Question

Assignment: Show Me the Sets Investigation

Karen got a bit confused in math class today when Mrs. Hudson was talking about the different subsets for classifying real numbers.


Create a visual representation of the relationships between subsets of the real number system and explain the relationships in words. Provide a real number that matches each description.
Draw a diagram to represent the relationships between subsets of the real number system. Include a sample number in each subset.






Explain the relationships in words. Use the sample numbers in your diagram and describe the classification. For example, 1/2 is a rational number, but it is not a whole number, natural number, or an integer.

Answer 1

Answer: Consider a power set
`\mathbb{R}` of real numbers.

The subsets of the power set are as follows:-

1. Natural number(
`\mathbb{N}`)={1,2,3,4,5,....}

2.Whole numbers
`\mathbb{W}`={0,1,2,3,4,......}

3.Integers(
`\mathbb{I}`)={.......-3,-2,-1,0,1,2,3,....}

4.Rational numbers(
`\mathbb{Q}`)=It contains all of the above subsets and fractions (where denominator ≠ 0) ,terminating and repeating decimals.

5.Irrational numbers=It contains numbers which cannot be expressed as the ratio of integers, and they are non-repeating, non-terminating decimals.