is superb.

user127001

Is it better than Hartshorne

Ram

f: P2#...#P2 (2n sums) to T2#......#T2(n sums). If I look at f_*(H^1) how does it look like? I mean can we say some thing about this with out any information on f?Lets take coefficients in Z2.

Mike

@Ted Does that mean you do or people do?

Ted Shifrin

03:33

Far better. It's not slavishly algebraic. It is based on analysis, geometry, topology. It's a very different style/approach to the subject.

Ram

by looking at cup products this looks like trivial in this case.

Ted Shifrin

Not trivial, @Ram, but easy, yes.

Yes @Mike :)

Ram

Me and Mike thought its trivial on H^1 isn't it?

Since in Orientable case we have, a_i cup a_i = 0, but in non orientable surface f_*(ai)^2 is zero iff ai is zero.

Ted Shifrin

Huh, what are you doing now, @Ram?

Ram

I mean, I am talking about generators of both cases

at H^1

Mike

03:36

@Ted Dles it play nice with complex functions? I want to simplify a function I have involving the principle branch of sqrt.

Ted Shifrin

It is not good about branches ... I've not tried that sort of thing.

Ram

and looking at cup product in H^2 (Sorry page expired)

Mike

Darn. I don't want to be too careful about this. But I need something to be.

Ted Shifrin

Ok, bedtime for me. Tennis early am

Night, all.

Ram

Ok, good night.

user127001

03:41

Night

sea turtles

04:49

what's an example of a distribution that is not a sum of dirac deltas weighted by normal functions?

Mike

05:25

@seaturtles what's a normal function

sea turtles

everyday, usual, familiar

Mike

and can you explain what you mean by weighting a dirac delta with a function? i don't know that notation/terminology.

sea turtles

$\sum_i f_i(x)\delta(x-a_i)$

Mike

right, but that reduces to a sum of dirac deltas weighted by complex numbers.

seems silly.

sea turtles

so $x\delta(x)=\sum c_i \delta(x-a_i)$ for complex numbers $c_i,a_i$?

erm

yes I suppose $f(x)\delta(x-a_i)=f(a_i)\delta(x-a_i)$

Mike

05:28

yop

sea turtles

so $f(x)+\sum c_i\delta(x-a_i)$ in that case

Mike

yeah that's the right question i think

sea turtles

that gives a "continuous part" and "discrete part" and this suggests the question if there's anything in between

Mike

the answer should be "yes", a couple months ago i'd be able to give an example on the spot

gimme a sec

@seaturtles the answer's definitely yes, but i can't find an example in my notes. (we should say $f$ is locally integrable to make the 'obvious' class of things work, but still be able to find stuff that's more general.)

@seaturtles oh, right. every measure gives you a distribution. convince yourself that there are more measures than $df + \sum c_i \delta(x-a_i)$

sea turtles

hmm

Mike

05:41

i don't have an example for that, either, but it's more "obviously true" to me

@seaturtles i just thought of an example, but it's gross

sea turtles

haha

my friend is such a heavy sleeper I just unlocked his cell phone with his finger

wish I knew how smartphones worked

Mike

06:34

wat

sea turtles

07:05

fingerprint authentication

Mike

ook

Freeze

@Sawarnik

Sawarnik

08:32

@freeze Hi.

usukidoll

08:47

hi hi

skullpatrol

yo yo

usukidoll

almost 700 reputation ^^

skullpatrol

nice

usukidoll

and I just made 700 ^^

skullpatrol

congrats :-)

over 9,000 hours later...

Sawarnik

09:00

@skullpatrol ?

usukidoll

09:11

need feedback
http://math.stackexchange.com/questions/771119/prove-that-if-t-in-t-and-q-in-q-but-q-neq-0-then-qt-in-t

Martin Sleziak

09:29

Should the question In a group of 26 people, is it possible for each person to shake hands with exactly 3 other people? be closed as a duplicate of Constructing Cubic Graphs of Even Order? The later is clearly more general. However, it uses somewhat different terminology.

usukidoll

you! -___- ^

Martin Sleziak

@usukidoll All that I am saying is that when I see this: Prove that if $t \in T$ and $q \in Q$, but $q \neq 0$ then $qt \in T$ I have no idea what the question is about.

usukidoll

oh o_o

Martin Sleziak

When I see: Is product of a transcendental number and a non-zero rational number again transcendental? I immediately know what the question is about.

usukidoll

strange.. I've written my questions like that for a while now... is it part of the reason why it's taking long for me to even get an answer sometimes?

