Any number, other than natural numbers, can be regarded as a real number. The collection of real numbers, which consists of all numbers greater than zero, is called the prime number sequence. Any real number greater than 0 is referred to as a prime number. A prime number can be thought of as being the greatest common factor (LCF) of all numbers less than it. Thus, the values of prime number sequences are used in the mathematical theory of prime numbers.
There are various different types of real numbers. Any real numbers smaller than zero are called rational numbers. Any real numbers that are greater than zero are considered irrational numbers. In addition, there are also numbers that are neither real nor irrational, but only possible to express in terms of both types.
The irrational number system refers to those numbers which are not possible to express using the natural number system. These are called super numbers or “fractals”. They are usually discovered by experiment or chance. One of them is the Fibonacci number, which was discovered in 16th century Italy. The real numbers that are neither real nor irrational are called real numbers.
To obtain the natural numbers from the irrational numbers, we need to combine both sets of real and irrational numbers into a single finite number system, and this is done using decimals. Decimals are simply sums of other real numbers. The products of these real numbers can be put together into a finite number series, which we call a prime number series. All these prime number series is actually a circle whose diameter exactly equals the sum of its radii.
This prime number series is actually an algorithm which produces the numbers by making use of all the factors which are necessary for it to be efficient. This algorithm was first revealed by Albert Einstein in his theory of relativity. This algorithm is not like a calculator that gives the results with just a few clicks. The algorithm has to be proved with a great deal of precision, for it to be used as a source of real numbers. Hence, no one is really satisfied with this algorithm.
The biggest problem that people have with the algorithm is that it cannot be used for the extraction of irrational numbers. It takes an incredible amount of time for any calculation with complex numbers to be done. Even the simplest calculations with real numbers can be very time consuming. Hence, the algorithm cannot be used for solving the problem of finding prime numbers using complex numbers. Another drawback of this algorithm is that it can only solve extremely complex problems, hence problems of elliptic equations or the arithmetic problem cannot be solved satisfactorily with this method.
On the other hand, if we take a look at the real numbers, they have no divisors and no digits after them. These numbers do not have any denominators and decimals. Therefore, if we try to solve a problem involving any kind of numbers using a number line then we will have to search through millions of such numbers using our algorithm. In fact, even numbers like pi cannot be found using the number line.
Hence, it is believed that real numbers are much better than hyperreal numbers. The main reason behind this belief is that these numbers do not contain any digit numbers. This means that any mathematical calculation can be carried out accurately with hyperreal numbers. In fact, any kind of calculation that uses any kind of real number can be called as a calculus problem. Hence, hyperreal numbers are said to be much better than real numbers in almost every way.