بسم الله ارحمن ارحيم                                 
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​        "mathematics is the Black woman of the sciences"
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                  Measure of a sphere:         measure- قدر (qadara)

                    - volume: (4/3) x (3.14) x (radius ^3)

                      - surface area: (4) x (3.14) x (radius ^2)



             axiom: the ratio of two natural numbers never equals zero



            theorem:   there is a ratio of two numbers; b / h ,  such that h never equals zero 


                             a  =  b / h  ;   h  =  0


                             a x  0  = b  ;   


                 b is not equal to 0  ;  there is no number 'a' multiplied by zero that equals b 


                           

                       example:     a   =   7 / 0  ;


                                              a x  0   =   7  ;


                                              there is no number 'a'  multiplied by 0 that equals 7












      angular velocity:   m  =   j / k                                                                     -  j (radians) 

       -  k  (time; seconds) 


       time (seconds)  =   radians / angular velocity                                                                                         =  (radians) / (radians s^-1)

                                 =  seconds

      

 angular velocity   =   radians per second ;   radians / s  =   (radians)  x (s^-1)

        - angular velocity is also called angular frequency ;   frequency  =  1/ s  =  s^-1

                                                                                

          - the geometric; circle (planar), is equal to 6.28 radians (360 degrees)

          - circle diameter is 3.14 radians (180 degrees)

          - 1 radian  =  57.30 degrees


            frequency   =   (speed of light) / (wavelength)

                   - speed of light  =  3 x 10^8  m/s

                  * when using the speed of light as the value, frequency becomes a type                         of frequency

    


           natural numbers  =  { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 ,  . . . . }








Numbers in a set  (a 'set'  is a group of variables; numerical, that can be defined from common characteristics; function activity. possible origin: kamit; set/ seth)

axiom:  if  m ≠ r ,  then   p  = r - m   is not equal to  0 .  if   m  =  r  , then   p  =   r  -  m   is equal to  0  . (maity, ghosh;  analysis differential calculus, 1960)

grouping - organize of variables from common characteristics.  a group of variables define a  set .  the  set  is the manipulative of the system activity/ function activity;

        list of numbers -  1, 2 , 3, 4, 5, 6, 7, 8

further study shows that it is a list of what is called natural numbers .  from the list of natural numbers, we group/ organize the following variables:

             { 2 , 4 , 6 , 8 }

the group of variables are organized from the common characteristic; even numbers.  once a group has been identified for manipulation, the function activity (mechanism) can be observed (experimental).  grouping is significant because it defines the boundaries of your system (as a student, you have to learn that you can create the system; creation - creator, Creator of the heaven and the earth.  as a student, you have to learn how to create the system; you are creating the system, defining the boundaries for what you want your system to do.  your system can be infinite- a system with no boundaries within the universal boundaries of the Creator/ the creation of the heaven and the earth or your system can be finite; the universal boundaries of the creation of heaven and earth are your system boundaries. 


from the above  set  of numbers; { 2, 4, 6, 8 } , you create a function, numerical;  s(m)  =  4 m + 3 , to describe the earth's rotation on its axis.  the variable  m  can represent any of the values in your  set .  this function is describing system activity (planetary).  the values of your function  s(m)  will not be correct because universe boundaries define the earth's rotation on its axis; approximately 24 hours . 


Kamitian Ruler of Measure: notice the infinite measure characters



number analysis: natural numbers {1, 2, 3, 4, ....}


Equality Construction;

- manipulation of magnitude (number value) from increase/ decrease of independent variable


in general, numbers (natural) have a finite/ discrete value (specific).  the value of the number is the magnitude of the number, which can be described in micro-environments (10 ^-9 m - 10^-16 m) as the nth dimension spatial position of the value (magnitude) on a number line (the position of a finite object/particle in space/ maatu مات ) from an origin (source/ cause).

مقدار - magnitude (maqad'aara); 1. maximum spherical distance; n dimensions, of impact (effect) from origin (cause);{particle physics}  2. number value (manipulation of number value; increase/ decrease); {arithmitic, algebra}

   

 equation 1.          s  =  h   ;          s = 10           h  =  ?


if variable s is equal to h, and the magnitude of s is 10, than the magnitude of h is 10.   


the understanding of number relations, and construction of equality solutions from variable representations begins with the understanding that different numerical values (natural) for equality are multiples of a coefficient value ; arithmitic expression of multiplication, for equality


  coefficient  =  س  ;  variable multiple of a numerical value/ magnitude

            

                  s = h ;                                        s = س h ;                                 s = س h                       * variables are not numerically (magnitude) defined; non-discrete/ infinite;

           10 x 1 =  1 x 10  = 10                       10 = 1 x 10                              10 =  2 x  5                               values /solutions have to be solved for/constructed


function;      r (س)   =  س  h   =  s ;


                       s   =   h       ;       s   =  س h