The Real Number System 103

Updated: Jan 5

Hello! Today I will be teaching you about the last three types of numbers on the rational number system! The real number system consists of six different types of numbers including real numbers, rational numbers, irrational numbers, non-integer fractions, integers, negative numbers, whole numbers, zero, and natural numbers. But we will only be focusing on negative numbers, zero, and natural numbers. Make sure to check out my last two posts if you haven’t learned about whole numbers, integers, rational numbers and irrational numbers, real numbers, and non-integer fractions. I hope you enjoy reading!


Many of you are probably familiar with negative numbers. But the reason why negative numbers are in the real number system is because negative numbers are needed to build off the real number system and to make up other number systems such as integers. But those of you who don’t know what negative numbers are, here is the definition...negative numbers are the opposite of positive numbers (not including zero.) By adding a negative number, you are doing the equivalent of subtracting that number. Negative numbers branch off of integers. And next to negative numbers are whole numbers. This is because negative numbers and whole numbers are integers. Only negative numbers wouldn’t work because integers including positive numbers are zero. And only whole numbers wouldn’t work because integers include negative numbers.


What is a natural number? A natural number, also known as counting numbers are positive numbers that start at 1 and go on and on to 2, 3, 4, 5, 6, 7, 8, 9, etc. Natural numbers need to be whole numbers so 0.432 would not be a natural number. Nor would any type of fraction or decimal that did not equal a whole number. Natural numbers along with zero make up whole numbers in the natural numbers.


Zero is not something you would probably expect to find here, but as I mentioned in the paragraph about negative numbers, some things in the real number system are there to help you understand other sections of the real number system. The real number system is more like a tree because it keeps branching down. But it is also different because the trunk is made up of the two branches branching off of it, and branches rely on the other branches above it to complete the system. An example is real numbers, real numbers consist of either an irrational number or a rational number. The irrational numbers and rational numbers are the branches making up real numbers. In our case, zero is here to make whole numbers. Natural numbers don’t include zero while zero is a whole number.


Thank you for reading about the real number system! Throughout these three lessons we’ve covered what the real number system is and the different components inside them including real numbers, rational numbers, irrational numbers, non-integer fractions, integers, negative numbers, whole numbers, zero, and natural numbers. In hope you enjoyed my posts and now know all about the different components of the real number system!


Question #1: What is a negative number?


  1. Negative numbers are the opposites of positive numbers (not including zero)

  2. Negative numbers are sad about everything

  3. Negative numbers are number who aren’t able to look at the positive side of things

  4. Negative numbers are the numbers that are 1, 2, 3, 4, 5 and so on


Question #2: What is a natural number?


  1. Natural numbers are all the whole positive numbers (not including zero)

  2. Natural numbers are numbers that aren’t processed

  3. Natural numbers are all the numbers that are a multiple of ten

  4. Natural numbers are numbers that are green


Question #3: What is zero?


  1. Zero is a number that doesn’t equal anything

  2. Zero is a number who likes zebras

  3. Zero is the name of my friend across the street

  4. Zero is a number that equals 4


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