The real number system
Download as PPTX, PDF1 like604 views
This document defines key concepts in the real number system including rational numbers, irrational numbers, integers, and subsets. It explains that real numbers contain both rational numbers (which can be expressed as fractions) and irrational numbers (which cannot). Various properties are discussed such as comparing and ordering real numbers. Examples are provided to demonstrate plotting numbers on a number line, determining if a number is rational or irrational, and arranging sets of numbers in ascending and descending order.
The real number system
- 1. THE REAL NUMBER SYSTEM
- 2. What is a Real Number? Is any element of R which contains Rational ( Q) numbers and Irrational (Q’) numbers
- 3. How would you plot the following real numbers in the number line? a) A= - 𝟐 b) B= 5 c) C= 𝞹 d) D= 0.5 e) E= ¾
- 4. Describe the relationship of the sets shown in the Venn Diagram RATIONAL NUMBERS(Q) IRRATIONAL NUMBERS(Q’) U 0 1 -2 -3 ¾ 15% 0.5 e −𝟐 𝞹 √𝟑
- 5. How do we define a Irrational number? A irrational number is a real number that can not be expressed as 𝑚 𝑛 where m and n is an integer (Z) an that n ≠ 0 .
- 6. How do we define a Rational number? A rational number is a real number that can be expressed as 𝑚 𝑛 where m and n is an integer (Z) an that n ≠ 0 .
- 7. What are the different subsets of the rational numbers? Non – integer Integers a) negative integers b) whole number - zero and natural numbers
- 8. REAL NUMBER (R) RATIONAL NUMBER, (Q) IRRATIONAL NUMBER, (Q’) NON-INTEGER INTEGERS, (Z) NEGATIVE INTEGERS,(𝒁−) WHOLE NUMBERS,(W) ZERO IRRATIONAL NUMBER, (Q’) POSITIVE INTEGERS,(𝒁+ ) (N)
- 9. Perform the indicated operations and write the answer in roster form and set builder form. 𝑍+ U 𝑍− R – Q ‘ Q ⋂ Q ‘ (Q ‘)’
- 10. Consider the given numbers which are on the left most column of the table. Check as many appropriate cells as applicable: numbers +Z -Z Whole number Natural number Rational number Irrational number Real number Non- negative Integer Non- integer 25 11 6.30 4 23 0 - 𝞹 2 2e
- 11. TRUE OR FALSE: Write True if the statement is always True and false if otherwise. All integers are real numbers Every whole number is greater than zero All integers are signed number All whole numbers are integers Every integer is a real number
- 12. TRUE OR FALSE: Write True if the statement is always True and false if otherwise. All real numbers are rational All rational numbers are integers All non - integers are rational Every integer is a whole number Irrational number are real numbers.
- 14. DETERMINE whether the following is rational or not. -20 ¼ 0.75 7/9 3 RATIONAL RATIONAL RATIONAL RATIONAL IRRATIONAL
- 15. “ TRICHOTOMY LAW” COMPARING REAL NUMBERS
- 16. “ TRICHOTOMY LAW” If a and b are real numbers, then one and only one of the following is true: i) a < b ii) a = b iii) a > b
- 17. How do we compare numbers? A= 5 C= 0 E= 𝟑 𝟐𝟕 G = 0.8 B = -5 D = 𝟕 𝟏𝟎 F = 3 H = 𝟒 𝟓
- 18. −7, − 19 11 , 0 , 𝑒, 7 , 18 5 , 4 ASCENDING ORDER How do we write {4, -7, 0, 18/5, -19/11, 7 , e } into ascending order ?
- 19. DESCENDING ORDER How do we write {4, -7, 0, 18/5, -19/11, 7 , e } into descending order ? 4, 18 5 , 7,e, 0, −19 11 , −7
- 20. ARRANGE THE Following numbers into ascending order: a) 𝞹, - 𝞹 , 0 , 2, -5, 5 b) 3. 5, 7 2 , 0.6 , 0.5, 0.05 , 50%
- 21. ARRANGE THE Following into descending order: a) 𝞹, - 𝞹 , 0 , 2, -5, 5 b) 3. 5, 7 2 , 0.6 , 0.5, 0.05 , 50% c) -3, -2, -1, 0, 1, 2, 3,