Sal Rahman

general recent conversations

$Mathematics$ Mathematics

Associated with Math.SE; for both general discussion & math qu...

Sal Rahman

Nov 11, 2024 14:58

Let's say someone has had a curve of the form $y - ax - b = 0$. I can immediately know what $a$ and $b$ are if they gave me two points on the curve.

Sal Rahman

Nov 11, 2024 14:57

@Jakobian yep

Sal Rahman

Nov 11, 2024 08:22

I could almost swear, that the only way to guarantee that everyone can agree what a specific line that someone is thinking of, all that someone needs to give is two points on the line, and everyone else can infer the line from those two points alone. But what about other curves? Is there a generic formula to determine what are the exact number of points needed to guarantee that all points lie on that curve? I'm talking about polynomials, by the ways.

Sal Rahman

Sep 14, 2024 23:17

And if $p = q$ on all points, then that means that the polynomials are exactly equal.

Sal Rahman

Sep 14, 2024 23:16

@Jakobian I don't think I am understanding your question. Probably because I always that thought it's not necessary that $p = q$ for all points, but there are points where $p = q$, and the total number of points where they are equal is not exceeding the product of their degrees, by Bézout's theorem.

Sal Rahman

Sep 14, 2024 21:40

@Joe Yeah, $x$ and $y$.

Sal Rahman

Sep 14, 2024 21:31

@Joe yeah, that sounds right

Sal Rahman

Sep 14, 2024 21:31

@BenSteffan The Cayley-Bacharach theorem wouldn't work had two cubics not been capable of intersecting at 9 points.

Sal Rahman

Sep 14, 2024 21:29

@BenSteffan I always thought that by Bézout's theorem, a degree $m$ polynomial will intersect with a degree $n$ polynomial through at most $mn$ points.

Sal Rahman

Sep 14, 2024 21:26

Rephrasing what I said: is it generally true that if two $m$-degree polynomials intersect at $m^2$ specific points, then a third $m$-degree polynomial that passes through $m^2-1$ points, then it must pass through the $m^2$th point as well?

Sal Rahman

Sep 14, 2024 21:25

@Joe yes! Thanks for pointing that out.

Sal Rahman

Sep 14, 2024 21:23

Is it generally true that if two $m$-degree polynomials intersect at $m^2$ specific points, then a third $m$-degree polynomial that passes through $m^2-1$ points, then it must pass through the $m$th point as well?

Sal Rahman

Jul 10, 2023 06:44

Outside of math, there is a concept of "solutions existing in search of a problem".

That idiom is often a pejorative. But I don't think that that it necessarily is a pejorative. I find that a lot of math theorems were discovered because someone was bored, and not necessarily trying to solve a real world problem. But ironically, some ideas are rediscovered and used in the real world, even if the person who originally discovered it may not have intended their theorem to ever be used.

Thoughts?

Sal Rahman

Jan 26, 2023 03:15

@TedShifrin $(1 + \dfrac{1}{n})^n < (1 + \dfrac{1}{n})^{n+1}$

Sal Rahman

Jan 26, 2023 03:10

I feel it should be obvious, but I am open to do the idea that there exists a function $f:\mathbb{R}\rightarrow\mathbb{R}$ where that is generally not true

Sal Rahman

Jan 26, 2023 03:07

(for $f(x) \neq 0$)

Sal Rahman

Jan 26, 2023 03:06

Is it generally true that if $f(x)^n < f(x)^{n+1}$, then $1 < f(x)$?

Sal

Nov 17, 2020 18:29

Another one of my dumb questions.

Is the expression $\lim_{x\to+\infty} \dfrac{1}{x} = 0$ just a postulate, or is there a proof for it?

Sal

Nov 14, 2020 03:13

Is there a proof that I can look up that shows that $\sum_{n=1}^\infty = \dfrac{x}{1-x}$?

Sal

Nov 14, 2020 03:11

Perhaps.

I'm just not familiar with infinite sums. All I know is that a similar expression $\sum_{n=1}^\infty \dfrac{1}{2^n}$ is just $1$.

Sal

Nov 14, 2020 03:08

I'm pretty sure it converges to some value, but can that general value be expressed as anything other than an infinite sum?

Sal

Nov 14, 2020 03:07

What's the general behaviour of $\sum_{n=1}^\infty x^n$ for $0 < x < 1$?

Sal

Nov 6, 2020 07:21

Thanks!

Sal

Nov 6, 2020 07:20

Dumb question: is this true? $$\sum_{n=1}^{\infty}f(n) = \lim_{N\to\infty}\sum_{n=1}^{N}f(n)$$

Sal

Oct 20, 2020 18:25

Thanks!

Sal

Oct 20, 2020 18:24

What does the vertical bar mean in a lot of maths that I see?

It typically looks like this: $f(x)\vert_0^\infty$

Salehen Rahman

May 5, 2018 22:05

Is my assessment correct, or incorrect?

Salehen Rahman

May 5, 2018 22:04

I just gave some thought to it.

