It's just sending a message as the constant term in a polynomial, and you distribute coordinate pairs to different people, and then if ever they need to reconstruct the polynomial, you need a certain number of them, from which you can interpolate.
I'm incapable of explaining anything, but in any event, it's just Lagrange interpolation over a finite field, and I know the only way you can have a field is with a prime modulo, but I don't understand why we must have inverse. I know it's helpful, but it doesn't seem necessary. But I don't think I was very clear. I'mma just surf google.
I've got a quick question on some notation I've not seen before, and how I'd plot the set of points on the $x-y$ plane. $ \{ (x,y) : x \in [ 1, 2 ], y \in [ 1, 2 ] \}$ Would this just be a square that I'd need to shade in, in the $x-y$ plane?
@Anthony Find me the proof that your algorithm works. I assume there's a proof somewhere. Once you see it, we can work backwards to see why we can't do it over $\Bbb Z$.
I don't care about $\mathbb Z$ I think they do that because we're working with computers, and we want things to be uniformly random. I just was wondering why we can't do it modulo a composite number.
@BalarkaSen Oh hold on. If say, our inequalities for $x$ and $y$ were strict as opposed to not strict, would I need to draw a dotted line on the vertices of the square, to show that $x \neq 1,2$ and $y \neq 1,2$, instead?
I happened to see a video about [Imagining 10th Dimension][1]. In that (17:03m) he say that Zero contains every possible values by referring to an author [GEVIN GIORBRAN][2] . It goes like this.
- 1+(-1)=0 - 2+(-2)=0 - 3+(-3)=0 - **∞+(-∞) = 0**
Considering Zero as the set containing -∞ and +∞, it can be the largest possible value. Any other values is simply the absence of the same negative value.
So 1 is the absence of (-1) from the whole set and so on. When put together will come to the conclusion that 1>2>3... which make no scene.
Yes. Later in the video this theory was mixed with matter and anti mater. Do you suggest asking this questiion in physics.sx ? Or is this just bullshit?
Well, in fact, if you are in $\Bbb Z$, not only $0$ but $1$ is also the largest element. $1 = -1 + 2 = -2 + 3 = -3 + 4 = \cdots$ so $1$ "contains" all elements too.
@BalarkaSen N contain everything below it can be true?
according to him it was like this .. If set a+b= c . we can say that c contain a and b. similarly inf+(-inf)=0 implys zero contain -inf and +inf. so making it the largest. ..
Well, there's certainly more than a little bit of Galois theory. But right now I'm not sure what your comparison is. Analogues of Galois theory that I know say "this thing is like groups; this subthing is like subgroups; this special subthing is like normal subgroups"
Say, covering space theory, or Galois theory itself.
If you want to mimick the fundamental theorem you've gotta find what characteristic subgroups correspond to.
Last time you were messing with this you were looking at extending that exact sequence, which is still something you can try to do, but that might involve learning more category theory/homological algebra than you want right now.
I don't get it. I am not a mathematician or a physicist. I am just a programmer. This is what I understood. I am not saying that what I say is right. I am just asking you to prove this wrong so that I can go sleep well..
rather than saying this is bullshit (which i agree) just prove that it is not possible.. that zero can never be the largest number and that logic which he said is wrong.
@BalarkaSen No, not really. But it seems like it's something you want to keep pursuing, and it could be a fun project. Trying to do some math instead of just learning it.
Rather: I don't know if there's more than meets the eye, and I don't plan to find out, I've got tests to study for :P
Can anybody help me out with sketching this set of points on the $x-y$ plane? $\{ (x, x+y) : x \in \mathbb{R}, y \in \mathbb{Z} \}$ I think that set of points describes the entire $x-y$ plane. Can anybody verify that?
I think I'm misinterpreting what the set is trying to describe. Would I be right in saying that in words, it'd read: "The set of all points of the form $(x, x+y)$ such that $x$ is real and $y$ is an integer"?
@TedShifrin I think I see what you mean. Lets say we were working with a set of coordinates in the complex plane. How would you then denote the set of all points of the form $(x,iy)$? So just like for the Cartesian plane, you'd say $(x,y) \in \mathbb{R}^2$, what would you write down for the complex plane?
Sorry for the late reply, but why would it be $\mathbb{C}^2$ as opposed to $\mathbb{C}$? I thought $\mathbb{C}$ was the set of all complex numbers of the form $x+yi$, where $x,y \in \mathbb{R}$ i.e. I thought that $\mathbb{C}$ could be represented on an Argand diagram which is analogous to the Cartesian plane.
Is that how it's written or have you forgotten parentheses etc.? If it's the former, note that BIDMAS is the order in which you must do the operations.
(Brackets, indices, division, multiplication, addition and finally subtraction.)
