natural numbers
Natural numbers are a set of positive integers starting from 1 and counting upwards
Natural numbers are a set of positive integers starting from 1 and counting upwards. They can be represented as {1, 2, 3, 4, 5, …}. The set of natural numbers is denoted by the symbol “N”.
Natural numbers are used to count objects or to represent the position of something in a sequence. For example, if you have 5 apples, you can represent the number of apples using the natural number 5. Similarly, if you are standing in a queue and you are the 3rd person, you can represent your position using the natural number 3.
Properties of Natural Numbers:
1. Closure: The sum or product of any two natural numbers is always a natural number. For example, 2 + 3 = 5, and 2 * 3 = 6, both of which are natural numbers.
2. Commutativity: The order of addition and multiplication does not affect the result. For example, 2 + 3 = 3 + 2, and 2 * 3 = 3 * 2.
3. Associativity: The grouping of three or more natural numbers, when added or multiplied, does not affect the result. For example, (2 + 3) + 4 = 2 + (3 + 4), and (2 * 3) * 4 = 2 * (3 * 4).
4. Identity: There exist an additive identity, which is 0, and a multiplicative identity, which is 1, in the set of natural numbers. For example, 2 + 0 = 2, and 2 * 1 = 2.
5. Distributivity: Multiplication distributes over addition. For example, 2 * (3 + 4) = (2 * 3) + (2 * 4).
It is important to note that natural numbers do not include zero or negative numbers. If you want to include zero in the set, you can use the set of whole numbers, denoted by “W” or “Z”. The set of whole numbers includes all the natural numbers along with zero {0, 1, 2, 3, 4, 5, …}.
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