/sqt/: Stupid Questions Thread

>How does x=0 make the simplified expression undefined?
it's undefined because if you want to evaluate it, you would have to divide 9*0^2 by (9*0^2)*(4*0+3), which is dividing 0 by 0.

>Also, if I have that sort of fraction and I simplify and for the simplified form x=0 is not undefined, but for the not-simplified form it is, does that mean that the function is undefined at x=0 or not?

it is undefined at x=0.
however you can do something called a continuous prolongation, which means taking the limit of a continuous function at the points where it is not defined (such as x=0 here). The limit when x goes to 0 is obviously 1/3. You can define a new function that is exactly equal to this one everywhere except for x=0, and associate a coherent value at x=0 to make that function continuous.

>it's undefined because if you want to evaluate it, you would have to divide 9*0^2 by (9*0^2)*(4*0+3), which is dividing 0 by 0.
Wait a second, isn't the simplified one the on on the right side?

>it is undefined at x=0.
Maybe the last part of your post answers this but just to make sure... If I get 2 functions
[eqn]fx)=\frac{1}{4x+3} \\ g(x) = \frac{9x^2}{9x^2(4x+3)}[/eqn]

Then those 2 functions do NOT have the same domain even if they seem to be equivalent (to me)? Because g(x) is undefined at 0 and f(x) is not

I guess this sort of kinda makes sense to me

Thanks for that, might have saved my sanity.

>multiplication is more intuitive than division
>addition is more intuitive than subtraction
>mx+c can be written on only one line and with no brackets
>mx+c cannot be accidentally written ambiguously, unlike y-b/m
>mx+c immediately tells you the gradient and y-intercept which means you can picture the line instantly, as opposed to third options like ax+by+c=0
>having a convention is a good idea, outside any concerns over which convention would be best

>y-b/m is ambiguous
Maybe you should revise order of operations this summer vacation user

oh never mind

the simplified expression is well defined, BUT it's not equal to the unsimplified one for x=0.

and yes, f and g do not have the same domain. but they take the same values on the intersection of their domains.

Maybe you need to focus on reading comprehension instead of looking for reasons to be a smug cunt. When somebody is scribbling down workings, situations like pic related will inevitably happen.

>being this butthurt
lel i was fucking with you bud

Shit man you sure got me gud how will my epeen ever recover

chill sometime

this. y=f(x) can in most cases not be solved for x. (only if f is injective)

Is there a program that will show you a Bloch sphere representation of a qubit in ket form? Right now I need to know what

[eqn]\frac{1}{\sqrt2}\left(\left|0\right\rangle-|1\rangle\right)[/eqn]

looks like, but I'll probably want to visualise other stuff later on.

Also thanks to the various anons who've been slowly teaching me QC over successive sqt threads.

you might need to code a script yourself.
In fact I would argue that coding something like that would teach you more (by making sure you understand everything) than using a premade program.

(this is the only contribution I can give since I don't know of any such program)

Fuck, you're probably right.

Carrying over my question. Can someone link me to or explain to me how to find a specific digit of pi in laymans.

I think there's a formula for base 16, not sure there is one for base 10. (Which is kind of a random base)

f being injective is nowhere near enough

Does anything change if the Schrödinger Equation for electrons in a potential is viewed in more than three dimensions?

How and why is the span of the kern of [math]\begin{bmatrix}
0&1&0\\
0&0&0\\
0&1&0\\
\end{bmatrix}[/math] equal to [math]\begin{bmatrix}
1\\
0\\
1\\
\end{bmatrix} and \begin{bmatrix}
-1\\
0\\
0\\
\end{bmatrix}[/math] ?

why are asians and indians so prominent in medicine and biology fields

Look at the definition of the kernel. Act on a generic element with that matrix and find out how many free parameters there are in the kernel. Then you'll see that these two basis vectors span the same space

Hello friends, is it safe to assume that you always pool the standard deviations of two sample populations when the sample sizes are small (n

They work their asses off in school since the ones that get to go to school know their chance dont waste their time and go into high paying fields that also allow them to work abroad, specifically the US.

Sorry but that just doesn't cut it, would you care to elaborate or rephrase what you just wrote? What does it mean to "act on a generic element with the matrix" and what are "free parameters in the kernel" ?

If I want to compare 2 algorithms that perform on around 50 data points and I have the mean absolute error for both -- how do I calculate if the difference between them is significant?

it's not

it's actually [1, 0, 0] and [0, 0, 1]

...
anything that is linearily independent with a 0 as the second coordinate is valid.

Those span the same set.

Is math.stackexchange the best site for menial math questions?

how do you find the exact value of the critical point of the gamma function?

no closed form

I'm taking a modern algebra course but unfortunately haven't had any number theory. Our text lays out some results of the latter that we'll need when working with groups, but doesn't go into why they are true.