Martin Sleziak

09:33

Informative titles are recommended, see How can I ask a good question?. (I left you this link in a comment.)

usukidoll

yeah -- I'm reading it now *scrolls through****** -______-*

Martin Sleziak

But as far as your question is correct I do not see based on what you claim this: As a result, $t \in T$, but $q \notin T$, so $qt \notin T$.

usukidoll

sorry.. I'm new to proof writing

practice makes perfect right ?

at least I"m not chucking the book out the window ... since the course was a roller coaster for me

What I'm trying to say is that although t is transcendental, q is a rational and by that prop... all rational numbers are algebraic which clearly breaks the definition of transcendental (numbers aren't algebraic period)

Martin Sleziak

This claim, if I understand you correctly, says that: Product of a transcendental number $t$ and an algebraic number $q$ is an algebraic number $qt$.

usukidoll

yeah, but clearly we can't have that for t if it's transcedental

Martin Sleziak

09:38

From the title of your question it seems that you are trying to prove that $qt$ is transcendental. But you end your proof claiming that $qt\notin t$.

usukidoll

blah ... q is rational... by the prop... it's algebraic... t is transcedental which means that it's not algebraic so we can't have $qt \in T$ because q isn't transcedental oh boy I should've put that instead of the massive symbol line

Martin Sleziak

Try $q=2$, $t=\pi$.

usukidoll

I'm disproving that statement.. because if q is rational... and by that prop all rational numbers are algebraic, then clearly it doesn't belong in transcendual

Martin Sleziak

The number $2\pi$ is not algebraic.

Which statement exactly do you want to disprove?

Or are you trying to prove it by contrapositive?

The main thing that bother me: You seem to be claiming that $t\in T$ $\land$ $q\in A$ $\implies$ $qt\in A$. This is not true.

Moreover I do not see at which place of your proof you are using $q\ne0$.

usukidoll

what the ! -_- $ t \in T$ that's transcendental It's NOT ALGEBRAIC! so that t shouldn't be in that A at all!

q is rational... by that prop all rational numbers are algebraic.. okkkkkk....... but is it going to be in T... no because anything in T is not algebraic.

Martin Sleziak

09:47

That's true. We have $q\notin T$, which is the same as saying $q\in A$.

I agree with this.

usukidoll

I haven't switched anything..I'm not doing converse... contrapositive...or negation .. just straight out disproving the statement... I saw right through

but for other proofs like oh relations...functions...cardinality... I'm screwed like crazy

Sawarnik

@MartinSleziak I found your name on Wikipedia :D

usukidoll

OO link!

Sawarnik

Just the name, not an article :D Here, en.wikipedia.org/wiki/Tibor_%C5%A0al%C3%A1t

Martin Sleziak

But if you are doing just direct proof, how come you end up with $qt\notin T$, when you are trying to show $qt\in T$?

usukidoll

09:49

I wanna disprove ^

Martin Sleziak

So you want to disprove the statement in the title of your question?

usukidoll

yesssssssssssss

how the heck can we have q in T if the def of T says that the number isn't algebraic

q is rational.. and by that prop... all rational numbers are algebraic

Martin Sleziak

Oh, I should have noticed this in your post: We are going to disprove this statement.

usukidoll

which is clearly a red flag

yeahhhhhhhhhhhhhh

Martin Sleziak

But I do think that the statement is true.

usukidoll

09:50

no......

I'm trying to disprove this part $qt \in T$

because how the heck can q be in T when it's rational and by prop... it's algebraic.. T doesn't have algebraic numbers...period.

$ t \in T@$ I understand that clearly

Martin Sleziak

But the claim does not say that q is in T.

usukidoll

$q \in Q$ which is rational

$t \in T$ transcendual

$ qt \in T $ so my q and t is supposed to be Transcendual

works for T, not for Q

Martin Sleziak

Why do you claim that $qt\in T$ implies that both q and t are transcendental?

