Number Systems – Concepts & Practice
Number Systems – Concepts & Practice
Concept 1 – Natural Numbers, Whole Numbers, and Integers
Natural Numbers, Whole Numbers, and Integers
\(\mathbb{N} \subset \mathbb{W} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R}\)
N = {1,2,3,...}, W = {0,1,2,3,...}, Z = {...,-2,-1,0,1,2,...}
Natural numbers (N) are counting numbers starting from 1. Whole numbers (W) include 0 along with natural numbers. Integers (Z) include all positive and negative whole numbers along with zero. Every natural number is a whole number, and every whole number is an integer. This hierarchy continues to rational and real numbers.
📖 Quick Reference
Natural numbers: 1, 2, 3, 4, 5, ...
Whole numbers: 0, 1, 2, 3, 4, 5, ...
Integers: ..., -3, -2, -1, 0, 1, 2, 3, ...
Smallest natural number: 1, Smallest whole number: 0
💡 Remember: N ⊂ W ⊂ Z. Natural numbers have no zero, whole numbers start from zero, integers include negatives.