In particular, why is the product of the the GCD and LCM of two numbers equal to the product of the two numbers? Is there any way to visualize this or get some intuition? I imagine it has something to do with the prime factorization of the two numbers (a concept of which I am only familiar with the definition).

let a and b be your two numbers, G their gcd, and L their LCM.

a=G*a'
b=G*b', where a' and b' are coprime.
G=a/a' = b/b'

prove that L=a*b' = b*a'

you really should get used to proving this stuff on your own user, it will help you greatly.

Come back to ask questions if you get stuck.

write down the prime factorizations.
the gcd has prime factorization with the minimum of the exponents of the numbers, lcm same but with the max.
the product then has min+max.
Please note that min(a,b)+max(a,b)=a+b

of course this only works in unique factorization domains

I'm a boring CS guy so cool math things are way beyond my game, but I saw that 1+2+3+4+...=infinity thing and it got me thinking. Say you have a sphere with a volume of 1 m^2. Then you put another sphere around that one, with a volume of 1+2 m^2. You put another one around that with a volume of 1+2+3 m^2. If you could keep doing this to infinity, would it not mean that the "infinity-ith" sphere would have a volume of -1/12, and therefore space in our universe must be finite since a negative volume can't exist? I'm sure this and similar things much more complicated than it have already been thought of, and I'm pretty sure there's still no consensus on the universe being infinite or not, so I'm wondering why this math magic is wrong more than anything else.

[eqn]
a=p_1^{\alpha_1}p_2^{\alpha_2}...p_k^{\alpha_k}
\\
b=p_1^{\beta_1}p_2^{\beta_2}...p_k^{\beta_k}
\\
GCD(a,b)=p_1^{min(\alpha_1, \beta_1)}p_2^{min(\alpha_2, \beta_2)}...p_k^{min(\alpha_k, \beta_k)}
\\
LCM(a,b)=p_1^{max(\alpha_1, \beta_1)}p_2^{max(\alpha_2, \beta_2)}...p_k^{max(\alpha_k, \beta_k)}
\\
GCD(a, b)*LCM(a, b)=p_1^{min(\alpha_1, \beta_1)+max(\alpha_1, \beta_1)}p_2^{min(\alpha_2, \beta_2)+max(\alpha_2, \beta_2)}...p_k^{min(\alpha_k, \beta_k)+max(\alpha_k, \beta_k)}=ab
[/eqn]

A volume of -1/12 m^2, that is, not that the unit of measurement matters much.

no

No. Volume is defined to always be non-negative. The whole -1/12 shit is retarded. In your volume stuff if I understood correctly the difference between consecutive radius goes to 0 when the number of spheres goes to infinity, but I'm not sure what you meant.

buh

That's my point - because the volume of the spheres should go to -1/12 if space in the universe is infinite, space in the universe can't be infinite. The whole thing seems silly, which is why I'm asking why it's silly.

the 1+2+3+...=infinity thing is silly.

We're talking about Euclidean geometry. Planes are infinite by axiom, so are lines, space, etc. So you're not taking any practical considerations into account.

Oh, shit, I'm a dummy. In my original post I meant to write 1+2+3+4+...=-1/12 if "..." goes to infinity. Yeah, my bad, without that my post makes no sense.

uhm, yeah, it kind of is.

>I meant to write 1+2+3+4+...=-1/12 if "..." goes to infinity
thats stupid. the partial sums diverge, there is no limit

and unless you know how to analytically continue the zeta function to -1, I recommend you never again write 1+2+...=-1/12, it makes you look like an idiot

Actually I caught what you meant but made a typo lol. Meant to say "1+2+3+...=-1/12 is silly". Don't put too much stock in it.

I've read into it a bit more than just the youtube videos and stuff, and I'm just curious as to why it doesn't apply like that. I don't know why it makes me look like an idiot to ask questions about math shit, other than this being Veeky Forums where everyone is an idiot but the posting user.

If I mix 1 oz of PH 3 liquid with 3 oz of PH 7 liquid, what will the result be? I said 4 oz of PH 10 liquid but my professor said to go back and do the reading, I can't find out how to do this properly though.

Are humans a solid, liquid, or gas?

use concentrations of H3O+.

-1/12 is a meme you dip

You fundamentally don't understand what pH means. Seriously, go back and do the reading.

This. Calculate oxonium concentrations using [math]Log[H_{3}O^{+}]^{2}=pH[/math] and work from there.
Remember, pH is just a convenient way of looking at oxonium concentration.

This. Calculate oxonium concentrations using [math]-Log[H_{3}O^{+}]=pH[/math] and work from there.
Remember, pH is just a convenient way of looking at oxonium concentration.

If you take a normal food and turn it into a liquid shake do you pee it out or poop it out?

bump, still no answer

What if f never hits y? Then there is no solution. Also the only injective polynomials are linear polynomials, and they certainly aren't the only ones with solutions (non unique solutions, but still).

you can't solve for y if there is no y to solve for.

you really need to understand what a matrix is user
if u1 u2 u3 are your basis vectors, the first column of the matrix is the image of u1, the second column is the image of u2 etc.

the image of u1 is 0, so u1 is in the ker.
the image of u3 is 0 so u3 is also in it.
the image of u2 is not 0, so u2 is not in the kernel.
so any linear combination of u1 and u3 is in the kernel.