What about $1\cdot\pi \in T$?

usukidoll

that's just a pi

if I multiply right through

Martin Sleziak

The product $1\cdot \pi$ is transcendental. But clearly, it is not true that both $1$ and $\pi$ are transcendental.

usukidoll

09:54

try q = 10 and t = $e$ >:)

Martin Sleziak

That's the same thing. Both $e$ and $10e$ are transcendental.

usukidoll

o_____O! oh f....... wait if I take the product of q and t then the result will be transcendental.... and it would belong in T

so I was just doing this proof with letters and not coming up with let q = 3 and t = $e$

sigh this is what happens when self studying fails and the prof fails to teach clearly

S_S

what if I'm not allowed to take the product of q and t... what happens then?

Martin Sleziak

I am not sure whether I was able to show you that you did not disprove the claim. But if you want to try to prove the claim, you could try proof by contradiction.

user3123545

hello

Martin Sleziak

You could say: Let us assume that $q\in\mathbb Q$ and $qt\notin T$. What can we say about $t$ then?

usukidoll

09:58

I would still disprove it like the wind >:D because assuming that I can't take the product or assign values to q and t . wham

t is not transcendual

which means t is algebraic like that q being a rational number and being algebraic by that prop

Martin Sleziak

If you manage to show that $q\in\mathbb Q$ and $qt\notin T$ implies that $t$ is algebraic, you get a contraction. And thus you get proof of the claim in the title of your question.

Sawarnik

@user3123545 hi.

usukidoll

but what if I still want to straight up disprove the statement... unless I was thinking about it wrong slightly for $qt \in T$

Martin Sleziak

But why do you want disprove a statement which is true?

usukidoll

because I have no solid guideline that's what.. I'm lost in proof writing land really along with the rest of the class, so I've been trying to reread again

user3123545

10:01

I had a question today, showing a diagram sort of, showing something like this: http://www.regentsprep.org/Regents/math/algtrig/ATS2/normal67.gif

now there were 2 hints, 16% on left showed 185 and 16% on end showed 215 (assume the 16% on left is 84 cause 100-16. Now they wanted me to find the avg in this all, i only know that 68% is 30 (215 - 185). How can I know the avg?

usukidoll

wow guess I need more time to master this cheese whiz

Martin Sleziak

It seems that we keep misunderstanding each other, so it is probably the best if I leave this for someone else.

usukidoll

damn I see the point now qt the product of q and t.. let q = 5 and t = $e$... so $5e \in t$ which means it does belong... I had no idea you can assign numerical values to these problems

sighhhhhhhhhhhh

Martin Sleziak

Anyway, I have edited your title, at least to include the information what $T$ means. (I think it is cleare that way.)

usukidoll

skull I'm sad now :(

damn it's like there are so many ways to look at the claims and there is the thought of what if this and what if that this that this this that

skullpatrol

10:05

Write down as much as you can...

usukidoll

ha ha very funny

I had no idea that I would be able to assign a number to q and t

Martin Sleziak

In fact, after some practice the proofs from introductory courses should not be that difficult. You basically have to write down the definitions and things that you know. If the proof is not working, that you try contradiction or contrapositive. If it is claim about integers, you can try induction.

usukidoll

I just looked at it with just the letters played

it's only my first one :/

Martin Sleziak

So it's basically mastering a few basic techniques. But you can achieve that only if you try enough exercises.

usukidoll

but at least I'm reading and trying :/

skullpatrol

10:08

What textbook are you using?

usukidoll

Passage to Abstract Mathematics

it's really a meh book

I learn better with ROsens DIscrete Math book thing and other materials

Martin Sleziak

@usukidoll So you have learned something new. In general it is useful to look for specific examples. For example, if I was trying to do some proof and if I had an idea: Now if I show that the product of two irrational numbers is again irrational, then I will be able to finish this proof. Maybe after few unsuccessful attempts I would notice that $\sqrt 2\cdot\sqrt 2=2$ is a counterexample to what I was trying to show. And I would realize that I have to try something else.

usukidoll

ok... so what about
prove that if $ t \in T $, then $ \frac{1}{t} \in T$. That should be easy.. since we have transcendental numbers that aren't algebraic... so if I let $t = e$, then $\frac{1}{e}$ and that would be in T?

skullpatrol

Have you gone to a university library and looked at what is available @usukidoll?

