Number Systems: Natural, Rational, and Real
The relationships between natural, rational, and real numbers. Understand if every natural number is rational, if every rational number is natural, if every natural number is a real number, and if every real number is natural. Delve into the characteristics of different number systems and their intersections.
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Presentation Transcript
Discussion Time Discussion Time Chapter 1: Number Systems Page 19 1
Question Posed: Question Posed: 1. Is every natural number rational? 2. Is every rational number natural? 3. Is every natural number a real number? 4. Is every real number natural? 2 Chapter 1: Number Systems (page 19)
Suggested solution: Suggested solution: 1. Is every natural number rational? Every natural number ? can be written as ? = ? 1, which is in the form ? ?, where ? and ? are real. Thus, every natural number is a rational number. 2. Is every rational number natural? No. Numbers such as 1 Thus, not every rational number is natural. 2 or 3 4 are rational but they are not natural. Natural numbers are whole numbers. 3 Chapter 1: Number Systems (page 19)
3. Is every natural number a real number? Yes. All natural numbers are rational. Real numbers is the set containing rational and irrational numbers. Thus, every natural number is real. 4. Is every real number natural? No. Real numbers contain rational and irrational numbers. Not all rational numbers are natural and irrational numbers are not natural as they are not whole numbers. Thus, not every real number is natural. 4 Chapter 1: Number Systems (page 19)