That's the point. y=f(x) cannot always be solved for x if f is not surjective. Injectivity is not even what matters here.

What are my options for grad school if I major ECE + CS?

it is.
a function cannot map to two value at the same time.
go back to fucking middle school m8

>oz
lmao you fucking cucks never fail to amuse me

This board is too fucking much sometimes.

Aight;
so polymeres are created by fixing two different monomers, each with their own functional groups. Each monomer has one of said group at each end of the molecule, which makes it possible to keep on making the polymere-chain longer.

Feel me? Right? K, so how do you stop the polymerisation?

I'm currently gonna transfer to a state university in the fall for computer engineering. I was thinking of getting into a trade while going to school. What's a good trade that you guys recommend as I study at a university? Hopefully a trade that won't take too long to learn and isn't expensive. I live in southern california if that makes a difference on trades.

I know that the order of an electric circuit equals the order of the DE that describes its behavior, and the natural response is the solution to the homogeneous DE, while the forced response is the solution to the inhomogeneous DE, but how can I identify which solution is which given only the total solution, and do I know the order of the circuits given the transfer function? I was only told that the forced response 'looks like' the excitation/forcing function, but how much does it have to look like?

Somewhere today I read that the natural response goes to zero as t->inf, is this always true? I've also read that solutions obtained from the transfer function poles are the natural response, what justifies this? And how is the order of a circuit related with the transfer function?

So i'm particularily interested in physics and chemistry (that includes biochem) and maybe even math. I want to study something were new breakthroughs for the future should be made. I that feel that advanced physics like quantum physics is maybe a bit too early for us to focus on, and that maybe we should take care of human problems first instead. Like cures and enhancements.

What's your opinion? Do you know of any studies that are currently undergoing rapid growth?

Where (in which book) can I read about (Riemannian..?) metrics induced by kinetic energy and what do I need to know to actually understand what that means?

How can I memorize the name/term/appearance of +150 structures on +150 preparations before Thursday?

>pic related
is vagina parts

Hello Veeky Forums
I'm sure this is incredibly stupid, but whatever.

Say you have two electromagnetic waves traveling down two wave guides that then combine at some point, what the hell do they make?

Do they overlap? combine? interfere with each other and bounce around like crazy?

What if they are...
Roughly the same wave?
Same wave length but different energy?
Two completely different waves?

This is all black magic to me but I'm just trying to get a general idea.

>trying to do physics without mathematics

this will amount to nothing. The result could be anything.

Ok, say two radio waves
>A: 20 MHz
>B: 30 MHz

You have to immerse yourself in it, like learning a language.

>immerse yourself in vagina

10/10 advice

you're such a colossal fagot I dont know whether I should even attempt to explain to you why you're so goddamn fuckings stupid.

here it is: if a function F is injective, then every value F(x) is uniquely identified by x, therefore you can solve y=F(x) for x.
You dont need surjectivity for that you humongous turd.

Here's an example: F going from the integers to the integers defined via F(n) = 2n.
This is injective, given some number 2n, I can always solve this for n
F is obviously not surjective, and it fucking doesnt have to be, you cocksucking middle schooler.
a left inverse G(x) would be given by G(x)=x/2. Note that this is not a right inverse of F, as G only maps even integers to integers.
(For F to also have a right inverse, it would need to be surjective. But to solve y=F(x) for x we only need a left-inverse.)

now kindly die in a fire

I can solve x^2+1=1 for x over the reals, uniquely even. I can't solve x^2+1=0.

... your point being?

>I can't solve x^2+1=0.
then try harder

quadratic polynomials are neither injective nor surjective over the reals.
your an retard

Got given a copy of pic related by my university today, to read over the summer before second year starts. Never really made notes from a book before (always used lecture slides/notes backed up with online material), what's the most efficient way to take notes from a book?

Also does anybody have experience with the book, how is it?

you won't need notes, you've got the book.
If you actually understand what's inside and are able to use it on examples, you will easily be able to find the information you're looking for in the book. Even years after.

For math, I summarize the chapters into important concepts with just enough information to refer to when solving problems. I also reword and use external knowledge from other math that feels relevant. Pretend you are summarizing for someone who knows the same things you do. That simple act goes a long way into solidifying the concepts. As for its actual utility, it's nice to end up with one or two pages to have by your side while doing homework and working on committing these concepts to memory.

I probably won't need it years after, they only gave it us for summer reading. We'll probably get a full course textbook like we did this year

You may want to check out the inverse function theorem.

keep going

Why did animals evolve from being hermaphrodite to being dioecious/separated sexes? What is the advantage in this?

It's easily searchable but here you go.