Mathematics

11:47 AM

[Random]

Update notation to :O:

$\underbrace{[...]}_{n} := [...]_n$

Therefore:

Let _ be the empty list

The sequence goes as follows:

_

$[0]_0$

$[0,1,2,...,n]_n$

$[0,1,2,..._{\text{Huge}}$

$[0,1,2,...]_{\omega}$

For a foundation where ordinals are defined:

$[0,1,2,...,\alpha]_{\alpha+1}$

$[0,1,2,...]_{\lambda}$

where $\lambda$ is a limit ordinal and $\alpha$ is any ordinal

Continue:

$[0,1,2,...]_m$

In general $[0,1,2,...]$ is a countable unbounded list. The subscript gives a notion on its "size" in terms of how many steps is needed before an entry arbitrary large is reached. In other words, the subscript gives a measure on how many steps before it effectively becomes something similar to a proper class in set theory

12:25 PM

Of course not intended for anyone, but some guy needs to stop posting crackpot theories related to set theory in Mathematics chatroom.

2

I never said what I said is true. The above is more like a brainstorming process than an actual theory, thus it is not even wrong

Everybody in this chatroom knew what I wrote is legitimate and what is nonsensical rambles

otherwise why would I use a [random]

I never said my comment was intended to anyone. Also, I don't think anybody reads what someone writes. (Again not indended towards anyone)

Of course, whether all of the above "response" is visible to any of you and whether any of you care is not my concern. As long The Plan remains unhindered, those who choose does not have not have a choice

(To the whole chatroom) I "respond" because I know what I wrote is nonsense and you guys knew it, as long you know when I am sane and the flooding controls is intact, then it will be ok

Hello anyone know how can 1.052 x 12.504 x 0.53 = 6.7280 ? The result should be 6.9717 which is way higher. I've seen this same calculation in a lot of lectures and in the chemistry book but what the heck?

Anyway, as a cautionary measure, better to once again reiterate that anything that follows after [random] does not necessary have to make sense. This is because they only make sense after an interaction with the community

12:35 PM

Anyway, again not indended to anyone, this site is for generally discussing math, not crackpot theories and random thoughts which occurs to brain. Someone may open a new room for that. Of course, if getting people's attention is the actual motto, then opening a room and talking there would work ...

Traffic of a very narrow topic in a new room is too low to be of significance

but perhaps:

4 hours ago, by The Great Duck

stop wasting them away in chat threads nobody is gonna read

Can someone tell me please why it is 6.7280 is it a mistake? It's driving me insane :)

I should figure out how to make those stream of consciousness more coherent

@someone We need to know where the 3 numbers came from first. What quantities are they representing

@Secret So why don't try thought dumping in The Nineteenth byte ? A lot of people frequent that room, so I think it's a fantastic idea !

uh, do you think the stuff I am talking about is even remotely related to programming and coding puzzles?

12:39 PM

@Secret It is just an example given to show how to calculate the number of significant figures in multiplication e.g 6.7208 = 6.7 which takes the least number of significant figures (0.53)

not related to math too. That's the point

@Secret that's the exact snippet from the book i.imgur.com/HNrOre5.png

Yeah I think I agree with you: 1.052*12.504*0.53=6.97173024 which to 2 sig fig should be 7.0

It is probably a mistake but the exact numbers are mentioned way often even in practice questions and power point slides :) so weird

you might want to check with your instructor. I cannot think of any round up nor round down that can produce 6.7208

12:55 PM

The book is insanely inconsistent in the second example of multiplication they did not round but only count the significant figures, but in subtraction they did in one example and not in the other smh.

hmm $$ \int \int_D 1-6x^2y dA, \quad D=[0,2]\times [-1,1] $$

you want to convert that to a double integral?

yes thats right

i don't understand the notation

$$\int \int_{-1}^{1} \int_{0}^{2}1-6x^2ydxdy$$ ??

also $[0,2]$ denotes closed interval ?

is it $[x]\times[y]$ ?

$0\le x \le 2$ and $-1 \le y \le 1$ is this same ?

Yup, square commonly denote that edge of the interval is closed

So basically you are integrating this function over a rectangular region

@Tuki this explains it pretty well tutorial.math.lamar.edu/Classes/CalcIII/DoubleIntegrals.aspx see R=[a,b] x [c,d]

1:04 PM

yes this is exactly what i wanted thanks @someone

1:17 PM

Just like how reality cannot handle infinite entities, the point is the chat will be plunged into unusability, and this is more than enough for the adversories to achieve their goal.

3

Alex K Chen: Yeah fine, I will deal with the flooding problem more seriously, so as not to accidentally flood someone else's screen

(uh, accidentally caught balarka and co in the middle of my rambling. I need to time more carefully since the chemistry event means he and his group are to be avoided from getting involved in these rambles which sounds like anti-normie stuff)

point is, I ramble a lot less when the topology people are here now, thanks to them helping me to better grasps the subject so I can actually said something more sensible

I will soon figure out manifolds, and after that, GR will no longer be so unintuitive to me

IP Address

hi

I have question

How would I prove the sequence i,-1,-i,1 where the nth term is given by i^n

Would I use proof by mathematical induction?

Anderson Felipe Viveiros

1:35 PM

@IPAddress Just use that $i^{4n+k}=i^{4n}i^k=(i^4)^ni^k=1^ni^k=i^k$

How do I solve this homework-like question?

Let $V$ be a vector space with inner product $\langle \, ,\,\rangle$ over the field $\Bbb K$ ($\Bbb R$ or $\Bbb C$). Suppose that the linear operator $T:V\to V$ is NORMAL, (i.e. there exists $T^\ast$ adjoint operator of $T$ and $T\circ T^\ast=T^\ast\circ T$).

If $T(v)=\lambda v\neq 0$, $T(u)=\mu u\neq 0$ and $\lambda\neq \mu\in \Bbb K$, then prove that $\langle u,v\rangle =0$.

IP Address

@AndersonFelipeViveiros thanks

Anderson Felipe Viveiros

@ip

* @IPAddress You're welcome

2:19 PM

so this notation $$ \int \int_D f(x,y) dA \quad D=[a,b]\times[c,d]=\int_{-1}^{1}(\int_{0}^{2}f(x,y)dy)dx $$ ??

hmm is false and i cannot remove this

@Shobhit you there ?

Shobhit

yes, but i dont have much time, exam tommorow @Tuki