Author – Andrew J Frost 10/06/2020 REV TWO PnonP
Primes Numbers – A prime number is any number that can only be divided by itself once.
Non-Prime – A number that is divisible by two or more other numbers.
Odd-Composite Numbers – A non-prime number; an odd number that has two or more factors.
Factors – Numbers that are multiplied together to get another number.
Prime Factors – Numbers that are prime and are multiplied together to create another number.
Number Line – the number line contains all the numbers counting from 1 onwards. In other words 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12…….. onwards to infinity.
Set S(af) – is the Set of Prime and Non-Prime Odd-Composite numbers.
Complementary and Complementarity – in this Paper, this refers to the Set S(af) which contains the Subsets of Primes and Odd-Composite Non-Primes. Each subset is complementary to the other and are shown to fit together in a immutable pattern.
Immutable Pattern – a pattern that is rigid and does not change.
Exponents – the exponent is the number used to express a power. As an example, two squared is two to the power of two = 22. The number used to express the power is the exponent 2.
Factorial of a positive integer n is denoted by n!. The symbol n! , is the product of all positive integers less than or equal to n. This is formularised as n ! = n ⋅ ( n − 1 ) ⋅ ( n − 2 ) ⋅ ( n − 3 ) ⋅ ⋯ ⋅ 3 ⋅ 2 ⋅ 1, where the dot “⋅” between numbers is the multiplication symbol used instead of x.
An example is 5! = 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 = 120. This means five times four equals twenty; then three times twenty equals sixty; and finally two times sixty equals one hundred and twenty. Obviously one times one hundred and twenty produces the same answer.