khaled

So, what books would be suggested for Mathematical Logic ..?

anyone ...

That is about the definition of the term "dimension". In your example, colour can be a dimension as well.

1D is a line, 2D is a plane, 3D is an object ...

and the 4th Dimension can be one of many things:

- Time

- Color

- Direction

- ...

If you are interested in physics you can consider every point (x,y,z) as an Atom

and the 4th dimension can consist many things related to Atoms in physics,

The structure can be applied in computer program to study physics of Particles ...

Also you can consider every point (x,y,z) as an Electron, and with giving the

required constraints for quantum mechanics, you can work on quantum

mechanics in visual ...

Best of luck,

are there general courses in Mathematics related to Mathematical Logic .. so that I can

look up courses that I can cross-attend in my university,

also, we share the same building with mathematics\science college,

so I can easily cross-attend ...

I think the fourth dimension is time, representation of a 3D object in the 4D space

would be either by using an Animation,

or by showing multiple copies of the object in 3D space where every copy has a Time tag,

I'm a bachelor-degree student, we studied Pre-Calculus, Calculus, Linear Algebra, Probability and Statistics, and Discrete Mathematics,

I can't ask the mathematics department to get a course,

and Yes, I'm asking for hints on a self-study on Mathematical Logic ...

I am a computer science student, interested in theoretical computer sciences ...

I have improved myself in Algorithms, and had a basic course in Discrete Mathematics,

My main interest lies in Mathematical Logic, and my question is

What do I need to get in order to improve myself in Mathematical Logic ..?

i heared it's possible, given an expression, we can embed pi fraction 22/7,

i know if you write (22/7)(double) in C it will return 3.14.. approximation

but if you embed the fraction in a dynamic expression in a function,

it will give more flexibility ...

like this,

first version:: given X: return (22/7) * (1/X) * 100,000,000

X=3 .. = 3.14159 / 3 = 1.04719666 * 100,000,000

.. = 104,719,666

2nd version:: given X: return 22/(7 * X) * 100,000,000

X=3 .. = 22 / 7*3 = 22/21 = 1.04761904 * 100,000,000

.. = 104,761,904

difference = 42,238

if this was a Money Transfer, 42,238$ is gone because of a miscalculation!

@hobz

im not expecting less iterations,

i am asking for a way to create a system for vectors,

the space is in [math]\mathbb{R}^2[/math],

can be then represented as a Matrix ...

i want to learn more about how can vectors help me maintaining

the matrix for example to do transformations, and renderring

objects in the 2D display ...

I have learned LaTeX because in my college i have to write reports and papers in LaTeX,

test:

[math]|x| = \{ \begin{matrix} \color{red}{-X}&\color{red}{if X<0}\\ \color{blue}{X}&\color{blue}{if X>0}\\ \end{matrix}[/math]

i just imagined a truck with the following written on its side,

Flying Hard-disk company !

,lol

1. the screen consist of PIXELS

2. consider screen as a matrix of m x n where each element is a PIXEL

3. in RGB color system, each PIXEL have a value consist of three components

... Red+Green+Blue where each component have a value from 0 to 255

MATRIX screen of size m x n:

| P1,1  P1,2   ....  P1,n |
| P2,1  P2,2   ....  P2,n |
|  .     ...           .  |
|  .       ...         .  |
| Pm,1  Pm,2   ....  Pm,n |

where, m x n = the screen resolution and 0 <= Px,y < 256

| algorithm (given x, y, c):

|

| 1. give the element Px,1 the value c

|

| 2. for every element from Px,2 to Px,y: Px,i = Px,i-1 +0.5

|

| 3. terminate

this method can create a linear gradient ...

now with any help from linear algebra mathematicians, we can improve general methods, to iterate through this matrix, with more unique mapping ...

.. waiting for replies, ideas, ...

what is the relation between the magnet we know [ N | W ]

and the inner core of the earth,

is it some kind of a special massive magnet,

or it works with different mechanism ..?

i don't know but,

files types have extension .xxx and its content start with a unique code [ CODE ... ]

now i get it ...

out of my study experience in computer science,

larger amounts of data = higher possible error %

He means a vehicle with lots of wheels and weighing a few tons. They're slower than electricity but can carry a lot.

i don't get it,

what have a truck with wheels to do with online gaming

.. and data transfer rate between Client & Server

So you can always find something very complicated that has quite simple origins.

Complex Geometry based on Euclid's Elements !

You mean the infinite square well!

that's the mathematical definition of "think out of the box" !

