Monday, June 5, 2023

1.1. The Real Number System
A number means something you can count, just like counting the number of coins one has or the number of students in a class. These are natural numbers which are normally used for counting and sometimes called counting numbers 

1.1.1. Natural Numbers
Natural numbers start from 1 to infinity ∞. Natural numbers are numbers you will use when counting things. For instance if you have to count the number of Oranges, you will start from 1.
Natural Numbers (N)  1,2,3,4,5,6,7,8,9,10,11,…………
1.1.2. Whole Numbers
Whole numbers start from 0 to infinity ∞. Whole numbers are Natural Numbers together with a zero.
Whole Number ( N): 0,1,2,3,4,5,6,7,8,….
1.1.3. Integers 
Integers are Whole Numbers plus negatives.
Integers (Z): …-4,-3,-2,-1,0,1,2,3,4,…
1.1.4. Rational Numbers
Rational Numbers are all numbers of the form a/b, where both a and b are integers. b cannot be zero. Rational numbers include fractions.

Fractions can be numbers which are smaller than 1, i.e 1/2 ; 1/4 and 4/7. These are called proper fractions. Fractions can also be  numbers bigger than 1 and they are called improper fractions), i.e. 4/2 ; 5/3 ; 7/2.

1.1.5. Irrational Numbers
Irrational Numbers cannot be expressed as ratio of integers. As decimals they never repeat or terminate.

1.1.6. The Real Numbers
The real numbers is the set of numbers containing all of the rational numbers and all of the irrational numbers.
1.1.7. Non Real Numbers ( Imaginary Numbers)
Not all numbers are real numbers. For instance all square roots of the negative numbers are imaginary numbers or non real numbers. For example √-2 , √-4, √-1 and √-22.

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Rational and Irrational Numbers
Rational Numbers

Irrational Numbers

Rational and Irrational Numbers

Rational and Irrational Numbers
Q1 Solutions

  1. Irrational, decimal does not terminate and has no repeated pattern.
  2. Rational, decimal terminates.
  3. Irrational, decimal does not terminate and has no repeated pattern.
  4. Rational, all integers are rational.
  5. Rational, decimal has repeated pattern.
  6. Rational, decimal has repeated pattern.