Martin Sleziak

It is good to look at specific example. But noticing that some claim is valid for one particular example is not the same as a proof of that claim.

To prove it, you should show that it is true for any $t\in T$, not only for $t=e$.

Maybe this would help: Can you show that $t\in A$ $\implies$ $\frac1t\in A$?

(Or maybe you have even learned theorem saying this.)

Of course, we assume $t\ne0$.

usukidoll

10:14

T being algebraic implies that $\frac{1}{t}$ is algebraic

Martin Sleziak

Well.

Now if you want to show for $t\ne 0$, $t\in T$ that the inverse $\frac1t$ is transcendental.

You could say: If $\frac1t$ were not transcendental, then it would be algebraic.

Sawarnik

..

usukidoll

ooooh by definition 2.7.8 A number s is an algebraic number when there exists some $p \in Z[x]$ such that $p(s) =0$. Let us denote the set $A = [x \in C $: x is algebraic]$

Martin Sleziak

But if $s=\frac1t$ is algebraic, then $1/s=1/(1/t)=t$ is .... ?

Off topic: You are doing Exercise 2.7.13 from that book, right?

usukidoll

HOW DID YOU KNOW THAT D: PSYCHIC POWERS? ^

if we have $ t \in A$ then there exists a polynomial $p \in Z[x]$ of the form that long string of polynomial stuff

Sawarnik

10:18

@usukidoll He must be having that book, or some pdf.

usukidoll

lol he must own the book...I can't find the pdf XD

Martin Sleziak

No, I do not have any psychic powers. If you do not mind, I will add the information to you post. (In general it is a good practice, that a question should contain the source. In particular, if you keep referring in your post to things like Proposition 2.7.9.

usukidoll

and this is why I prefer differential equations over this ROFL

uh huh

damn this sucks with a show off professor. no one is passing really everyone failed the 2 midterms

lol everyone will fail the final

and just give mercy grades of C to make us feel better.. . -__--

I don't wanna learn like this! I swear my uni has less quality control than my community college

my entire calc iv was like that. everyone failing the homework, midterms, and final, yet everyone got C's. So yeah you can do whatever like not show up for class and you can pass.. super sarcasm

Sawarnik

mathoverflow.net/questions/164473/… Interesting :D

Martin Sleziak

I prefer to post links in chat like this: Have you solved problems in your sleep? at MathOverflow.

Sawarnik

10:22

@MartinSleziak How do you do it?

Martin Sleziak

@Sawarnik Have a look here to see the source.

Sawarnik

@MartinSleziak Oh! Nice.

Martin Sleziak

For each chat message you have arrow icon on the left, where you can click on reply to this message, or permalink or on history.

If you choose history, you will see the source code of the message. (And of all revisions, if it was edited.)

Sawarnik

Yes, I see.

Martin Sleziak

You can find much more about various ways how to format links in markdown help. But most of that is about post - AFAIK only this version works in comments and in chat.

usukidoll

10:39

:( I wish I had a better professor who taught the most important course in the universe

user127001

12:15

What course again

Awal Garg

0

Q: Does a dot or period (.) get italicized or capitalized?

When we italicize text with the dot (.) or period symbol, does it actually change the (.). So, is . different from . Can anyone tell which of them is italicized? And same way for capitalization. . different from . Does it matters? P.S. I am not sure if I should ask this here, ...

font

user127001

2 hours later...

Awal Garg

this is important for math people

skullpatrol

says who

user127001

Font

Karl Kronenfeld

12:17

, ,

Sawarnik

12:31

@AwalGarg I think no.

skullpatrol

. normal . italicized

Karl Kronenfeld

@AwalGarg serious business

Hawk

@robjohn are you here? I need your help...

ccorn

@skullpatrol Indeed, in font families with square dots, the italic font has a slanted square dot

skullpatrol

@ccorn I am of the opinion that a point has no size.

ccorn

12:38

@skullpatrol What's your opinion about periods?

skullpatrol

same, they are full stops

Awal Garg

did someone ping me?

skullpatrol

5 mins ago, by Karl Kronenfeld

@AwalGarg serious business

Awal Garg

@Sawarnik what do you think is no?

