Discussion – Natural Numbers
The set of natural numbers includes 0 and every natural number that follows it. In other words, the set of natural numbers starts with 0 and goes up to infinity. Every positive integer falls within this set. Natural numbers are also known as counting numbers. They can count objects in a set (Sowder, Sowder & Nickerson, 2012). The natural number that corresponds to the number of elements in a set is called the cardinality of the set. ℕ denotes the countable infinity of natural numbers. The first natural number is 0, and the successor of a natural number n is n+. They include 0, natural numbers, and negative integers. For example, 0, 1, 2, -12, -14 are all natural numbers. The natural numbers are countable. It means that given any two natural numbers, A and B, there exists a bijection between them.
Prime and Composite Numbers
Prime numbers are natural numbers divisible only by themselves and number one. However, one is not considered a prime number because it is divisible only by itself. Prime numbers are important in mathematics because they are the building blocks of other number systems. Examples include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 (Samson, 2020). The prime factors of a number are the prime numbers that divide it without a remainder. Composite numbers are natural numbers that are not prime numbers. A composite number can be divided by two different natural numbers other than itself and one. For example, the number six is composite because it can be divided by two different natural numbers other than six and one. The number two is the smallest prime number. Even numbers are composite numbers because they can be divided by two. The number two is an even number, also a composite number.
References
Samson, D. S. (2020). The Power of Prime Factorisation. Learning and Teaching Mathematics, 28(2020), 15-18.
Sowder, J., Sowder, L., & Nickerson, S. (2012). Reconceptualizing mathematics. Macmillan Higher Education.
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Natural Numbers
Describe the set of natural numbers in your own words. What is the difference between a prime number and a composite number?
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