How can there be more chemicals than there are atoms in the universe if the chemicals are made out of atoms?

it's a simple mathematical induction,

if we say ,for example, that all atoms in the universe are K

then how many combination are possible ? answer = K!

K! > K

Sisyphus,

sorry, and i won't write my new thoughts in Replies again ...

or maybe im not good enough to be a scientist,

what do you mean by "the truck",

you mean the Package that holds data for transfer ?

if numbers would be real,

2.x + 2.x = 5.xx

2 + 2 ≈ 5

or if numbers have powers,

2^x + 2^y = 5 ..ex: 2^0 + 2^2 = 5

or that it is a false degoma,

2 + 2 = 5 (FALSE)

..etc

im not totally mathematician, and it was always complex to me,

actually im an Arabic person ...

but im a researcher in mathematical logic, and discrete mathematics,

sometimes i use Linear Algebra and Probability & Statistics, but i only know the simple principles ...

try to think of the Screen of a Computer with resolution of N x M in pixel

.. as a Matrix of size n x m

so i was thinking about a way to work on a matrix using iterators, and a recursive factorization function for the diagonal ...

if we use a pattern/series/stream iterators, but we want to make a unique representation

but what if we use mathematics to solve this problem, and exactly i mean Linear Algebra

try to think of the screen as n x m Matrix,

then we can have n horizontal iterators + m vertical iterators,

and the intersection of different iterators give us the ability to control the pattern,

.. also, we can try using diagonal-point recursive factor function

example:

| a b c |
| d e f |
| g h i |

a 3x3 matrix, so we have 3 vertical iterators + 3 horizontal iterators denoted as:

v1 v2 v3 + h1 h2 h3

and we have the diagonal-point recursive factor function is DPF-function(..)

a = f(v1,h1) b = f(v2,h1) c = f(v3,h1)

d = f(v1,h2) e = f(v2,h2) f = f(v3,h2)

g = f(v1,h3) h = f(v2,h3) i = f(v3,h3)

void f( int Vx, int Hy)
{
    Current.color = Current.getColor() + Vx() + Hy() ;

    if( Vx.X() == Hy.Y() )
         DPF-Function( Vx.X(), Hy.Y() );
}

what do you think ..?

Qu.1. What are the steps to be followed, when finally you execute “project” starting from source code preparation?

Answer.1. steps:

1. you have to use #include "f1.c" & #include "f2.c" in main.c

2. you compile using a C or C++ compiler which is in Windows dev-cpp or Microsoft Visual C++ express ..etc ,and in Linux gcc or g++ in the terminal

3. execute your program in windows it's a .exe file ,and in Linux it's a.out

Qu.2. Is it possible to compile the file main.c, without having files f1.c, f2.c? Mention an option of a compiler that you know which is used to accomplish this.

Answer.2. No, there is no possibility for doing that, because of two things:

1. if files are #included "...", you have to have them with the main.c

2. if you remove lines of #include "...", you will get errors for functions that have no definition,

Qu.3. Will there be any difference in the final executable, if it is produced for a 32 bit system / 64 bit system? Name a command by which you can find out the type of the executable file.

Answer.3. a 32-bit executable is totally different than 64-bit exe,

.. you can notice that problem when you try to run a 16-but exe program on windows xp !

and to find its type is possible from right-click => properties in Windows,

Qu.4. Suppose now the file f1.c contains a function f1, which is completely defined in that file and file f2.c, which contains a function f2, which is also completely defined in that file. The file main.c can either call f1 or f2. How can you ensure that the executable file will only contain the code for that function and no redundant code?

Answer.4. when you do a normal inclusion using #include "file.c" it's known as the static inclusion where the Linker links the included files simply, weather its functions were called or not,

the way you want is known as dynamic inclusion, #include <library.h>, where you have to do three steps:

1. create a library reference file file.lib, placed into /lib file

2. create a dynamically-linked-library file file.dll, placed into /system file

3. write the include library with only declarations, file.h

4. make the Linker know that there are dynamically-linked-libraries needed

.. the way to write .lib and .dll files is not easy

Qu.5. Please see, what type of assembly code is created, corresponding to the function call statements in your system

Answer.5. the assembly code is "another story" because it depends on the Compiler, the Compiler technology, and not only the Architecture of the machine, but also the operating system it's compiled for ...

.. but most of personal computers are on the 80/86 architecture, also calling functions requires special jumps after saving state in ASM

-----------------------------------

good luck

bandwidth to data in a Network Link

is just equivalent to,

speed to object in Space