Question

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. For example, 1/2 is a rational number, but it is not a whole number, natural number, or an integer.

Answer 1

let me give the significations following
natural numbers :ACA counting numbers the numbers you naturally say when counting.
whole numbers: include all natural numbers zero
Integers: include all whole numbers and their opposites.
Rational: can be written ASA fraction or ratio of two integers also decimals that terminate or repeat
Irrational: can not be written a fraction, decimals, do not terminate or repeat.

Answer 2

1, 0, -30,000, 1/3, pi

Explanation:

Natural Numbers, the counting set. N = {1,2,3,...}

1 rock,

a)Whole Numbers set was developed when it was necessary to pick a number for the no quantity. the Zero
`Z_(z>=0)`.

Z ≥ 0. There is no official symbol for this Set.

1 rock smashed the barn. My stocked harvest in there turned out to worth $ 0

b)Integers Numbers was developed mainly to tackle financial matters.

Introducing the negative numbers. Z={...-3,-2,-1,0,1,2,3,...}

1 rock smashed the barn. My stocked harvest in there turned out to worth $ 0. The bank said I owe $ -30,000. -30,000 is an integer but not natural nor whole

c) Rational Numbers. They were developed as a set when fractions appeared. Q ={ ...-5/7.,....0,..1/2,}

1 rock smashed the barn. My stocked harvest in there turned out to worth $ 0. The bank said I owe $ -30,000. My accountant said even if I sold my property all I could earn is 1/4 of my debit. 1/4 is not an Integer, or Whole or Natural one.

d) Irrational Numbers

In this set all numbers that cannot be written as
`(a)/(b)` rational, like
`√(2)`

1 rock smashed the barn. My stocked harvest in there turned out to worth $ 0. The bank said I owe $ -30,000. My accountant said even if I sold my property all I could earn is 1/3 of my debit. I ran for credit in circles after running {\displaystyle \pi }\pi lap around my smashed barn.

e) Real Numbers

This set contains all of these previous sets. But not all Real Numbers are Natural, Whole, Integer, Rational, Irrational numbers.

1 rock smashed the barn. My stocked harvest in there turned out to worth $ 0. The bank said I owe $ -30,000. My accountant said even if I sold my property all I could earn is 1/3 of my debit. I ran for credit in circles after running {\displaystyle \pi }\pi lap around my smashed barn, before I had to say anything my wife said...

"Hey Joe, is there anything wrong? You were murmuring some Real numbers randomly. Can I help you dear?"