@skullpatrol yeah, i see that now.

ccorn

@skullpatrol I'd rather go with Einstein. If a dot can stop something, it must have size, otherwise it would be a singularity.

2

Sawarnik

12:40

@AwalGarg That . gets italicized and ...

Awal Garg

@Sawarnik oh.

Sawarnik

@Hawk HELLO!

Hawk

@Sawarnik helo helo!

Awal Garg

@Sawarnik actually, it gets. zoom in like 200% and you will see

Sawarnik

@AwalGarg orly. let me check.

skullpatrol

12:42

@ccorn I only like a few of his quotes and that is not one of them.

Awal Garg

@skullpatrol If I was wrong, one was enough?

ccorn

@skullpatrol Agreed, but still suited for application to italicised dots :-)

skullpatrol

:D

Awal Garg

oh yes, a colon also applies to that question, isn't it?

skullpatrol

yes, and a semicolon

Sawarnik

12:45

@skullpatrol no, i think.

Karl Kronenfeld

Certainly a colon gets italicized.

Awal Garg

@Sawarnik did u see the difference?

@KarlKronenfeld but its made of two periods

Sawarnik

@AwalGarg wait, i m bit overloaded now, so sometime later..

Karl Kronenfeld

@AwalGarg yes, I really like your idea

skullpatrol

but they are aligned

:

Awal Garg

12:47

@KarlKronenfeld i think, it would be easier to see the effect in a colon because the hinge point of slanting the character is farther away from one of the dots

@skullpatrol yeah, thats what I mean

Karl Kronenfeld

@AwalGarg yep

Awal Garg

But, I wonder, do the individual dots also tilt...

ccorn

@AwalGarg: While we are at it: Does a space character get italicised? IMHO spaces are not rendered as glyphs...

Awal Garg

@ccorn It specifically does not matter...

ok wait, it does...

Hawk

@skullpatrol two dots are always aligned, aren't they?

skullpatrol

12:50

@Hawk vertically

Karl Kronenfeld

@AwalGarg If nothing else, it gives us the measure of the angle at which the dot would tilt.

Awal Garg

if the character after the space is not italicized, then it would matter

Hawk

@skullpatrol does the direction actually matter?

Awal Garg

@KarlKronenfeld i knew it would be mathematical.

ccorn

@AwalGarg You are thinking of the space character as a white box I suppose?

Awal Garg

12:51

@ccorn yeah... umm, you make a point

it might be a horizontal line

skullpatrol

@Hawk on a page, yes

Awal Garg

ok, underscore _ applies to the question as well

Hawk

@skullpatrol how? they are afterall two dots, you can always join 2 dots with a straight line...

skullpatrol

_

Awal Garg

that as well is a horizontal line

ccorn

12:52

Next detail: In serifed italic fonts, are the serifs slanted?

skullpatrol

_

Awal Garg

_ ___

i_i (i am trying to italicize _)

skullpatrol

3 mins ago, by Karl Kronenfeld

@AwalGarg If nothing else, it gives us the measure of the angle at which the dot would tilt.

Awal Garg

actually, a dot should be an ideal circle...

but, we don't come across ideal things

ccorn

@AwalGarg Actually, a dot should ideally blend in with the surrounding text...

Awal Garg

12:54

@ccorn why?

skullpatrol

17 mins ago, by skullpatrol

@ccorn I am of the opinion that a point has no size.

ccorn

s/blend/fit/

Awal Garg

@skullpatrol everything is made of points, so, everything is of no size?

skullpatrol

no

Awal Garg

@skullpatrol you are contradicting your own point now

btw, anyone here knowing PHP?

skullpatrol

12:57

no

ccorn

@AwalGarg no

Awal Garg

@skullpatrol explain

ccorn

@AwalGarg Fortunately not. I am versed in Perl however.

Karl Kronenfeld

@AwalGarg we can pretend, as long as you don't post a wall of code

I also know some perl

Awal Garg

@KarlKronenfeld @ccorn do you happen to know about - Object of class mysqli_result could not be converted to string

ccorn

12:59

@AwalGarg dunno, but SQL results should probably be arrays

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$Mathematics$ Mathematics