Mathematics - 2017-03-20 (page 5 of 5)

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Mary Star

23:08

@TedShifrin Ah ok!! Thank you!! :-)

SteamyRoot

Hmmm... Are there any magic tricks for determining whether some crazy function is actually rational?

Mary Star

If we have the vectors $\vec{u}, \vec{v}\in \mathbb{R}^2$. Do we consider them as line segments that start deom origin? Or from an arbitrary point?

Daminark

23:24

@Mary There are a few ways to look at them, when I noticed them in a physics context, they were more directed line segments, to emphasize that the information they carry in terms of magnitude and direction

Now I'm not really taking physics, I do analysis/linear algebra, and a vector registers more instinctively as a point

Mary Star

I want to describe the set of vectors $\vec{z}=\lambda \vec{u}+(1-\lambda )\vec{v}$.

So, do we consider the vectors $\vecu}$ and $\vec{v}$ as line segments from origin, and $\vec{z}$ are all the points on the line segment that connects the endpoints of the vectors $\vec{u}$ and $\vec{v}$ ? @Daminark

Daminark

Yup

For $\lambda$ between $0$ and $1$

You can get that by thinking about them as points as well

You let $\lambda$ run between $0$ and $1$, and trace which point you reach each time

Supposing you could do this uncountable process in, say, 23 seconds, you would find that this leads to tracing every point in the line segment between them

Mary Star

Ah ok. What is more convenient in calculus? Do we consider them mostly as points or as line segments?

Daminark

In single variable calculus you aren't really playing too much with vectors

It's all numerical anyway

(As in, functions $f:\mathbb{R}\to\mathbb{R}$)

Mary Star

Yes. What about two-variable calculus?

Daminark

23:39

In my experience, the primary advantages of looking at vectors as arrows come from either having them represent quantities where there is some sense of a duality of information

You have the length of a vector and its direction, so in subjects like physics, thinking about vectors as such will help

In math, though, you tend to not really be looking at vectors as representing things, they're merely the objects you're working with

The other advantage is visualization, which you lose in multi because you can't visualize more than 3 dimensions well

You often deal with functions mapping $\mathbb{R}^n$ to $\mathbb{R}^m$, sometimes you go even more general than that

At which point you're best off thinking about stuff as points

(You don't even really think of the functions as being of multiple variables, in my experience, more as functions mapping a point in one space to a point in another)

Mary Star

Ah ok!! Thank you!! :-)

Meow Mix

Hi @Dami

Daminark

How's it going @Meow?

Meow Mix

I'm hungry.

Daminark

23:54

Haha, well, hopefully you're gonna get to eat soon

Also hey @Adeek!

Meow Mix

I can't.

Adeek

Hey @Daminark @MeowMix

Daminark

Hey @Akiva!

Akiva Weinberger

Hi all

Meow Mix

I'm trying to lose weight.

Daminark

23:54

And I mean, it is nearly 8, so wouldn't you have dinner soon?

Oh, I see

Yeah it'll be real tough at first

Adeek

hi @AkivaWeinberger

how can I write an arrow above it is the map name ?

Meow Mix

Right now I'm ~40 kg

Adeek

that is $\rightarrow$ with a name of the map above it ?

Meow Mix

\overset{}{\rightarrow} $\overset{\text{test}}{\rightarrow}$

Adeek

okay cool

Meow Mix

23:57

If you want to TeX commutative diagrams, consider looking into TikzCD

Adeek

okay I remember I am using something fancy in my blog like TikzCD but I just need something simple for a commutative algebra question I want to ask.

Meow Mix

@Dami Target weight is <38kg

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