1. What is a Number System?
A number system is a set of symbols (digits) and rules for writing and operating on numbers.
Example: In the decimal system, we use 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
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2. Types of Number Systems
(A) Based on Mathematics
1. Natural Numbers (N)
Counting numbers: 1, 2, 3, 4, …
No zero, no negative numbers.
2. Whole Numbers (W)
Natural numbers + zero: 0, 1, 2, 3, …
3. Integers (Z)
Whole numbers + negative numbers: …, -3, -2, -1, 0, 1, 2, 3, …
4. Rational Numbers (Q)
Numbers that can be written as p/q where q ≠ 0.
Includes fractions and repeating/terminating decimals.
Example: 3/4, 0.5, -2.
5. Irrational Numbers
Numbers that cannot be written as p/q.
Non-repeating, non-terminating decimals.
Example: √2, π.
6. Real Numbers (R)
All rational and irrational numbers together.
7. Imaginary Numbers
Numbers involving √(-1), written using i or iota.