Chapter 4 : Random Functions

Chapter 4  Random Functions

you know about what is random number and random function. all random function are logarithmic in nature because we are performing an operation on natural numbers.

2.1 Properties of random function

1. Every random function is logarithmic function with a random base.

2. When any number is divided by 0 it becomes the universal set of random numbers having range (-∞,+∞) .

3. Property of logarithmic are applied in random function.

4.d(1),G(1),h(1),i(1),j(1) have different values..

5. Random numbers have different value for a fixed number but have finite value.

6. Random number-random number≠0 . it don't obey the law of mathematics so it is also called
quantaum mathematics.

 

2.2 GOD function

Let a random number b be defined as    bp=p     where p is prime, and range of b is 1<b≤33 .

Also    d(y) = logb(y)

In simple words if y = p^a*q^b           where p, q are prime   then

  d(y)= a*p+q*b

Graph of god function

2.3 Helium function

Let a random number b_0  be define as

           p=b_0*(p-1)       Having range 1<b_0≤2     and    h(y) = logb_0y

Graph of helium function

2.4    Geo function

Let a random number g0 ,having range from 2≤g0<∞     and it is related to prime as

           g_0∈{2,3,5,7,…}                                              G(y) = logg_0y

Graph of  geo function

If   y = p^a*q^b             where   p , q are prime  then

G(y) = a+b   also    d(y)=g0 G(y)

there are more random function which i will discuss later.