09-12-2018, 11:23 AM
Algorithm : An algorithm is a series of well defined steps which gives a procedure for solving a type of problems.
Lemma : A lemma is a proven statement used for proving another statement
The Fundamental Theorem of Arithmetic:
Every composite number can be expressed as the product of powers of primes and this factorisation is unique, apart from the order in which the prime factors occur. Fundamental theorem of arithmetic is also called a Unique
Factorisation Theorem
Composite number = Product of prime numbers
Or
Any integer greater than 1 can either be a prime number or can be written as a unique product of prime numbers.
e.g.,
(i) 2 -- 11 = 22 is the same as 11 -- 2 = 22. [ignoring the order]
(ii) 6 can be written as 2 -- 3 or 3 -- 2, where 2 and 3 are prime numbers.
(iii) 15 can be written as 3 -- 5 or 5 -- 3, where 3 and 5 are prime numbers.
The prime factorisation of a natural number is unique, except to the order of its factors.
e.g., 12 made by multiplying the prime numbers 2, 2 and 3 together,
12 = 2 -- 2 -- 3
We would probably write it as 12 = 2 2 -- 3
It is still a unique combination of (2, 2 and 3).
Lemma : A lemma is a proven statement used for proving another statement
The Fundamental Theorem of Arithmetic:
Every composite number can be expressed as the product of powers of primes and this factorisation is unique, apart from the order in which the prime factors occur. Fundamental theorem of arithmetic is also called a Unique
Factorisation Theorem
Composite number = Product of prime numbers
Or
Any integer greater than 1 can either be a prime number or can be written as a unique product of prime numbers.
e.g.,
(i) 2 -- 11 = 22 is the same as 11 -- 2 = 22. [ignoring the order]
(ii) 6 can be written as 2 -- 3 or 3 -- 2, where 2 and 3 are prime numbers.
(iii) 15 can be written as 3 -- 5 or 5 -- 3, where 3 and 5 are prime numbers.
The prime factorisation of a natural number is unique, except to the order of its factors.
e.g., 12 made by multiplying the prime numbers 2, 2 and 3 together,
12 = 2 -- 2 -- 3
We would probably write it as 12 = 2 2 -- 3
It is still a unique combination of (2, 2 and 3).