How to Name Sets of Numbers

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Naming sets of numbers is something you can do with both real and imaginary numbers. Name sets of numbers with help from an experienced mathematics educator in this free video clip.

Part of the Video Series: Math Lessons & Tips
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Video Transcript

Hi, my name is Marija, and today I'm going to show you how to name sets of numbers. So the biggest set of numbers is the real numbers versus the imaginary numbers so we're going to leave the imaginary numbers on the side over here. Those are really the only i and the multiples of i. So when we start talking about real numbers, there's a lot of different subcategories. And the two biggest ones are your rational numbers, and your irrational numbers. And if you look at the word rational, you see the word ratio in it. And a ratio is a fraction. So rational numbers are any number that can be written as a fraction. So that can be five because five can be written as five over one, or that can be something like seven over 13. So any number that can be written as a fraction is called a rational number. Now if you're writing decimals, a decimal is rational as long as it either stops so for example .284 there's three digits and then no more, it stops, or if it's a decimal that repeats. So for example .38 with a bar over it that means that it's going to continue on forever but it does have a pattern. It goes .383838 so on and so forth. So as a decimal a rational number is going to either stop at a certain point or repeat. As a fraction it just needs to be able to be written as a fraction. Your irrational numbers are numbers that cannot be written as fractions so those are decimals such as .284... so three dots indicate this number does not stop and it also does not have a pattern. So because it does not stop and does not have a pattern, it's called irrational. Now within your rational numbers, there are integers. Now the integers are the numbers that can be written as a denominator of one. As a fraction with a denominator of one. So for example five is an integer because it can be written as five over one. Seven over 13 is not an integer because it cannot be written as a number over one, it's got to be over 13 or a higher number. So integers can be written as two over one or just three or negative four, all of these numbers are integers. So these are basically the numbers that you see on your number line. From the negatives to the positives and including zero. OK. Within the integers you also have whole numbers which is a smaller group of numbers and this excludes the negative integers. So your whole whole numbers are zero and all of your positive integers. So the integers are all the negatives, positives and zero on your number line and the whole numbers are just zero and the positive numbers. And this is a break down of your different types and categories and sets of numbers.


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