I think this is how the probabilities should be distributed within the set:

Each element has a bias; the probability that an element is picked is predicated by its bias divided by the sum of all biases.

Salehen Rahman

May 5, 2018 22:00

The sum of the probabilities should remain the same.

Salehen Rahman

May 5, 2018 21:59

The probability distribution should (I think) be determined by 1) the number of elements, and 2) the bias assigned to each element.

Salehen Rahman

May 5, 2018 21:57

For the lack of a better word, the "bias" will remain the same.

Salehen Rahman

May 5, 2018 21:57

Each element is independent from one-another.

Salehen Rahman

May 5, 2018 21:43

Let's say we have a set, and each element of the set has a probability attached that determines how likely is it that it will be picked, if we are to randomly sample from the set.

Let's say, we are to permanently remove one or more elements from the set, what happens to the probability distribution of the set?

My intuition would claim that we should just normalize the probabilities.

Thoughts?

Salehen Rahman

Jul 11, 2017 01:53

@AkivaWeinberger thanks!

Salehen Rahman

Jul 11, 2017 01:52

It's been a long time since I had last touched linear algebra, but for any matrices, $A$, $B$, and $C$, such that $A \cdot B \cdot C$ is defined, is $A \cdot (B \cdot C)$ also defined?

Salehen Rahman

Mar 31, 2017 05:17

I completely forgot my algebra.

I have two bottles. One bottle has an unlimited amount of a solution of $70$% isopropyl alcohol (IPA) & $30$% water, and another with an unlimited amount of just water. If I wanted a liquid solution of some finite amount, how much of each should I mix to get a mixture of $60$% IPA and $40$% water?

I could have extracted the IPA from the 7:3 IPA & water solution, but that's not as easy as doing some math. However, I completely forgot on how exactly I can solve this.

Salehen Rahman

Jan 21, 2017 21:13

@Tobias, right, thanks!

Salehen Rahman

Jan 21, 2017 21:12

@TobiasKildetoft Thanks! Where can I read more about this?

English Language & Usage: Multi-Layer…

Not for the faint of heart or those easily triggered by Englis...

Sal Rahman

Apr 25, 2021 18:46

Funnily enough, I was reminded of a word "pronoia". I did not find that in a thesaurus.

So I look up "pronoid". That word exists. Haha.

Sal Rahman

Apr 25, 2021 18:37

What would go in the blank?

Sal Rahman

Apr 25, 2021 18:35

"A cynic will bemoan people's self-interest"

"A ____ will believe in people's good intentions"

Sal Rahman

Apr 25, 2021 18:21

> Is there a word for someone who is "naively generous"?
>
> The closest word that I can think of is "simp", but that only applies to someone who has a romantic interest in someone else.
>
> What would be a better word?

For context, I'm trying to find a word that is polar opposite of someone who people would describe to be "cynical"; that is someone who strongly believes that there is no "good in people's hearts", and that "everyone is out to look for themselves," and that the only way that the world works is that "everyone works for their own self-interest, otherwise nothing would get done."

Sal Rahman

Apr 25, 2021 18:05

Is there a word for someone who is "naively generous"?

The closest word that I can think of is "simp", but that only applies to someone who has a romantic interest in someone else.

What would be a better word?

The DMZ

A serious place where infosec is discussed PS we don't do hard...

Sal

Sep 23, 2020 05:12

Erm… for the above question, flip the word "private" for "public", and vice versa.

Sal

Sep 23, 2020 05:07

Challenge that I'm faced with when doing client-side verification:

how do I update the private key, if the public key needs to change? If I hard code the private key, then I will need to deploy a new JavaScript bundle.

If I have the private key be downloaded from the server, then I can't help but feel that I may as well have the token verification be done on the server anyways.

Sal

Sep 23, 2020 05:04

Challenges that I'm faced with when doing server-side verification:

the client will have to _always_ issue an AJAX request to have the token verified (server-side verification is almost trivial, so let's discount this as a potential challenge).

Sal

Sep 23, 2020 05:02

If I were perfectly honest: I want to do client side, because I've spent enough time trying to figure out on how to get client-side verification working, that the sunk cost effect is really getting to me.

Sal

Sep 23, 2020 05:01

OK, I have my own biases, and I need some outside opinion on this.

I have a p2p application, and I'm torn between having signed messages be verified either application-side or server-side.

The token signing happens on the server.

Now I'm wondering where should verification happen: application side, or server side?

Salehen Rahman

Feb 22, 2017 02:01

I apologize if the above question is not a good fit for this chat room. Given how "The DMZ" is essentially a chat room for security.se, and also, assuming by the name, I would imagine that we are almost free to talk about anything, so long it falls within the realm of security.

Salehen Rahman

Feb 22, 2017 01:55

Has anyone here watched a film/tv show/news media recently that got you cringing/facepalming really hard for negatively portraying the use of encryption? I'm trying to look for a topic for an academic paper. The topic should be about "how the media shapes the morality of ______."