Answer :

Understanding Real Numbers and their subtypes

1.  Real Numbers

Real numbers are a broad category of numbers that include all the numbers you use in everyday life. Real numbers can be divided into two types: rational and irrational numbers.

2.  Rational Numbers

  • These are the real numbers that can be expressed as a fraction of two integers (where the denominator should not be zero.

    [tex]\bullet\ \text{Examples: }\dfrac{1}{2},\ -\dfrac{4}{7},\ 0.75,\ 0,\ 1, -1, -2,\ \text{etc.}[/tex]

3.  Irrational Numbers

  • These are the real numbers that cannot be expressed as a fraction of integers. Their decimal goes on forever without repeating.

    [tex]\bullet\ \text{Examples: }\sqrt2,\ \pi,\ e\text{(the base of natural logarithm).}[/tex]

4.  Integers

  • Integers are the rational numbers excluding the fractional numbers which can be positive, negative or zero.
  • Examples: 0, -1, 1, 2, 3, -2, etc.

5.  Natural numbers ([tex]\Large\text{$\mathbb{N}$}[/tex])

  • Natural numbers are the all positive integers that you use for counting.
  • Examples: 1, 2, 3, 4, 5, etc.

6.  Whole numbers

  • Whole numbers are the natural numbers including zero.
  • Examples: 0, 1, 2, 3, 4, 5, etc.

7.  Fractions

  • Fractions are the rational numbers that represents a part of a whole, written using numerator and denominator.

    [tex]\bullet\ \text{Examples: }\sqrt2,\ \pi,\ e\text{(the base of natural logarithm).}[/tex]

I will make a family tree diagram of real numbers so that you can understand the concepts better.

I didn't include numbers like terminating decimals, repeating non-terminating decimals, even numbers, odd numbers, prime numbers and composite numbers but they are also real numbers.

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